THESIS in PDF

THESIS in PDF
The growth of galaxies and
their gaseous haloes
Freeke van de Voort
The growth of galaxies and
their gaseous haloes
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden,
volgens besluit van het College voor Promoties
te verdedigen op woensdag 28 maart 2012
klokke 16:15 uur
door
Frederieke van de Voort
geboren te Eindhoven
in 1983
Promotiecommissie
Promotor:
Prof. dr. J. Schaye
Overige leden:
Prof. dr. M. Franx
Prof. dr. K. H. Kuijken
Dr. J. Brinchmann
Dr. D. Kereš (University of California, San Diego, USA)
To Craig
Table of Contents
1
2
3
Introduction
1.1 Structure formation in the Universe
1.2 Cosmological simulations . . . . . .
1.3 This thesis . . . . . . . . . . . . . . .
1.4 Outlook . . . . . . . . . . . . . . . . .
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The rates and modes of gas accretion onto galaxies and
haloes
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Model variations . . . . . . . . . . . . . . . . .
2.2.2 Maximum past temperature . . . . . . . . . .
2.3 The temperature-density distribution . . . . . . . . .
2.4 Defining gas accretion . . . . . . . . . . . . . . . . . .
2.4.1 Identifying haloes and galaxies . . . . . . . . .
2.4.2 Selecting gas particles accreted onto haloes . .
2.4.3 Selecting gas particles accreted onto galaxies .
2.5 Total gas accretion rates . . . . . . . . . . . . . . . . .
2.5.1 Accretion onto haloes . . . . . . . . . . . . . .
2.5.2 Accretion onto galaxies . . . . . . . . . . . . .
2.6 Hot and cold accretion onto haloes . . . . . . . . . . .
2.6.1 Dependence on halo mass . . . . . . . . . . . .
2.6.2 Smooth accretion versus mergers . . . . . . . .
2.6.3 Dependence on redshift . . . . . . . . . . . . .
2.6.4 Effects of physical processes . . . . . . . . . .
2.7 Hot and cold accretion onto galaxies . . . . . . . . . .
2.7.1 Effects of physical processes . . . . . . . . . .
2.8 Comparison with previous work . . . . . . . . . . . .
2.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
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1
2
7
9
12
their gaseous
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The drop in the cosmic star formation rate below redshift 2 is caused
by a change in the mode of gas accretion and by active galactic nucleus
feedback
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Accretion and mergers . . . . . . . . . . . . . . . . . . . . . .
3.3 Global accretion and star formation . . . . . . . . . . . . . . . . . .
3.4 Effect of AGN feedback . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
15
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48
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61
62
63
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67
72
74
4 Properties of gas in and around galaxy haloes
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
4.2 Simulations . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Variations . . . . . . . . . . . . . . . . . . .
4.2.2 Identifying haloes . . . . . . . . . . . . . .
4.2.3 Hot- and cold-mode gas . . . . . . . . . . .
4.3 Physical properties: dependence on radius . . . .
4.3.1 Density . . . . . . . . . . . . . . . . . . . . .
4.3.2 Temperature . . . . . . . . . . . . . . . . . .
4.3.3 Maximum past temperature . . . . . . . .
4.3.4 Pressure . . . . . . . . . . . . . . . . . . . .
4.3.5 Entropy . . . . . . . . . . . . . . . . . . . .
4.3.6 Metallicity . . . . . . . . . . . . . . . . . . .
4.3.7 Radial velocity . . . . . . . . . . . . . . . .
4.3.8 Accretion rate . . . . . . . . . . . . . . . . .
4.3.9 Hot fraction . . . . . . . . . . . . . . . . . .
4.4 Dependence on halo mass . . . . . . . . . . . . . .
4.5 Inflow and outflow . . . . . . . . . . . . . . . . . .
4.6 Effect of metal-line cooling and outflows driven
and AGN . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Evolution: Milky Way-sized haloes at z = 0 . . . .
4.8 Conclusions and discussion . . . . . . . . . . . . .
A
Resolution tests . . . . . . . . . . . . . . . . . . . .
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supernovae
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77
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95
96
101
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114
5 Cold accretion flows and the nature of high column density H i absorption at redshift 3
119
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3 Gas samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.4.1 Gas and H i fractions . . . . . . . . . . . . . . . . . . . . . . . 127
5.4.2 Spatial distribution: A visual impression . . . . . . . . . . . 130
5.4.3 The column density distribution function . . . . . . . . . . . 132
5.5 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . 136
6 Soft X-ray and ultra-violet metal-line
galaxies
6.1 Introduction . . . . . . . . . . . . .
6.2 Method . . . . . . . . . . . . . . . .
6.2.1 Simulations . . . . . . . . .
6.2.2 Identifying haloes . . . . .
6.2.3 Emission . . . . . . . . . . .
6.3 Results . . . . . . . . . . . . . . . .
6.3.1 Soft X-ray . . . . . . . . . .
emission from the gas around
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141
142
143
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148
6.4
6.3.2 Low-redshift UV . .
6.3.3 High-redshift UV . .
6.3.4 Low-redshift Hα . .
Discussion and conclusions
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155
161
166
166
Nederlandse samenvatting
169
De groei van sterrenstelsels en hun gasrijke halo’s . . . . . . . . . . . . . 169
De inhoud van dit proefschrift . . . . . . . . . . . . . . . . . . . . . . . . 170
De toekomst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
References
175
Publications
183
Curriculum Vitae
185
Acknowledgements
187
1
Introduction
Galaxy formation has undergone fast development in the past few decades, both
theoretically and observationally. The number of observed galaxies is expanding rapidly and observations are pushing to lower masses and higher redshifts.
Diffuse gas has been observed in absorption against bright background objects
and in emission around galaxies. Simulations predict that the spatial distribution of the intergalactic medium, the cosmic web, has a profound impact on the
evolution of galaxies. Gas accretion provides the fuel for star formation, which
is inhibited by outflows powered by supernova explosions and active galactic
nuclei (AGN). Star formation and feedback produce and distribute metals in the
surrounding medium, which aids the process of galaxy formation. To understand the assembly of galaxies, we need to understand how they are fuelled.
Introduction
1.1 Structure formation in the Universe
More than thirteen billion years ago the Universe was almost completely homogeneous. Tiny gas density fluctuations of the order 10−5 grew into everything
we can see today. Structure on the largest scales is completely governed by
gravity. The matter is concentrated in a ‘cosmic web’ of sheets and filaments
that are determined by the original fluctuations and the cosmological parameters, principally Ωm , ΩΛ , h, σ8 , and n. The values of these parameters can be
derived from accurate observations of the cosmic microwave background, the
radiation emitted by recombining protons and electrons and redshifted by a factor of about 1100, and of the large-scale distribution of matter (e.g. Spergel et al.,
2003; Komatsu et al., 2011).
The distribution of matter is not spherically symmetric, so the collapse will be
different in different directions. First collapse happens in one dimension, forming sheets. When collapse happens in two dimenions, filaments form. In the end,
collapse occurs in three dimension and haloes are formed. An illustration of the
gas distribution in the present-day Universe is shown in Figure 1.1. Assuming
spherical collapse, the internal density for collapsed haloes is ρcoll ≈ 18π 2 hρm i
(Padmanabhan, 2002), where hρm i is the cosmic mean matter density:
hρm i = Ωm ρcrit = Ωm (1 + z)3 ρcrit,0 = Ωm (1 + z)3
3H02
,
8πG
(1.1)
where H0 is the z = 0 value of the Hubble parameter and G is the gravitational
constant. The mass of this object then is Mhalo = 43 πρcoll R3vir , from which we can
derive an expression for the virial radius:
Rvir ≈
2GMhalo
H02 Ωm 18π 2
!1/3
1
1+z
(1.2)
or
2
Rvir ≈ 3.4 · 10 kpc
M
12
10 M⊙
1/3
Ωm H02
1.3 × 10−36 s−2
!−1/3
1
.
1+z
(1.3)
Galaxies form inside their much larger haloes in the highest density peaks
and are dominated by baryons, because gas is able to cool, whereas dark matter
can only lose energy due to gravitational interactions, e.g. dynamical friction.
Galaxy properties therefore depend on other things than just gravity. The gas
behaves like an ideal gas. Its pressure increases when its volume decreases
or its temperature increases. It can move supersonically and it can therefore
experience shocks, converting its kinetic energy into thermal energy.
While the collapse of dark matter halts as it reaches virial equilibrium in
haloes, baryons can radiate away their binding energy, allowing them to collapse
2
Structure formation
Figure 1.1: Zoom-in from 50 h−1 Mpc to 10 h−1 Mpc to 2 h−1 Mpc of the gas density in a
2 h−1 Mpc slice of the Universe at z = 0, centred on a massive halo (Mhalo = 1013.5 M⊙ ),
showing the filaments of the cosmic web and the haloes embedded within them. The
colour bar is logarithmic, the same in all panels, and runs from the mean cosmic density
(blue) to 104 times the mean density of the Universe (red). The simulation used is the
reference simulation in a (50 h−1 Mpc)3 volume from the OWLS project (Schaye et al.,
2010).
3
Introduction
further and fragment into smaller structures, such as stars and galaxies. The
cooling time can be defined as the ratio of the thermal energy density of the gas
and the cooling rate, which depends on the density, temperature, and metallicity
of the gas, because it may be dominated by metal-line emission.
After virialization, a gas cloud can be in one of three regimes. If the characteristic cooling time exceeds the Hubble time-scale, the gas will not be able to
radiate away the thermal energy that supports it and will therefore not collapse.
If, on the other hand, the cooling time is smaller than the Hubble time, but larger
than the dynamical time-scale, then the cloud can adjust its density and temperature quasi-statically. It will increase both its density and its temperature while
maintaining hydrostatic equilibrium. Finally, if the cooling time is shorter than
the dynamical time, the cloud will cool faster than it can collapse, lowering the
Jeans mass and possibly leading to fragmentation. This is the regime in which
galaxies are thought to form (Rees & Ostriker, 1977; Silk, 1977).
We can divide the gas in the Universe into a couple of different phases in
temperature-density space. Their relative importance at z = 4, 2, and 0 is shown
in Figure 1.2. Gas with densities up to ∼ 102 times the cosmic average density represents the intergalactic medium (IGM). In the beginning, there was no
structure and all gas had densities very close to the cosmic mean and therefore
all gas started out in the IGM. At later times, a significant fraction of this gas
resides in filamentary structures. The gas can be heated to temperatures above
105 K when kinetic energy, generated by gravitational infall or galactic winds,
is converted into thermal energy. We refer to this tenuous, shock-heated gas as
the warm-hot intergalactic medium (WHIM). The WHIM also includes denser
halo gas. The intracluster medium is the very hot T > 107 K gas located in
galaxy groups and clusters. Gas at overdensities ρ/hρi > 102 , but at much lower
temperature (T < 105 K), resides mostly in the densest parts of filaments and
low-mass haloes. Gas at very high densities nH > 0.1 cm−3 is located inside
galaxies, in the interstellar medium (ISM).
Although the IGM completely dominates the mass budget at high redshift,
by z = 0 the WHIM carries about the same amount of mass (Davé et al., 2001).
The ICM is never very important, because the highest-mass objects are rare (e.g.
Shull et al., 2011). The amount of gas in the ISM and in low-temperature halo
gas peaks at z = 3 − 2 and declines thereafter (e.g. van de Voort et al., 2011b)
In the low-density IGM, the dominant cooling process is the expansion of
the Universe. As the gas reaches higher densities, radiative cooling becomes
more important. The cooling time tcool is shorter at higher redshift, because the
density, ρ, is higher and tcool ∝ ρ−1 . The Hubble time tH is also shorter, but
with a weaker dependence, tH ∝ ρ1/2 . Hence, galaxy formation will depend on
redshift. The so-called cooling radius is the radius, from the halo centre, where
tcool equals tH . If the cooling radius lies well inside the halo, which is the case
for high-mass haloes, a quasi-static, hot atmosphere will form. Accretion onto
the galaxy is then regulated by the cooling function. If, on the other hand, this
4
Structure formation
Figure 1.2: Distribution of baryonic matter amongst the different gas phases and stars.
The cold IGM (grey) dominates, but becomes less important towards lower redshift. The
WHIM (orange) becomes more important towards lower redshift. The ICM (red) is never
very important. The amount of cold halo gas (blue) and ISM (purple) is largest at z ≈ 2.
The stellar mass keeps building up down to z = 0. The simulation used is the reference
simulation in a (50 h−1 Mpc)3 volume from the OWLS project (Schaye et al., 2010).
radius is larger than the virial radius, then there will be no hot halo and the gas
will not go through an accretion shock at the virial radius. The rapid cooling of
gas in low-mass haloes was already shown by Rees & Ostriker (1977) and White
& Rees (1978). The accretion rate onto the central galaxy then depends on the
infall rate, but not on the cooling rate (White & Frenk, 1991).
Because haloes are not spherical, the cooling radius will not be the same
for the entire halo. Gas can accrete onto a halo from the low-density IGM or
along filaments of the cosmic web. The different gas densities will impact the
temperature of the gas. As mentioned before, the gas needs to radiate away
its energy to reach higher densities and thus to be able to enter a galaxy. Metalline emission dominates the cooling function for metallicities Z/Z⊙ & 0.1, which
peaks at T ≈ 105−5.5 K (Wiersma et al., 2009a). Gas at much higher temperatures
will cool slowly. This gives rise to a bimodal temperature distribution for gas
that accretes onto a massive halo (Kereš et al., 2005; Dekel & Birnboim, 2006).
Star formation in galaxies is fuelled by the accretion of gas from their haloes.
Haloes replenish their gas reservoir by accreting from the IGM. When gas accretes onto a halo it can be shock-heated to the virial temperature of that halo
and reach a quasi-static equilibrium supported by the pressure of the hot gas.
We call this form of gas accretion ‘hot-mode accretion’ (Katz et al., 2003; Kereš
et al., 2005). Because gas accreted onto high-mass haloes along filaments of the
cosmic web or in clumps, or onto low-mass haloes, may not experience an accretion shock at the virial radius and will therefore remain cold until it accretes
onto the central galaxy or is hit by an outflow, we refer to this mode of accretion
as ‘cold-mode accretion’ (Katz et al., 2003; Kereš et al., 2005). Both modes can
coexist. Especially at high redshift, cold streams penetrate the hot, virialized
haloes of massive galaxies (Kereš et al., 2005; Dekel & Birnboim, 2006; Ocvirk
5
Introduction
et al., 2008; Dekel et al., 2009a; Kereš et al., 2009a; van de Voort et al., 2011a;
Powell et al., 2011).
After gas has become part of the multiphase ISM of a galaxy, stars can form
out of it. Star formation in galaxies is observed to follow a close relation between
the gas surface density and the star formation rate surface density (Kennicutt,
1998). The gas surface density can be related to the gas volume density and
both are a function of the total thermal pressure (Schaye & Dalla Vecchia, 2008).
The observed gas consumption time-scale, i.e. the gas mass divided by the star
formation rate, is of the order of a Gyr.
In the absence of any feedback mechanism, gas accretion and star formation
happen too efficiently and the amount of baryons in stars would greatly exceed
the observed amount. Outflows are routinely detected in the form of blueshifted
interstellar absorption lines in the spectra of star-forming galaxies (e.g. Steidel
et al., 2010; Rubin et al., 2010; Rakic et al., 2011a), in X-ray emission and in hydrogen Balmer-α line emission (e.g. Lehnert et al., 1999; Cecil et al., 2001; Veilleux
et al., 2005). Single supernova explosions can temporarily outshine their host
galaxy. The material from the star that is expelled at high velocity, sweeps up
material in front of it, thus evacuating a bubble of hot gas around the original
star. When many supernovae occur in the same region, the bubbles can overlap and form superbubbles, which can lead to large-scale galactic outflows (e.g.
Weaver et al., 1977; Mac Low & Ferrara, 1999).
Supermassive black holes are present in all massive galaxies (e.g. Kormendy
& Richstone, 1995; Ferrarese & Merritt, 2000). Material accreting onto these black
holes is thought to release some of its rest mass energy to power active galactic nuclei (AGN) (Salpeter, 1964). AGN are invoked as a mechanism powerful
enough to quench star formation in the most massive galaxies by driving gas
out at high velocities.
Stars produce heavy elements, which can be distributed in their surroundings
by stellar winds and supernova explosions. These metals are ejected from the
galaxy by galactic winds driven by supernovae or AGN and enrich the halo gas
as well as part of the IGM (e.g. Wiersma et al., 2011). The enrichment enhances
the cooling rate of the gas and previously ejected gas can be reaccreted by the
same object or a different one (Oppenheimer et al., 2010). Because of large-scale
outflows, the IGM, haloes, and galaxies are intimately connected and the cycle
of baryons becomes complicated as outflows and inflows interact.
Even though there is plenty of observational evidence for galactic outflows,
inflows are not commonly seen. It is, however, quite possible that the inflowing
material has such small cross-sections that the signal is completely swamped by
outflowing material (e.g. Faucher-Giguère & Kereš, 2011; Stewart et al., 2011a).
Hot, hydrostatic halo gas is routinely studied using X-ray observations of galaxy
groups and clusters and has perhaps even been detected around individual
galaxies (e.g. Crain et al., 2010a,b; Anderson & Bregman, 2011). As of yet, there
6
Simulations
is no direct evidence of cold-mode accretion, although there are some possible
detections in emission (Rauch et al., 2011) and absorption (Ribaudo et al., 2011;
Giavalisco et al., 2011).
Diffuse gas can be detected in absorption using a bright background source.
UV and X-ray absorption line studies have revealed cold, neutral gas and the
WHIM. Their interpretation is not easy, as there is only information along the
line of sight and no information about the spatial extent of the absorbing cloud
and often the location of the nearest galaxy is unknown. The neutral hydrogen
column density distribution has been measured over ten orders of magnitude in
NH i (e.g. Tytler, 1987; Kim et al., 2002; Péroux et al., 2005; O’Meara et al., 2007;
Prochaska & Wolfe, 2009; Noterdaeme et al., 2009; Prochaska et al., 2010). Low
column density (NH i < 1017.2 cm2 ) material is known as the Lyman-α forest
and originates mostly in the photo-ionized IGM (e.g. Bi et al., 1992; Cen et al.,
1994; Hernquist et al., 1996; Theuns et al., 1998; Schaye, 2001a). Higher column
density systems originate from gas in haloes and galaxies. By correlating the
H i absorption in the spectra of background quasars with both the transverse
and line of sight separations from foreground galaxies, Rakic et al. (2011b) have
recently detected strong evidence for infall of cold gas on scales of ∼ 1.4 − 2.0
proper Mpc at z ≈ 2.4.
The gas emissivity in X-ray and UV scales with the square of the density. The
signal is thus dominated by high-density regions. In this way, emission line studies complement the absorption line studies. They have the added advantage of
providing a two-dimensional image, in addition to the third dimension provided
by the redshift of the emission line, allowing us to study the three-dimensional
spatial distribution. The interpretation of emitting gas would therefore be easier,
but because the emission is very faint, detecting it is still a challenge.
How all processes occurring in galaxy formation interact is a field of active
research. One can use numerical simulations as a tool to study this interplay
and to predict the observational consequences.
1.2 Cosmological simulations
Because the time-scales involved in galaxy formation are generally very long
compared to a human life time, numerical simulations are an excellent tool to
study structure formation dynamically. Additionally it is possible to study a
particular process by running two simulations, one with and one without it.
The complex, non-linear behaviour of the density perturbations necessitates the
use of supercomputers to perform the calculations. Numerical simulations have
significantly improved our understanding of the large-scale structure in the Universe. Even though we know very little about the physical nature of dark matter
and dark energy, the standard cosmological constant or vacuum-dominated cold
dark matter (ΛCDM) model reproduces the observed large-scale structure and
clustering of galaxies really well (Weinberg et al., 2004; Springel et al., 2005a).
7
Introduction
Despite its many successes, this model is not sufficient to explain the properties
of galaxies. Baryonic processes, that are not all well understood, are essential ingredients. Through feedback they can even impact the dark matter distribution,
a process that one should take into account when doing precision cosmology
(van Daalen et al., 2011; Semboloni et al., 2011).
Most cosmological simulations, i.e. simulations of structure formation in a
representative part of the universe, use particles to discretize the mass, because
of the superior spatial resolution to grid-based codes. The spatial resolution
is automatically higher in denser regions, where galaxies form. Little time is
spent on calculations in low density regions, where properties do not change
rapidly anyway. Another advantage of particle-based simulations is that there is
no preferred spatial direction and the resolution is increased continuously from
low- to high-density regions. An advantage that is particularly important for
this thesis is that we can trace the mass back in time to investigate its history.
The advantage of grid-based codes is that they are superior in resolving discontinuities, such as shocks. Turbulence and instabilities are also more easily
resolved. An added advantage is that one can choose a different property than
density as a refinement criterion and achieve high resolution in any region of
interest.
The expansion of the universe is dealt with by using comoving coordinates.
In physical space every volume element expands by an equal amount, set by the
cosmological parameters. To deal with the thermodynamic property of baryons,
smoothed particle hydrodynamics (SPH) can be used, in which some properties
of particles, e.g. density and metallicity, are smoothed over space by a spline
kernel function. Unfortunately, in SPH simulations shocks are not resolved as
true discontinuities, but they are smeared out over a few smoothing lengths,
leading to in-shock cooling (Hutchings & Thomas, 2000). This problem can be
avoided by using a sufficiently high resolution (Creasey et al., 2011).
Although cosmological simulations can provide sufficiently accurate calculations for diffuse gas, once the gas reaches high densities, that are characteristic of
the ISM, the multiphase medium cannot be resolved. The formation of individual stars from molecular clouds is not (yet) possible in cosmological simulations.
The effect that stars have, through e.g. ionizing photons, metal production, stellar winds, and supernova explosions, has to be modelled with subgrid prescriptions. Subgrid models are also needed for radiative cooling, because it happens
on the atomic level, and for accretion onto black holes, because the scale of the
accretion disc is not resolved.
The goal of developing subgrid models is that, even though the small-scale
physics is dealt with in an approximate, global sense, its effect is the same on
scales that are resolved. Unfortunately it is not always clear what the largescale effect should be and there is a lot of (unwanted) freedom in the subgrid
modelling. The OverWhelmingly Large Simulations (Schaye et al., 2010, OWLS)
project contains a suite of more than fifty cosmological, hydrodynamical sim8
This thesis
ulations. There is a reference model and all other simulations are variations
on this model, in the sense that only one parameter or one model was varied
at a time. Even though there are certainly uncertainties associated with these
simulations, their importance can be quantified by comparing simulations with
different resolution and different subgrid physics. In this thesis we use a subset
of the OWLS runs and will focus on the properties of gas accretion and their
consequences, the effect of feedback, and the observational signature of diffuse
gas outside galaxies.
1.3 This thesis
Numerical studies of the nature of gas accretion have revealed a bimodality, at
least for massive haloes. The temperature of gas accretion onto haloes is either
. 105 K or close to the virial temperature of the halo (Kereš et al., 2005; Dekel
& Birnboim, 2006; Ocvirk et al., 2008; Dekel et al., 2009a; Kereš et al., 2009a; van
de Voort et al., 2011a; Powell et al., 2011). Even though dividing accreting gas
into two modes does not change the problem simulations have with reproducing
observations, it can shed light on the physical mechanism behind it. In this thesis
the following open questions will be addressed:
1. What are the properties of accreting gas? How do the properties of gas
accretion onto haloes affect the accretion onto galaxies and subsequently
the star formation rates of the galaxies?
2. What is the impact of realistic outflows on the inflowing gas? Is star formation quenched by ejecting gas from the ISM or by preventing it from
accreting? Which processes set the global star formation rate?
3. Has cold-mode accretion already been observed as H i absorption systems?
If so, in what kind of objects is it found? Is the cold-mode gas accreting for
the first time or reaccreting?
4. Can we observe halo gas in emission in the near future? If so, which metal
lines would be most promising and what do they tell us about the physical
state of the gas?
A brief summary of the contents of this thesis is given below.
Chapter 2: Gas accretion onto galaxies and haloes
We found that gas accretion is mostly smooth, with mergers only becoming
important for groups and clusters. Without supernova or AGN feedback the gas
accretion rate onto haloes scales like the dark matter accretion rate. The same
is not true for gas accretion onto galaxies, because the gas has to cool before it
can enter the ISM of the galaxy. Including feedback from supernovae or AGN
reduces the halo accretion rate by factors of a few and galaxy accretion rates
by up to an order of magnitude, because outflowing gas prevents the inflowing
9
Introduction
gas from accreting. Galactic winds increase the halo mass at which the central
galaxies grow most efficiently by about two orders of magnitude to Mhalo ≈
1012 M⊙ .
Gas accretion is bimodal, with maximum past temperatures either of the
order of the virial temperature or . 105 K. We define cold-mode (hot-mode)
accretion as gas that is accreted and whose temperature did not exceed (did
exceed) 105.5 K before it accreted onto a galaxy. The fraction of the gas accreted
onto haloes in the hot mode is insensitive to feedback and metal-line cooling. It
increases with decreasing redshift, but is mostly determined by the halo mass. In
contrast, for accretion onto galaxies, the cold mode is always significant and the
relative contributions of the two accretion modes are more sensitive to feedback
and metal-line cooling. (This work has been completed and published, van de
Voort et al. 2011a.)
Chapter 3: The drop in the cosmic SFR below redshift 2
Given that hot- and cold-mode accretion vary with redshift and halo mass,
we determine their roles in shaping the global star formation rate density. Including feedback processes is essential to match observations of the global star
formation rate density, because it reduces the star formation rate in low- and
high-mass galaxies. The cosmic star formation rate is observed to drop sharply
after z = 2. We find that the drop in the star formation rate follows a corresponding decline in the global cold-mode accretion rate density onto haloes, but
with a delay of the order of the gas consumption time-scale in the interstellar
medium.
In contrast to cold-mode accretion, which peaks at z ≈ 3, the hot mode
continues to increase to z ≈ 1 and remains roughly constant thereafter. By
z = 0, the hot mode strongly dominates the global accretion rate onto haloes,
but most of the hot halo gas never accretes onto galaxies. AGN feedback plays
a crucial role by preferentially preventing the gas that entered haloes in the hot
mode from accreting onto their central galaxies. Consequently, in the absence
of AGN feedback, gas accreted in the hot mode would become the dominant
source of fuel for star formation and the drop-off in the cosmic star formation
rate would be much less steep. (This work has been completed and published,
van de Voort et al. 2011b.)
Chapter 4: Gas properties in and around haloes
We study the properties of gas inside and around galaxy haloes as a function
of radius and halo mass. The properties of cold- and hot-mode gas are clearly
distinguishable in the outer parts of massive haloes. The cold-mode gas is mostly
confined to clumpy filaments that are in pressure equilibrium with the diffuse,
hot-mode gas. Besides being colder and denser, cold-mode gas typically has a
much lower metallicity and is much more likely to be infalling. However, the
spread in the properties of the gas is large. Due to a strong cooling flow near the
central galaxy, the properties of gas accreted through the cold and hot modes in
10
This thesis
the inner halo are indistinguishable. Stronger feedback results in larger outflow
velocities and pushes hot-mode gas to larger radii. The differences between
cold- and hot-mode gas resemble those between inflowing and outflowing gas,
although they are somewhat smaller. The gas properties evolve as expected
from virial arguments, which can also account for the dependence of many gas
properties on halo mass. (This work has been completed and submitted, van de
Voort & Schaye 2012.)
Chapter 5: Cold flows as H i absorption systems
We use the OWLS reference simulation that has been post-processed with radiative transfer to study the contribution of cold flows to the observed z = 3
column density distribution of neutral hydrogen, which our simulation reproduces. We have found that nearly all of the H i absorption arises in gas that
has remained colder than 105.5 K, at least while it was extragalactic. In addition, the majority of the H i is rapidly falling towards a nearby galaxy, with
non-negligible contributions from outflowing and static gas. Above a column
density of NH i = 1017 cm−2 , most of the absorbers reside inside haloes, but the
interstellar medium only dominates for NH i > 1021 cm−2 . Haloes with total
mass below 1010 M⊙ dominate the absorption for 1017 < NH i < 1021 cm−2 , but
the average halo mass increases sharply for higher column densities.
Systems with NH i > 1017 cm−2 are closely related to star formation: most
of their H i either will become part of the interstellar medium before z = 2 or
has been ejected from a galaxy at z > 3. Cold accretion flows are critical for
the success of our simulation in reproducing the observed rate of incidence of
damped Lyman-α and particularly that of Lyman limit systems. We therefore
conclude that cold accretion flows exist and have already been detected in the
form of high column density H i absorbers. (This work has been completed and
is in press, van de Voort et al. 2012.)
Chapter 6: Metal-line emission from galaxy haloes
The gas outside of galaxies is diffuse and therefore faint. With current and upcoming instruments we may be able to detect the halo gas in emission, even
if only in a statistical sense. We calculate the expected metal-line emission as
a function of radius from the central galaxy and compare it to the capabilities
of current and future facilities. We found that detecting metal-line emission in
the UV from halo gas at high redshift will be a challenge for upcoming instruments. When stacking galaxies to reduce the noise, it is in principle possible to
observe C iii, C iv, O vi, Si iii, and Si iv out to 10 − 20 per cent of the virial radius in haloes larger than 1011 M⊙ . These lines are somewhat brighter in haloes
at low redshift, but future UV missions should aim to achieve a flux limit of
10−19 ergs s−1 cm2 arcsec2 . At low redshift, proposed X-ray telescopes can detect
O viii emission out to the virial radius of groups and clusters. C vi, N vii, and
O vii can also be detected to smaller radii, 0.1 − 0.5Rvir . Actually observing this
gas would enable us to confirm or revise what we have learned from simula11
Introduction
tions. (This work is in an advanced stage of preparation and will be submitted
soon.)
1.4 Outlook
Research will never truly be finished, because there will always be new questions
that arise. Significant progress will be made in the near future in the study
of galaxy formation, both observationally and theoretically. As observations
improve, simulations will have to improve as well. Higher spatial resolution
and time resolution will lead to improvements, especially when it goes hand in
hand with the development of more advanced subgrid models.
Although we can quantify the uncertainties with the suite of simulations used
for this thesis, many of the observed properties of galaxies are not reproduced
by a single simulation. The Evolution and Assembly of GaLaxies and their Environments (EAGLE) project will be the largest SPH simulation down to z = 0
as of yet, with a resolution high enough to resolve the Jeans scale up to the star
formation threshold and a volume large enough to contain a significant amount
of massive haloes. The strategy is to tune the feedback parameters to match the
observed stellar mass function and the stellar mass-halo mass relation. This will
result in a large sample of relatively realistic, well-resolved massive galaxies and
will therefore be well-suited for comparing to observations.
Radiative transfer is usually not taken into account in cosmological simulations. Instead, all the gas is assumed to be optically thin and is exposed to
the same ionizing UV background radiation. In reality, inhomogeneous ionizing
radiation from local sources and self-shielding of the gas can change the temperature and density of gas in haloes and in the IGM, so it should be included.
Recent progress in radiative transfer modelling will make this feasible.
Numerical simulations help us investigate what is happening outside of
galaxies, but we need to observe the material to confirm our ideas. Future instruments that have been designed for the detection of UV and X-ray emission will
certainly aid our understanding. In particular, next year MUSE, an integral field
spectrograph, will be installed on the VLT, which is expected to detect many
sources, in emission and absorption (Bacon et al., 2010). Additionally, proposed
X-ray missions would be ideal for detecting metal-line emission from the WHIM
in the centres and outskirts of massive haloes and studying the gas properties
(e.g. den Herder et al., 2011).
Lyman-α radiation is an important tool for observing the distant Universe,
because it is much brighter than metal-line emission. Its interpretation is still
a challenge, because the Lyman-α line is a resonant line and photons scatter
many times before escaping, which strongly affects the line profile. Lymanα radiative transfer simulations will allow us to disentangle radiative transfer
effects from the kinematics of the gas in a statistically meaningful sample and
help to interpret observations.
12
2
The rates and modes of gas
accretion onto galaxies and their
gaseous haloes
We study the rate at which gas accretes onto galaxies and haloes and investigate
whether the accreted gas was shocked to high temperatures before reaching a
galaxy. For this purpose we use a suite of large cosmological, hydrodynamical simulations from the OWLS project, which uses a modified version of the
smoothed particle hydrodynamics code gadget-3. We improve on previous
work by considering a wider range of halo masses and redshifts, by distinguishing accretion onto haloes and galaxies, by including important feedback
processes, and by comparing simulations with different physics.
Gas accretion is mostly smooth, with mergers only becoming important for
groups and clusters. The specific rate of gas accretion onto haloes is, like that
for dark matter, only weakly dependent on halo mass. For halo masses Mhalo ≫
1011 M⊙ it is relatively insensitive to feedback processes. In contrast, accretion
rates onto galaxies are determined by radiative cooling and by outflows driven
by supernovae and active galactic nuclei. Galactic winds increase the halo mass
at which the central galaxies grow the fastest by about two orders of magnitude
to Mhalo ∼ 1012 M⊙ .
Gas accretion is bimodal, with maximum past temperatures either of order
the virial temperature or . 105 K. The fraction of gas accreted onto haloes in
the hot mode is insensitive to feedback and metal-line cooling. It increases with
decreasing redshift, but is mostly determined by halo mass, increasing gradually
from less than 10% for ∼ 1011 M⊙ to greater than 90% at ∼ 1013 M⊙ . In contrast,
for accretion onto galaxies the cold mode is always significant and the relative
contributions of the two accretion modes are more sensitive to feedback and
metal-line cooling. On average, the majority of stars present in any mass halo at
any redshift were formed from gas accreted in the cold mode, although the hot
mode contributes typically over 10% for Mhalo & 1011 M⊙ .
Thus, while gas accretion onto haloes can be robustly predicted, the rate
of accretion onto galaxies is sensitive to uncertain feedback processes. Nevertheless, it is clear that galaxies, but not necessarily their gaseous haloes, are
predominantly fed by gas that did not experience an accretion shock when it
entered the host halo.
Freeke van de Voort, Joop Schaye, C. M. Booth,
Marcel R. Haas, and Claudio Dalla Vecchia
Monthly Notices of the Royal Astronomical Society
Volume 414, Issue 3, pp. 2458-2478 (2011)
Introduction
2.1 Introduction
In the standard cosmological constant or vacuum dominated cold dark matter (ΛCDM) model mass assembles hierarchically, with the smallest structures
forming first. While the collapse of dark matter halts as it reaches virial equilibrium in haloes, baryons can radiate away their binding energy, allowing them to
collapse further and fragment into smaller structures, such as stars and galaxies.
These galaxies then grow through mergers and gas accretion.
After virialization, a gas cloud can be in one of three regimes. If the characteristic cooling time exceeds the Hubble time-scale, the gas will not be able to
radiate away the thermal energy that supports it and will therefore not collapse.
If, on the other hand, the cooling time is smaller than the Hubble time, but
larger than the dynamical time-scale, then the cloud can adjust its density and
temperature quasi-statically. It will increase both its density and temperature
while maintaining hydrostatic equilibrium. Finally, if the cooling time is shorter
than the dynamical time, the cloud will cool faster than it can collapse, lowering the Jeans mass and possibly leading to fragmentation. This is the regime in
which galaxies are thought to form (Silk, 1977; Rees & Ostriker, 1977). In reality
the situation must, however, be more complicated as the density, and thus the
cooling and dynamical times, will vary with radius.
Gas falling towards a galaxy gains kinetic energy until it reaches the hydrostatic halo. If the infall velocity is supersonic, it will experience a shock and heat
to the virial temperature of the halo. According to the simplest picture of spherical collapse, all gas in a dark matter halo is heated to the virial temperature of
that halo, reaching a quasi-static equilibrium supported by the pressure of the
hot gas. Gas can subsequently cool radiatively and settle into a rotationally supported disc, where it can form stars (e.g. Fall & Efstathiou, 1980). We call this
form of gas accretion ‘hot accretion’ (Katz et al., 2003; Kereš et al., 2005).
Within some radius, the so-called cooling radius, the cooling time of the gas
will, however, be shorter than the age of the Universe. If the cooling radius lies
well inside the halo, which is the case for high-mass haloes, a quasi-static, hot
atmosphere will form. Accretion onto the galaxy is then regulated by the cooling
function. If, on the other hand, this radius is larger than the virial radius, then
there will be no hot halo and the gas will not go through an accretion shock at the
virial radius. Because gas accreted in this manner may never have been heated
to the virial temperature, we refer to this mode of accretion as ‘cold accretion’
(Katz et al., 2003; Kereš et al., 2005). The rapid cooling of gas in low-mass haloes
was already shown by Rees & Ostriker (1977) and White & Rees (1978). The
accretion rate onto the central galaxy then depends on the infall rate, but not on
the cooling rate (White & Frenk, 1991). Simulations confirmed the existence of
gas inside haloes which was never heated to the virial temperature of the halo
(Katz & Gunn, 1991; Kay et al., 2000; Fardal et al., 2001; Katz et al., 2003).
The cooling time tcool is shorter at higher redshift, because the density, ρ, is
higher and tcool ∝ ρ−1 . The Hubble time tH is also shorter, but with a weaker
15
Gas accretion onto galaxies and haloes
dependence, tH ∝ ρ−1/2. Hence, the mode of gas accretion onto galaxies will
depend on redshift, with cold accretion more prevalent at higher redshifts for
a fixed virial temperature. The mode of gas accretion will also depend on halo
mass. Higher-mass haloes have higher virial temperatures and thus, at least for
T & 106 K, longer cooling times. Hence, hot accretion will dominate for the
most massive haloes. The dominant form of accretion will thus depend on both
the mass of the halo and on the accretion redshift (Katz et al., 2003; Birnboim
& Dekel, 2003; Kereš et al., 2005; Ocvirk et al., 2008; Kereš et al., 2009a; Brooks
et al., 2009; Crain et al., 2010a).
Although both analytic and semi-analytic studies of galaxy formation usually
assume spherical symmetry (e.g. Binney, 1977; White & Frenk, 1991; Birnboim &
Dekel, 2003), numerical simulations show different geometries. As the matter in
the Universe collapses, it forms a network of sheets and filaments, the so-called
‘cosmic web’. Galaxies form in the densest regions, the most massive galaxies
where filaments intersect. These structures can have an important effect on gas
accretion. If a galaxy is being fed along filaments, the average density of the
accreting gas will be higher. The cooling time will thus be smaller and it will be
easier to radiate away the gravitational binding energy. Filaments may therefore
feed galaxies preferentially through cold accretion. Both modes can coexist.
Especially at high redshift, cold streams penetrate the hot virialized haloes of
massive galaxies (Kereš et al., 2005; Dekel & Birnboim, 2006; Ocvirk et al., 2008;
Kereš et al., 2009a; Dekel et al., 2009a).
Galaxy colours and morphologies are observed to be roughly bimodal. They
can be divided into two main classes: blue, star forming spirals and red, passive
ellipticals (e.g. Kauffmann et al., 2003; Baldry et al., 2004). The latter tend to
be more massive and to reside in clusters. It has been suggested by Dekel &
Birnboim (2006) that this observed bimodality is caused by the two different
mechanisms for gas accretion. If, for example, feedback from active galactic
nuclei (AGN) were to prevent the hot gas from cooling, massive galaxies with
little cold accretion would have very low star formation rates. If, on the other
hand, cold accretion flows were less susceptible to such feedback, then low-mass
haloes could host discs of cold gas, which could form stars efficiently. However,
this cannot be the whole story, because suppressing star formation from gas
accreted in the hot mode is not nearly sufficient to reproduce the observations
(Kereš et al., 2009b).
In this work we use a large number of cosmological, hydrodynamical simulations from the OverWhelmingly Large Simulations project (OWLS; Schaye et al.,
2010) to investigate accretion rates, the separation of hot and cold modes, and
their dependence on halo mass and redshift. Our work extends earlier work in
several ways. By combining simulations with different box sizes, each of which
uses at least as many particles as previous simulations, we are able to cover a
large dynamic range in halo masses and a large range of redshifts. While earlier
work used only a single physical model, our use of a range of models allows
us to study the role of metal-line cooling, supernova (SN) feedback, and AGN
16
Simulations
feedback. Some of these processes had been ignored by earlier studies. For example, Kereš et al. (2005, 2009a,b) ignored metal-line cooling and SN feedback.
Using a semi-analytic model, Benson & Bower (2010) emphasized the importance of including the effect of feedback. Brooks et al. (2009) did not include
metal-line cooling, but did include SN feedback. Ocvirk et al. (2008) included
both metal-line cooling and weak SN feedback, but could only study the highredshift behaviour as their simulation was stopped at z ≈ 1.5. AGN feedback
was not included by any previous study, although Khalatyan et al. (2008) did
show the existence of cold accretion in a simulation of a single group of galaxies
with AGN feedback. In contrast to previous work, we distinguish between accretion onto haloes and accretion onto galaxies (i.e. the interstellar medium, or
ISM). We find that while hot mode accretion dominates the growth of high-mass
haloes, cold mode accretion is still most important for the growth of the galaxies
in these haloes. The different physical models give similar results for accretion
onto haloes, implying that the results are insensitive to feedback processes, but
the inclusion of such processes is important for accretion onto galaxies.
This paper is organized as follows. The simulations are described in Section 2.2, including all the model variations. In Section 2.3 we describe some
properties of the gas in the temperature-density plane for our fiducial simulation. The ways in which haloes are identified and gas accretion is determined
is discussed in Section 2.4. The accretion rates for all simulations can be found
in Section 2.5, for accretion onto haloes as well as for accretion onto galaxies. In
Section 2.6 we compare hot and cold accretion onto haloes for the different simulations and we do the same for accretion onto galaxies in Section 2.7. Finally,
we compare our results with previous work in Section 2.8 and summarize our
conclusions in Section 2.9.
2.2 Simulations
To investigate the temperature distribution of accreted gas, we use a modified
version of gadget-3 (last described in Springel, 2005b), a smoothed particle hydrodynamics (SPH) code that uses the entropy formulation of SPH (Springel &
Hernquist, 2002), which conserves both energy and entropy where appropriate.
This work is part of the OWLS (Schaye et al., 2010) project, which consists of a
large number of cosmological simulations, with varying (subgrid) physics. We
first summarize the subgrid prescriptions for the reference simulation. The other
simulations are described in Section 2.2.1. As the simulations are fully described
in Schaye et al. (2010), we will only summarize their main properties here.
The cosmological simulations described here assume a ΛCDM cosmology
with parameters as determined from the Wilkinson microwave anisotropy probe
year 3 (WMAP3) results, Ωm = 1 − ΩΛ = 0.238, Ωb = 0.0418, h = 0.73,
σ8 = 0.74, n = 0.951. These values are consistent1 with the WMAP year 7
1 The
only significant discrepancy is in σ8 , which is 8% lower than the value favoured by the
17
Gas accretion onto galaxies and haloes
simulation
L100N512
L100N256
L050N512
L025N512
L025N256
L025N128
Lbox
(h−1 Mpc)
100
100
50
25
25
25
N
5123
2563
5123
5123
2563
1283
mDM
(M⊙ )
5.56 × 108
4.45 × 109
6.95 × 107
8.68 × 106
6.95 × 107
5.56 × 108
mgas
(M⊙ )
1.19 × 108
9.84 × 109
1.48 × 107
1.85 × 106
1.48 × 107
1.19 × 108
zfinal
Nhalo (z = 2)
Nhalo (z = 0)
0
0
0
2
2
0
10913
838
12648
12768
1653
159
18463
2849
15884
338
18
Table 2.1: Simulation parameters: simulation identifier, comoving box size (Lbox ), number of dark matter particles (N, the number of
baryonic particles is equal to the number of dark matter particles), mass of dark matter particles (mDM ), initial mass of gas particles (mgas ),
final simulation redshift, number of resolved haloes (containing more than 250 dark matter particles) at z = 2 (Nhalo (z = 2)), and number
of resolved haloes (containing more than 250 dark matter particles) at z = 0 (Nhalo (z = 0)).
Simulations
data (Komatsu et al., 2011).
A cubic volume with periodic boundary conditions is defined, within which
the mass is distributed over N 3 dark matter and as many gas particles. The
box size (i.e. the length of a side of the simulation volume) of the simulations
used in this work is 25, 50, or 100 h−1 Mpc, with N = 512, unless stated otherwise. The (initial) particle masses for baryons and dark matter are 1.2 ×
Lbox
N −3
3 N −3 M and 5.6 × 108 (
108 ( 100 Lhbox
)3 ( 512
) M⊙ , respectively,
⊙
−1 Mpc ) ( 512 )
100 h−1 Mpc
and are listed in Table 2.1, as are the number of resolved haloes at z = 2 and
z = 0. We use the notation L***N###, where *** indicates the box size and ###
the number of particles per dimension. The gravitational softening length is
N −1 −1
h kpc comoving, i.e. 1/25 of the mean dark matter par7.8 ( 100 Lhbox
−1 Mpc )( 512 )
N −1 −1
h kpc
ticle separation, but we imposed a maximum of 2 ( 100 Lhbox
−1 Mpc )( 512 )
proper.
The primordial abundances are X = 0.752 and Y = 0.248, where X and Y
are the mass fractions of hydrogen and helium, respectively. The abundances of
eleven elements (hydrogen, helium, carbon, nitrogen, oxygen, neon, magnesium,
silicon, sulphur, calcium, and iron) released by massive stars (type II SNe and
stellar winds) and intermediate mass stars (type Ia SNe and asymptotic giant
branch stars) are followed as described in Wiersma et al. (2009b). We assume the
stellar initial mass function (IMF) of Chabrier (2003), ranging from 0.1 to 100 M⊙ .
As described in Wiersma et al. (2009a), radiative cooling and heating are computed element-by-element in the presence of the cosmic microwave background
radiation and the Haardt & Madau (2001) model for the UV/X-ray background
from galaxies and quasars.
Star formation is modelled according to the recipe of Schaye & Dalla Vecchia
(2008). The Jeans mass cannot be resolved in the cold ISM, which could lead to
artificial fragmentation (e.g. Bate & Burkert, 1997). Therefore a polytropic equa−3
tion of state Ptot ∝ ρ4/3
gas is implemented for densities exceeding nH = 0.1 cm ,
where Ptot is the total pressure and ρgas the density of the gas. It keeps the
Jeans mass fixed with respect to the gas density, as well as the ratio of the
Jeans length and the SPH smoothing kernel. Gas particles with proper densities nH ≥ 0.1 cm−3 and temperatures T ≤ 105 K are moved onto this equation
of state and can be converted into star particles. The star formation rate (SFR)
per unit mass depends on the gas pressure and is set to reproduce the observed
Kennicutt-Schmidt law (Kennicutt, 1998).
Feedback from star formation is implemented using the prescription of Dalla
Vecchia & Schaye (2008). About 40 percent of the energy released by type II
SNe is injected locally in kinetic form. The rest of the energy is assumed to be
lost radiatively. Each gas particle within the SPH smoothing kernel of the newly
formed star particle has a probability of being kicked. For the reference model,
the mass loading parameter η = 2, meaning that on average the total mass of
the particles being kicked is twice the mass of the star particle formed. Because
WMAP 7-year data.
19
Gas accretion onto galaxies and haloes
simulation
REF
NOSN
NOSN_NOZCOOL
NOZCOOL
WML4
WML1V848
DBLIMFCONTSFV1618
WDENS
AGN
Z cool
η
AGN
Lbox and N
2
0
0
2
4
1
2
no
no
no
no
no
no
no
all listed in Table 2.1
L100N512 at z = 2
L100N512, L025N512
L100N512, L025N512
L100N512, L025N512
L100N512, L025N512
L100N512, L025N512
no
yes
L100N512, L025N512
L100N512, L025N512
yes
yes
no
no
yes
yes
yes
vwind
(km/s)
600
0
0
600
600
848
600 & 1618
yes
yes
density dependent
600
2
20
Table 2.2: Simulation parameters: simulation identifier, cooling including metals (Z cool), wind velocity (vwind ), wind mass loading (η),
and AGN feedback included (AGN). Differences from the reference model are indicated in bold face. The last column gives the box size
and particle number, from Table 2.1, used with these simulation parameters (Lbox and N).
Simulations
the winds sweep up surrounding material, the effective mass loading can be
higher. The initial wind velocity is 600 km/s for the reference model, which is
consistent with observations of starburst galaxies, both locally (Veilleux et al.,
2005) and at high redshift (Shapley et al., 2003). Schaye et al. (2010) showed
that these parameter values yield a peak, global star formation rate density that
agrees with observations.
The simulation data is saved at discrete output redshifts with interval ∆z =
0.125 at 0 ≤ z ≤ 0.5, ∆z = 0.25 at 0.5 < z ≤ 4, and ∆z = 0.5 at 4 < z ≤ 9. This is
the time resolution used for determining accretion rates.
2.2.1 Model variations
To see whether or not our results are sensitive to specific physical processes or
subgrid prescriptions, we have performed a suite of simulations in which many
of the simulation parameters are varied. These are listed in Table 2.2.
The importance of metal-line cooling can be demonstrated by comparing the
reference simulation (REF) to a simulation in which primordial abundances are
assumed when calculating the cooling rates (NOZCOOL). Similarly, the effect of
including SN feedback can be studied by comparing a simulation without SN
feedback (NOSN) to the reference model. Because the metals cannot be expelled
without feedback, they pile up, causing efficient cooling and star formation. To
limit the cooling rates, we performed a simulation in which both cooling by
metals and feedback from SNe were ignored (NOSN_NOZCOOL). Simulation
NOSN_L025N512 was stopped just below z = 4 and the z = 0.125 snapshot is
missing for NOSN_L100N512. We therefore cannot always show results for this
simulation.
In massive haloes the pressure of the ISM is too high for winds with velocities
of 600 km/s to blow the gas out of the galaxy (Dalla Vecchia & Schaye, 2008).
Keeping the√
wind energy per unit stellar mass constant, we increased the wind
velocity by 2 to vwind = 848 km/s, while halving the mass loading to η = 1
(WML1V848). To enable the winds to eject gas from haloes with even higher
masses, the velocity and mass loading can be scaled with the local sound speed,
while keeping the energy injected per unit stellar mass constant (WDENS).
To investigate the dependence on SN energy given to the ISM, we ran a
simulation using almost all of the energy available from SNe. The wind mass
loading η = 4, a factor of two higher than in the reference simulation. The wind
velocity is the same, vwind = 600 km/s (WML4).
There is some evidence that the IMF is top-heavy in extreme environments,
like starburst galaxies (e.g. Padoan et al., 1997; Klessen et al., 2007; Dabringhausen et al., 2009). We have performed a simulation in which the IMF is topheavy for stars formed at high pressures, Ptot /kB > 1.7 × 105 cm−3 K, where kB
is Boltzmann’s constant, and therefore in high-mass haloes. The critical pressure was chosen such that ∼10% of the stars are formed with a top-heavy IMF.
It results in more SNe per solar mass of stars formed and therefore stronger
21
Gas accretion onto galaxies and haloes
winds. More energy is therefore put into the winds blown by these star particles, vwind = 1618 km/s and η = 2 (DBLIMFCONTSFV1618).
Finally, we have included AGN feedback (AGN). Black holes inject 1.5% of
the rest-mass energy of the accreted gas into the surrounding matter in the form
of heat. The model is described and tested in Booth & Schaye (2009), who also
demonstrate that it reproduces the observed mass density in black holes and
the observed scaling relations between black hole mass and both central stellar
velocity dispersion and stellar mass. McCarthy et al. (2010) have shown that our
model AGN reproduces the observed stellar mass fractions, SFRs, stellar age
distributions and thermodynamic properties of galaxy groups.
2.2.2 Maximum past temperature
The Lagrangian nature of the simulation is exploited by tracing each fluid element back in time, which is particularly convenient for this project, in which
we are studying the temperature history of accreted gas. During the simulations the maximum temperature, Tmax , and the redshift at which it was reached,
zmax , were stored in separate variables. The variables were updated for each
SPH particle at every time step for which the temperature was higher than the
previous maximum temperature. The artificial temperature the particles obtain
when they are on the equation of state (i.e. when they are part of the unresolved
multiphase ISM) was ignored in this process. This may cause us to underestimate the maximum past temperature of gas that experienced an accretion shock
at higher densities. Ignoring such shocks is, however, consistent with our aims,
as we are interested in the maximum temperature reached before the gas entered
the galaxy.
Shock heating could be missed if the particle heats and cools rapidly in a single time step. In SPH simulations, a shock is smeared out over a few smoothing
lengths, leading to in-shock cooling (Hutchings & Thomas, 2000). We find the
1/3
(1 + z)1/2 km/s.
average value for the infall velocity to be ∼ 5 × 102 1013MM
⊙
On average the SPH smoothing length at halo accretion is ∼ 102 kpc (comoving) for all L100N512 simulations and at all redshifts. The particle will take
−1/3
108 1013MM
(1 + z)−3/2 years to traverse this distance. A shock will there⊙
fore take at least a few times 108 years. In reality the accretion shock will proceed almost instantaneously, minimizing radiative losses. In the simulations
described here gas cools at each time step, so also while it is being shocked. The
finite spatial resolution can thus result in lower maximum temperatures than
the actual post-shock temperatures. If this effect were important, increasing the
resolution would increase the hot fraction, i.e. the fraction of the gas that is accreted in the hot mode, because the accretion shocks would be less broadened.
The opposite is the case, as we will show in Figure 2.9.
Even with infinite time resolution, the post-shock temperatures may, however, not be well defined. Electrons and protons will temporarily have different
22
23
Simulations
Figure 2.1: Current temperature (left) and maximum past temperature (right) against current overdensity for gas particles at z = 2 in the
reference simulation in a 50 h−1 Mpc box. The logarithm of the total gas mass in a pixel is used for colour coding. The black lines separate
the different phases of the gas. Gas with T & 105 K has been shock heated. The T − ρ relation for cold, low-density gas (T . 105 K and
ρ . 10hρi is set by heating by the UV background and adiabatic cooling. At ρ/hρi > 101.5 radiative cooling dominates over cooling by the
expansion of the Universe. Gas with nH > 0.1 cm−3 (ρ/hρi > 104.3 at z = 2) is assumed to be part of the unresolved, multiphase ISM and
is put on an effective equation of state. The ‘temperature’ of this gas merely reflects the pressure of the multiphase ISM and is therefore
not used to update Tmax . The scatter in the equation of state is caused by adiabatic cooling of inactive particles in between time steps. Gas
that is condensing onto haloes or inside haloes has Tmax & 104.5 K, which reflects the peak in the T-ρ relation (at ρ/hρi > 101.5 , T ∼ 104.5 K)
visible in the left panel.
Gas accretion onto galaxies and haloes
temperatures in the post-shock gas, because they differ in mass, an effect that
we have not included. It will take a short while before they equilibrate through
collisions or plasma effects. Another effect, which is also not included in our
simulations, is that shocks may be preceded by radiation from the shock, which
may affect the temperature evolution.
2.3 The temperature-density distribution
The left-hand panel of Figure 2.1 shows the mass-weighted distribution of gas in
the temperature-density plane at z = 2 for simulation REF_L050N512. Gas with
densities up to ∼ 102 times the cosmic average density represents the diffuse intergalactic medium (IGM). A significant fraction of this gas resides in filamentary
structures. It can be heated to temperatures above 105 K when kinetic energy,
generated by gravitational infall or galactic winds, is converted into thermal energy. We refer to this tenuous, shock-heated gas as the warm-hot intergalactic
medium (WHIM). The intracluster medium (ICM) is the very hot T & 107 K gas
located in galaxy groups and clusters. Gas at overdensities ρ/hρi & 102 , but
much lower temperatures (T ∼ 104 K) resides mostly in filaments and low-mass
haloes.
Most of the gas is located in the purple region, with ρ/hρi < 10. The temperature of this gas is determined by the combination of photoheating by the UV
background and adiabatic cooling by the expansion of the Universe. Although
the slope of this temperature-density relation is close to adiabatic, it is actually
determined by the temperature dependence of the recombination rate (Hui &
Gnedin, 1997).
The turnover density, above which the typical gas temperatures decrease,
occurs when radiative cooling starts to dominate over adiabatic cooling. The
overdensity at which this happens depends on redshift. At z = 2 it occurs
at ρ/hρi ≈ 101.5. The distribution of the WHIM (broad red region, with T >
105 K) is set in part by the cooling function, to which especially heavier atoms,
like oxygen, contribute. In particular, the lack of dense gas (ρ/hρi & 103 ) with
105 K . T . 107 K is due to radiative cooling.
Gas with proper hydrogen number density nH > 0.1 cm−3 , corresponding
at this redshift to overdensity ρ/hρi > 104.3, represents the ISM. This highdensity gas is put on an equation of state if its temperature was below 105 K
when it crossed the density threshold, because the cold and warm phases of this
dense medium are not resolved by the simulations. Therefore, the temperature
merely reflects the imposed effective pressure and the density should be interpreted as the mean density of the unresolved multi-phase ISM. The spread in the
temperature-density relation on the equation of state is caused by the adiabatic
extrapolation of inactive particles between time steps. In addition, the relation
is broadened by differences in the mean molecular weight, µ, of the gas, which
depends on the density, temperature and elemental abundances of the gas.
The right-hand panel of Figure 2.1 shows the maximum past temperature
24
Defining gas accretion
reached at z ≥ 2, as a function of the z = 2 baryonic overdensity. All dense gas
has reached temperatures of & 104.5 K at some point. Dense (ρ/hρi > 101.5) gas
cannot have Tmax much below 104.5 K, because of photoheating2 . The maximum
past temperature tends to remain constant once the gas has reached densities
& 102 hρi, resulting in the horizontal trend in the figure. There is no dense
ρ/hρi ∼ 104gas at the highest maximum temperatures (above 107 K), because
the cooling time of gas that is heated to this temperature at lower densities
(ρ/hρi ∼ 102−3) is longer than a Hubble time, preventing it from cooling and
reaching higher densities.
The maximum past temperature reached for dense gas depends on whether
the gas has been heated to the virial temperature of its halo and on whether it
has been shock-heated by galactic winds.
2.4 Defining gas accretion
To see how haloes accrete gas, we first need to find and select the haloes. This can
be done in several different ways and we will discuss three of them. Although
we choose to use the one based on the gravitational binding energy, our results
are insensitive to the halo definition we use. Finally, we link haloes in two
subsequent snapshots in order to determine which gas has entered the haloes.
2.4.1 Identifying haloes and galaxies
The first step towards finding gravitationally bound structures is to identify dark
matter haloes. These can for example be found using a Friends-of-Friends (FoF)
algorithm. If the separation between two dark matter particles is less than 20%
of the average separation (the linking length b = 0.2), they are placed in the
same group. Because the particles all have the same mass, a fixed value of b will
correspond to a fixed overdensity at the boundary of the group of ρ/hρi ≈ 60
(e.g. Frenk et al., 1988). Assuming a radial density profile ρ(r ) ∝ r −2 , corresponding to a flat rotation curve, such a group has an average overdensity of
hρhalo i/hρi ≈ 180 (e.g. Lacey & Cole, 1994), close to the value for a virialized object predicted by the top-hat spherical collapse model (e.g. Padmanabhan, 2002).
The minimum number of dark matter particles in a FoF group is set to 25. Many
of the smallest groups will not be gravitationally bound. Baryonic particles are
placed in a group if their nearest dark matter neighbour is part of the group.
Problems arise because unbound particles can be attached to a group, physically distinct groups can be linked by a small (random) particle bridge, and because substructure within a FoF halo is not identified. We use subfind (Springel
et al., 2001; Dolag et al., 2009) on the FoF output to find the gravitationally bound
particles and to identify subhaloes. The properties of gas that is being accreted
are expected to depend on the properties of the parent (or main) halo in which
2
Exceptions are gas that reached high densities before reionization, which happens at z = 9 in
our simulations, and gas with very high metallicities.
25
Gas accretion onto galaxies and haloes
the subhaloes are embedded. We therefore only look at accretion onto these
main haloes and exclude gas accretion by satellites.
Another way of defining haloes is to use a spherical overdensity criterion.
The radius Rvir , centred on the most bound particle of a FoF halo, is found within
which the average density agrees with the prediction of the top-hat spherical
collapse model in a ΛCDM cosmology (Bryan & Norman, 1998). All the particles
within Rvir are then included in the halo.
We chose to use only main haloes identified by subfind, but we have checked
that our results do not change significantly when using FoF groups or spherical
overdensities instead.
Except for Figures 2.2, 2.9, and 2.15, we include only main haloes containing
more than 250 dark matter particles in our analysis of halo accretion. This corresponds to a minimum total halo mass of Mhalo ≈ 1011.2 M⊙ in the 100 h−1 Mpc
box, 1010.3 M⊙ in the 50 h−1 Mpc box, and 109.4 M⊙ in the 25 h−1 Mpc box. For
these limits our mass functions agree very well with the Sheth & Tormen (1999)
fit.
For each resolved halo, we identify the ISM of the central galaxy with the star
forming (i.e. nH > 0.1 cm−3 ) gas particles in the main halo which are inside 15%
of the virial radius (Sales et al., 2010). We use 15% of the virial radius to exclude
small star forming substructures in the outer halo, which are not identified by
subfind. Gas accretion onto satellite galaxies is excluded.
Because the galaxy is much smaller than its parent halo, it is not as well
resolved. When investigating accretion onto galaxies (as opposed to haloes), we
therefore impose a 1000 dark matter particle limit, corresponding to a minimum
total halo mass of Mhalo ≈ 1011.8 M⊙ in the 100 h−1 Mpc box, 1010.9 M⊙ in
the 50 h−1 Mpc box, and 1010.0 M⊙ in the 25 h−1 Mpc box. The exceptions are
Figure 2.2 and 2.15, which show accretion rates and hot fractions down to 1 dex
below this limit. See Section 2.5 for more discussion on convergence.
2.4.2 Selecting gas particles accreted onto haloes
We select gas particles accreted onto haloes as follows. For each halo at z = z2
(which we will also refer to as ‘the descendant’) we identify its progenitor at the
previous output redshift z1 > z2 . We determine which halo contains most of the
descendant’s 25 most bound dark matter particles and refer to this halo as ‘the
progenitor’. If the fraction of the descendant’s 25 most bound particles that was
not in any halo at z1 is greater than the fraction that was part of the progenitor,
then we discard the halo from our analysis, which rarely happens above our
resolution threshold. If two or more haloes contain the same number of those
25 particles, we select the one that contains the dark matter particle that is most
bound to the descendant.
We identify those particles that are in the descendant, but not in its progenitor
as having been accreted at z2 ≤ z < z1 . The accreted particles have to be gaseous
at z1 , i.e. before they were accreted, but can be either gaseous or stellar at redshift
26
Total gas accretion rates
z2 . The accreted gas can have densities exceeding the star formation threshold,
in which case it cannot obtain a higher maximum past temperature. Gas can be
accreted multiple times.
To distinguish mergers from smooth accretion, we exclude accreted particles
that reside in (sub)haloes above some maximum mass at redshift z1 . We would
like to have a criterion that is not directly dependent on resolution, so that the
same objects are included in runs with different particle numbers if the simulations are converged with respect to resolution. We therefore set this maximum
allowed halo mass to 10% of the descendant’s (main halo) mass. Thus, smooth
accretion excludes mergers with a mass ratio greater than 1:10. We experimented
with different thresholds and the results are insensitive to this choice.
2.4.3 Selecting gas particles accreted onto galaxies
We consider particles that are part of the ISM or stellar at z2 , and that were
gaseous but not part of the ISM at z1 , to have been accreted onto a galaxy at
z2 ≤ z < z1 . Gas can be accreted multiple times. Accretion onto the ISM and
accretion onto a galaxy are the same in this study and these terms are used
interchangeably.
In this way, accretion through galaxy mergers is automatically excluded, because the gas that is part of the ISM of another galaxy at z1 is excluded. We can
allow for mergers by identifying those particles that are in the galaxy at z2 , but
were not in the progenitor galaxy at z1 .
2.5 Total gas accretion rates
For brevity, accretion between, for example, z = 2.25 and z = 2 will be referred
to as accretion just before z = 2.
The average total gas accretion rate of a halo depends on its mass. Figure 2.2
shows the average specific accretion rates Ωm Ṁgas /Ωb Mhalo , where Ωm and
Ωb are the matter and baryon density parameters, respectively, as a function of
halo mass for z = 2 (top panel) and z = 0 (bottom panel) for haloes containing at
least 100 dark matter particles for various simulations using the reference model.
Thick curves show the specific accretion rates onto haloes. We have divided the
gas accretion rate by the total halo mass and baryon fraction Ωb /Ωm , so that the
normalization gives an estimate of the time it would take a halo to grow to its
current mass with the current accretion rate.
The thin curves in Figure 2.2 show specific smooth accretion rates onto galaxies against halo mass. While the inverse of the specific halo accretion rate equals
the time it takes to grow the halo at its current accretion rate, the same is not
true for the specific galaxy accretion rate, because we divide by the halo mass
rather than by the galaxy mass. This definition allows us, however, to directly
compare the two accretion rates.
27
Gas accretion onto galaxies and haloes
Figure 2.2: Specific gas smooth accretion rates onto haloes (higher, thick curves) and
central galaxies (lower, thin curves) against total halo mass at z = 2 (top panel) and z = 0
(bottom panel). The normalization for halo accretion gives an estimate of the time it
would take a halo to grow to its current mass at the current accretion rate. The same is
not true for galaxy accretion, since we use the same normalization as for halo accretion.
Both panels show simulations spanning a factor 64 in mass resolution. Each mass bin
contains at least 10 haloes. Big (small) arrows correspond to the adopted resolution limit
for accretion onto haloes (galaxies) for L025N512 (red), L050N512 (blue), L100N512 (black)
and L100N256 (green). The specific halo accretion rate is converged and increases slightly
with halo mass. The specific galaxy accretion rate is not fully converged at z = 2, but
the convergence is better at z = 0. The galaxy accretion rate increases with halo mass
for Mhalo < 1012 M⊙ and decreases with halo mass for higher halo masses. It is much
smaller than the halo accretion rate.
28
Total gas accretion rates
Comparing the three thick curves in each panel, we see that the specific halo
accretion rate is converged with the numerical resolution. It increases with halo
mass, especially at low halo masses. The specific galaxy accretion rate (thin
curves) is not fully converged at z = 2, but the convergence improves at z = 0
(compare the two highest resolutions, dotted and solid curve, at the high mass
end). Below Mhalo < 1012 M⊙ the specific galaxy accretion rate increases more
steeply with halo mass than the specific halo accretion rate. Above this halo
mass, the specific galaxy accretion rate decreases steeply, whereas the rate keeps
increasing for haloes. The accretion rate onto galaxies is always much lower than
the halo accretion rate and this difference is larger at z = 0. Hence, only a small
fraction of the gas accreted onto haloes ends up in galaxies and the efficiency of
galaxy formation is highest in haloes with Mhalo ≈ 1012 M⊙ .
The dynamic range covered by these simulations is very large, because we
use different box sizes. The resolution increases with decreasing box size. We
have performed box size convergence tests (at fixed resolution), but do not show
them as the convergence with box size is excellent for all halo masses. Increasing
the resolution shows that the halo accretion rates are not fully converged around
the 100 particle resolution threshold adopted in Figure 2.2. In this regime, halo
mergers cannot always be identified. In the rest of this paper, we therefore set
the minimum halo mass for accretion onto haloes to correspond to 250 dark
matter particles, as indicated by the big arrows.
The galaxy accretion rates diverge at the low-mass end. This is expected,
because haloes with 100 dark matter particles will have very few star forming
gas particles and because 15% of the virial radius is close to the spatial resolution
limit. We will therefore only include the haloes where 15% of the virial radius is
larger than 5 times the softening length and therefore consisting of at least 1000
dark matter particles, as indicated by the small arrows. The galaxy accretion
rates at the high-mass end are not completely converged at z = 2. The accretion
rate decreases by up to a factor of two if the mass resolution is increased by a
factor of 64. With increasing resolution, more gas reaches higher densities. If
this gas becomes star forming before accreting onto the central galaxy, it is not
included in the smooth accretion rate. If we instead include galaxy mergers (not
shown), which increases the accretion rate for high-mass galaxies slightly, then
the results are in fact fully converged for the 50 and 25 h−1 Mpc box.
The bottom panel shows that the convergence is better at z = 0.
Although the results of these convergence tests are encouraging, we caution
the reader that we cannot exclude the possibility that higher resolution simulations would show larger differences. For example, Dalla Vecchia & Schaye (2008)
found that higher resolution is required to obtained converged predictions for
the galactic winds. On the other hand, it is not clear the resolution requirements
inferred by Dalla Vecchia & Schaye (2008) carry over to the present simulations,
because they used idealized, isolated disc galaxies that started with thinner stellar disks than are formed in our simulations and their gas disks were initially
embedded in a vacuum.
29
Gas accretion onto galaxies and haloes
2.5.1 Accretion onto haloes
Figure 2.3: Specific gas accretion rates onto haloes for redshifts z = 5 (black, top curve)
to z = 0 (green, bottom curve) against the total halo mass at the redshift of accretion for
the simulation REF_L050N512. We added the highest mass bins from REF_L100N512 to
extend the dynamic range. The solid curves are for smooth accretion, whereas the dotted
curves show the specific accretion rate due to mergers with mass ratios greater than
1:10. Each mass bin contains at least 10 haloes. Dashed lines show fits to dark matter
accretion rates (Dekel et al., 2009b; Neistein et al., 2006). The specific smooth accretion
rate decreases with redshift and increases only mildly with halo mass. Except for clusters
(Mhalo ≥ 1014 M⊙ ) at z = 0, halo growth is dominated by smooth accretion.
Figure 2.3 shows the average specific gas accretion rate onto haloes as a function of halo mass for z = 5 (black, top curve) to z = 0 (green, bottom curve)
for run L050N512. We also show the high-mass bins from L100N512, which are
not sampled by L050N512, because of its smaller volume. The solid curves show
the rates for smooth accretion, the dotted curves for mergers with mass ratios
greater than 1:10. The specific smooth accretion rate decreases with decreasing
redshift and increases slowly with halo mass. The accretion rate, as opposed to
the specific accretion rate, is thus roughly proportional to the halo mass.
Our accretion rates are generally in quantitative agreement with other simulations (Ocvirk et al., 2008; Kereš et al., 2005). They also agree well with a fit
to an analytic prediction for dark matter accretion rates based on the extended
30
Total gas accretion rates
Press-Schechter formalism given by Dekel et al. (2009b) and derived by Neistein et al. (2006). This fit is shown by the dashed lines. For low-mass haloes
(Mhalo ≤ 1012 M⊙ ) at 0 ≤ z ≤ 2 the accretion rate is lower than predicted. This
suppression is due to SN winds, as we will discuss below. Without SN feedback,
the gas accretion rates follow the dark matter accretion rates also for low-mass
haloes at low redshift.
The specific gas accretion rate through mergers is much lower than the specific smooth accretion rate, except for high-mass haloes (Mhalo & 1014 M⊙ ) at
z = 0. The dominance of smooth accretion is consistent with recent work on
dark matter accretion, which has shown that mergers with mass ratios greater
than 1:10 contribute less than 20-30% to the total halo accretion and at least 1040% of the accretion is genuinely diffuse (Fakhouri & Ma, 2010; Angulo & White,
2010; Genel et al., 2010; Wang et al., 2011).
The power of the OWLS project lies in the fact that many simulations have
been performed with different prescriptions for physical processes such as cooling and feedback. They have been described in Section 2.2. Figure 2.4 shows
how the different physical processes affect the specific halo accretion rates at
z = 2 (black curves) and at z = 0 (red curves). At z = 2, we include results from
both the L025N512 and L100N512 versions of each model in order to extend the
range of halo masses. These simulations have different box sizes and differ by a
factor of 64 in mass resolution. For some models the run with lower resolution
and larger box size, which is used for the high halo masses, is not fully converged, resulting in discontinuities. Only the L100N512 simulations were run
down to z = 0.
The first thing to notice is the fact that the halo smooth accretion rates are
very similar for all models. For the simulations with strong winds (DBLIMFCONTSFV1618) or AGN feedback (AGN) the rates are smaller than those for the
reference model by up to 0.3-0.4 dex. The other models differ even less, except
for the run without SN feedback (NOSN_NOZCOOL) which predicts 0.6 dex
higher accretion rates at the lowest halo masses. The differences are similar at
the two redshifts.
The left panel of Figure 2.4 shows the effect of excluding metal-line cooling
and SN feedback. The simulations without SN feedback (NOSN, which is only
available for L100N512 at z = 2, and NOSN_NOZCOOL) have nearly completely
flat specific accretion curves. As is the case for dark matter accretion rates, there
is only a small increase with halo mass (see Figure 2.3). Including SN feedback
with vwind = 600 km/s (REF and NOZCOOL) reduces the accretion rates for
low-mass haloes by up to 0.6 dex (at Mhalo = 1010 M⊙ ). It is possible that
the true accretion rates are the same, but some gas is pushed out of the halo
before a snapshot is made and is therefore not counted as having accreted. A
more likely possibility is, however, that galactic winds prevented the gas around
low-mass haloes from accreting. Hence, more gas remains available for accretion
onto massive galaxies which explains why those have somewhat higher accretion
rates if SN feedback is included. Excluding metal-line cooling has no effect on
31
32
Gas accretion onto galaxies and haloes
Figure 2.4: Specific gas smooth accretion rates onto haloes against total halo mass at z = 2 (top, black curves) and at z = 0 (bottom, red
curves) for different simulations. The normalization gives an estimate of the time it would take a halo to grow to its current mass at the
current accretion rate. The curves at low (high) halo masses are for simulations in a 25 (100) h−1 Mpc box using 2×5123 particles. The
solid curves use a simulation with the reference parameters (REF) and are repeated in all panels. The different simulations are described in
Section 2.2.1. Each mass bin contains at least 10 haloes. Each halo contains at least 1000 dark matter particles for the z = 2 curves. This is
higher than our resolution limit for accretion onto haloes, but it removes the overlap between simulations of different resolution. Each halo
at z = 0 contains at least 250 dark matter particles. Left panel: Turning off feedback from SNe results in up to 0.6 dex higher accretion rates,
for low-mass haloes. Middle panel: Increasing the wind velocity causes the specific accretion rate to decrease by up to 0.2 dex, over the mass
range where the feedback is efficient. Right panel: Efficient feedback from a top-heavy IMF or from AGN even reduces the accretion rates
for the highest halo masses, although the differences between these models are still small, at most 0.3 dex.
33
Total gas accretion rates
Figure 2.5: Specific gas smooth accretion rates onto galaxies against halo mass for different simulations. The curves at low (high) halo
masses are derived from simulations in a 25 (100) h−1 Mpc box using 2 × 5123 particles. The line styles, colours, and normalization are
identical to those used in Figure 2.4. The normalization does not give an estimate for the time it would take the galaxy to grow, because
we divide by the halo mass, not the galaxy mass. Each mass bin contains at least 10 haloes. In the absence of SN feedback the specific
accretion rate onto galaxies declines with halo mass, indicating that gas accretes less efficiently onto galaxies in higher-mass haloes. Leaving
out metal-line cooling decreases the accretion rate most strongly for Mhalo ∼ 1012 M⊙ . Efficient SN feedback reduces the accretion rates
substantially for galaxies in low-mass haloes, resulting in a peak in the specific gas accretion rate at Mhalo ∼ 1012 M⊙ . The effects of
feedback and metal-line cooling are much stronger for accretion onto galaxies than for accretion onto haloes and can result in differences
of an order of magnitude.
Gas accretion onto galaxies and haloes
the halo accretion rates. This indicates that halo accretion rates are not set by
cooling.
SN feedback models with higher wind velocities, but using the same amount
of energy per unit stellar mass, plotted in the middle panel of Figure 2.4, give
lower accretion rates over the range of masses for which the winds are able
to eject gas. Higher wind velocities keep the feedback efficient up to higher
halo masses (Dalla Vecchia & Schaye, 2008; Schaye et al., 2010, Haas et al. in
preparation).
The right panel shows the results for models that use more energy for feedback than the reference model. A top-heavy IMF in starbursts (DBLIMFCONTSFV1618) reduces the accretion rates by up to 0.3 dex. AGN feedback (AGN)
reduces the accretion rates by up to 0.4 dex for Mhalo & 1011 M⊙ .
In summary, metal-line cooling does not significantly change the halo accretion rates, but very efficient feedback from stars and/or AGN can suppress the
accretion rates by factors of a few.
2.5.2 Accretion onto galaxies
The three lower, thin curves in the top and bottom panels of Figure 2.2 show
specific smooth accretion rates onto galaxies (i.e. the ISM) against total halo
mass at z = 2 and 0, respectively. The specific accretion rate peaks at Mhalo ≈
1012 M⊙ . At z = 0 the peak occurs at slightly higher halo masses. For both
redshifts the peak falls at Tvir ∼ 106 K, close to the bump in the cooling curve
due to iron (Wiersma et al., 2009a). At higher halo masses, and thus higher
virial temperatures, cooling times become long, preventing shocked gas from
condensing onto galaxies. At lower halo masses, feedback prevents gas from
entering the ISM. For Mhalo ≈ 1012 M⊙ the galaxy accretion rate is about a
factor of two lower than the halo accretion rate, but the difference is much larger
for other halo masses.
Figure 2.5 shows the same as Figure 2.4, but for accretion onto galaxies. For
models WDENS, DBLIMFCONTSFV1618, and AGN the convergence is poor for
the low-resolution runs, as can be seen from the discontinuities. Because the
feedback in these models depends on the gas density, they are sensitive to the
resolution (Schaye et al., 2010). Note, however, that the difference in mass resolution is enormous, a factor of 64, and that the high-resolution model may thus
be much closer to convergence than the comparison suggests. Nevertheless, we
caution the reader that the accretion rates may be different for higher resolution
simulations.
The variations in the feedback prescriptions result in similar differences as
for accretion onto haloes, although they are generally much larger. Excluding
metal-line cooling gives slightly different results than halo accretion.
For Mhalo . 1013 M⊙ less gas reaches the star formation threshold (i.e. accretes onto galaxies) without metal-line cooling (NOZCOOL), particularly for
Mhalo ∼ 1012 M⊙ at z = 2 and Mhalo ∼ 1012.4 M⊙ at z = 0. The reduction is less
34
Accretion onto haloes
Figure 2.6: PDF of the lookback time at which the maximum past temperature (evaluated
at z = 0) was reached for gas accreted just before z = 5, 4, 3, 2, 1, and 0 in black, blue, purple, red, orange, and green, respectively, combining REF_L050N512 and REF_L100N512.
The top x-axis indicates the corresponding redshift. The maximum temperature reached
by a gas particle is associated with the accretion event, as evidenced by the fact that the
PDFs peak at the accretion redshift.
than 0.4 dex at z = 2, but a full order of magnitude at z = 0. For Mhalo & 1013 M⊙
more gas accretes onto galaxies at z = 0 if metal-line cooling is excluded. Because there is less cooling, less gas accretes onto low-mass galaxies and at high
redshift. Therefore, there is more gas left to accrete onto high mass galaxies at
low redshift.
For simulations without SN feedback the specific galaxy accretion rate peaks
at Mhalo ∼ 1010 M⊙ , which is two orders of magnitude lower than when SN
feedback is included. Without SN feedback, the galaxy accretion rates are a bit
lower for high halo masses. This could be because much of the gas that accreted
onto a halo at higher redshift has in that case already been accreted onto the
galaxy’s progenitors. Alternatively, the galaxy accretion rates could be higher
in the presence of SN feedback due to the increased importance of recycling. If
winds are able to blow gas out of the galaxy, but not out of the halo, as may be
the case for high-mass haloes, then the same gas elements may be accreted onto
the galaxy more than once (Oppenheimer et al., 2010). For Mhalo . 1011 M⊙ at
z = 2 and Mhalo . 1012 M⊙ at z = 0, on the other hand, the accretion rates are
higher, because more gas accretes onto the halo and because there is no feedback
to stop halo gas from accreting onto the galaxy.
Galaxy accretion rates are thus much more sensitive to metal-line cooling
and to SN and AGN feedback than halo accretion rates. The difference between
models can be as large as 1 dex. Feedback processes determine the halo mass
for which galaxy formation is most efficient.
35
Gas accretion onto galaxies and haloes
2.6 Hot and cold accretion onto haloes
Figure 2.6 demonstrates that most of the gas reaches its maximum temperature
around the time it is accreted onto a halo. Here the probability density function
(PDF) of the lookback time at which the gas reaches its maximum temperature,
evaluated at z = 0, is shown for baryonic particles that were accreted as gas
particles onto haloes at different redshifts. The vertical dotted lines show the
times at which the gas was accreted onto a halo. The fact that the PDFs peak
around the accretion redshifts shows that the maximum temperature is usually
related to the accretion event.
Some of the gas reaches its maximum temperature significantly later than
the redshift at which it was accreted. When two galaxies merge, gas can shock
to higher temperatures. Gas can also be affected by winds resulting from SN
feedback. Because we are primarily interested in gas accretion, we will from
now on evaluate the maximum past temperature of the gas at the first available
output redshift after accretion.
Gas can be accreted cold onto haloes with well developed virial shocks if
its density is sufficiently high, as can for example be the case in filaments. To
illustrate this we show in the left two columns of Figure 2.7 the gas overdensity
and the temperature in a cubic region of 1 h−1 Mpc (comoving) centred on
three example haloes at z = 2 taken from the full sample of 12768 haloes in
the high-resolution reference simulation (REF_L025N512). The haloes have total
masses Mhalo ≈ 1012.5, 1012, and 1011.5 M⊙ (from top to bottom), corresponding
to comoving virial radii of 379, 264, and 170 h−1 kpc, respectively, shown as white
circles in the temperature plots. Their virial temperatures are Tvir ≈ 106.3, 106.0,
and 105.7 K, respectively. The colour scales are the same for all three haloes.
We can immediately see that the average temperature increases with halo mass.
Hot gas, heated either by accretion shocks or SN feedback, extends to several
virial radii. Without SN feedback, the hot gas would trace the virial radius more
accurately for the two lowest mass haloes, as can be seen for the 1012 M⊙ halo
in Figure 2.13.
Most of the gas around the 1012.5 M⊙ halo has been heated to temperatures
above 106 K and the halo will get most of its gas through hot accretion. Cold
streams do penetrate the virial radius, but they seem to break up as they get
close to the centre. Even so, a number of small, dense clumps do survive and
remain relatively cold. Such cold clumps originating from filamentary gas were
also studied by Sommer-Larsen (2006) and Kereš & Hernquist (2009).
The 1012 M⊙ halo is located at the intersection of three filaments. The gas in
the filaments is denser and colder than in the surrounding medium. The cold
streams become narrower as they get closer to the centre. They are compressed
by the high pressure, shock-heated gas around them (Kereš et al., 2009a). Cold
streams bring gas directly and efficiently to the inner halo.
The 1011.5 M⊙ halo is embedded in a single filament. It has the lowest virial
temperature, so the hot gas is much colder than in the highest mass halo. Cold
36
Accretion onto haloes
37
Figure 2.7: Gas overdensity (first and third columns) and temperature (second and fourth columns) in a cubic region of 1 h−1 comoving
Mpc (first and second columns) and 250 h−1 comoving kpc (third and fourth columns) centred on haloes of Mhalo ≈ 1012.5 , 1012 , and
1011.5 M⊙ (from top to bottom) at z = 2 for simulation REF_L025N512. The white circles indicate the virial radii of the haloes, as computed
using the overdensity criterion from Bryan & Norman (1998). Cold, dense streams bring gas to the centre. The temperature of the hot gas
increases with halo mass. Hot accretion dominates for high-mass haloes, cold accretion for low-mass haloes. The galaxies in the centres of
these haloes are discs, surrounded by cold gas. This cold gas is in clumps (Mhalo ≈ 1012.5 ), disrupted streams (Mhalo ≈ 1012 ), or smooth
streams (Mhalo ≈ 1011.5 ).
Gas accretion onto galaxies and haloes
streams are most prominent and broadest in this halo. This halo will get most
of its gas through cold accretion.
The right two columns of Figure 2.7 shows zooms of the central 250 h−1 kpc
(comoving). The 1012.5 M⊙ halo contains a large number of cold clumps. The
galaxies in the 1012 and 1011.5 M⊙ haloes are being fed by cold, dense streams.
All of these galaxies have formed discs. The galaxy in the 1012.5 M⊙ halo has
clear spiral arms and a bar-like structure. The galaxy in the 1012 M⊙ halo has a
very small disc with cold gas around it, which looks more disturbed. The galaxy
in the 1011.5 M⊙ halo is fairly large with a lot of cold material accreting onto it.
The maximum temperature reached by shock-heated gas is expected to scale
with the virial temperature of the halo. However, we do not expect the ratio of
Tmax and Tvir to be exactly unity, because of departures from spherical symmetry, adiabatic compression after virialization, and the factor of a few difference
between different definitions of Tvir .
Dividing Tmax by Tvir would take out the redshift and halo mass dependence
of the virial temperature. We calculate the virial temperature as follows
G2 H02 Ωm 18π 2
54
!1/3
µmH 2/3
Mhalo (1 + z),
kB
2/3
µ M
halo
≈ 3.0 × 105 K
(1 + z ) ,
0.59
1012 M⊙
Tvir =
(2.1)
where G is the gravitational constant, H0 the Hubble constant, µ the mean molecular weight, mH the mass of a hydrogen atom, and kB Boltzmann’s constant3 .
2.6.1 Dependence on halo mass
Figure 2.8 illustrates the dependence of the maximum past temperature on halo
mass. Shown are scatter plots of the maximum past temperature reached by gas
accreting onto haloes just before z = 2 (top panel) and z = 0 (bottom panel)
against the mass of the halo at these redshifts. The logarithm of the accreted gas
mass per (h−1 Mpc)3 in a pixel is used for colour coding. The virial temperature
is indicated by the black line.
A clear bimodality is visible for accretion at z = 2, with a minimum at Tmax ≈
105.5 K, indicated by the dotted line. This minimum coincides with a maximum
at T ≈ 105−5.5 K in the cooling function (e.g. Wiersma et al., 2009a). For gas
accreted in the hot mode, which includes most of the gas accreting onto highmass haloes, the maximum past temperature is within a factor ≈ 3 of the virial
temperature and displays the same dependence on mass. The temperature of
the gas accreted in the cold mode is independent of halo mass.
At z = 0, the lowest Tmax values are higher than at z = 2. This shift occurs
because the density, and hence the cooling rate, increases with redshift. At fixed
3
This definition is a factor 2/3 lower than the virial temperature used by some other authors (e.g.
Barkana & Loeb, 2001).
38
Accretion onto haloes
Figure 2.8: Maximum past temperature at z = 2 (top panel) and z = 0 (bottom
panel) against total halo mass of the gas smoothly accreted onto haloes for models
REF_L025N512 and REF_L100N512 (top panel) and REF_L050N512 and REF_L100N512
(bottom panel). The logarithm of the total gas mass per (h−1 Mpc)3 in a pixel is used for
colour coding. The solid line indicates the virial temperature of the halo. The dotted
line shows Tmax = 105.5 K, where there is a minimum in the mass per pixel at z = 2.
The temperature of gas that is accreted hot scales with the virial temperature. For lowmass haloes, the temperatures of hot and cold accreted gas are comparable. Hot mode
accretion is more important for higher halo masses and lower redshifts.
39
Gas accretion onto galaxies and haloes
halo mass, the highest Tmax values are lower at z = 0, because the virial temperature of a halo at fixed mass decreases with decreasing redshift, as can be seen
from Equation 2.1. For haloes with virial temperatures Tvir . 105 K it becomes
impossible to tell from this plot whether or not the gas has gone through a
virial shock because the virial temperature is similar to the maximum past temperature reached by gas accreting in the cold mode. This makes it difficult to
separate hot and cold accretion for low-mass haloes at low redshift. As we will
show below, separating hot and cold accretion using a fixed value of Tmax /Tvir is
more difficult than using a fixed value of Tmax , because the minimum in the distribution is less pronounced and because it evolves (Kereš et al., 2005). In most
of this paper, we will therefore use a fixed maximum temperature threshold of
Tmax = 105.5 K.
The relative importance of hot accretion increases with halo mass (e.g. Ocvirk
et al., 2008). The top panel of Figure 2.9 shows the fraction of gas smoothly accreting onto haloes in the hot mode, just before z = 2 for simulations REF_L100N512, REF_L050N512, and REF_L025N512. The bottom panel shows this for
accretion just before z = 0 for simulations REF_L100N256, REF_L100N512, and
REF_L050N512. A particle accreted just before z = 2 is considered to have been
accreted hot if Tmax (z = 2) ≥ 105.5 K. The error bars show the 1σ halo to halo
scatter.
We have checked, but do not show, that the results are fully converged with
box size for fixed resolution. In each panel the three simulations span a factor 64 in mass resolution. The hot fraction decreases slightly with increasing
resolution, but the differences are very small. This slight decrease could arise
because higher density regions inside clumps and filaments are better sampled
with increasing resolution, leading to higher cooling rates in cold gas.
Hot mode accretion becomes indeed more important for higher mass systems. This is expected because only sufficiently massive haloes are capable of
providing pressure support for a stable virial shock (e.g. Birnboim & Dekel,
2003). The median hot fraction (not shown) behaves similarly to the mean, although it is smaller for low-mass haloes.
There is no sharp transition from cold to hot accretion. At z = 2, the hot
mode accretion increases from 20% to 80% when halo mass increases from 1011
to 1013 M⊙ . The properties of galaxies are therefore not expected to change
suddenly at a particular halo mass as has been assumed in some semi-analytic
models (e.g. Cattaneo et al., 2008; Croton & Farrar, 2008).
In Figure 2.10 we compare this result to that obtained when we define hot
mode accretion using a maximum temperature threshold that depends on the
virial temperature. Using Tmax = Tvir shows that, even for the most massive
haloes, only about 40% of the gas reaches a temperature higher than Tvir at
z = 2. At z = 0 about 70% of the gas accreting onto massive haloes reaches
Tvir . Because gas going through a virial shock may only heat to a factor of a
few below Tvir , this definition does not discriminate well between hot and cold
accretion. If we decrease the critical Tmax /Tvir , then the hot fraction gets close to
40
Accretion onto haloes
Figure 2.9: Average fraction of the gas, smoothly accreted onto haloes between z = 2.25
and z = 2 (top panel) or between z = 0.125 and z = 0 (bottom panel), that has maximum
past temperature Tmax ≥ 105.5 K. The different curves are from simulations of the same
reference model but spanning a factor of 64 in mass resolution for each panel. The
error bars show the 1σ halo to halo scatter for simulation REF_L100N512. Each mass
bin contains at least 10 haloes. Arrows correspond to the adopted resolution limit for
accretion onto haloes. Cold mode accretion dominates for Mhalo < 1012 M⊙ , but the
transition is very gradual.
41
Gas accretion onto galaxies and haloes
Figure 2.10: The average fraction of the gas, accreted onto haloes just before z = 2 (top
panel) or z = 0 (bottom panel), that has maximum past temperature above a certain temperature threshold. The results are for simulation REF_L050N512 with the highest mass
haloes from REF_L100N512. The thresholds for the blue, purple, red, orange, and green
curves (bottom to top) are Tmax /Tvir = 1, 10−0.25 , 10−0.5 , 10−0.75 , and 0.1, respectively.
The black curve shows the average fraction with Tmax ≥ 105.5 K and is identical to the
black curve in Figure 2.9. Each mass bin contains at least 10 haloes. The hot fraction
depends strongly on the choice we make for the threshold, particularly for lower-mass
haloes.
42
Accretion onto haloes
our previously determined value for the high-mass haloes. For low-mass haloes,
however, this results in a sharp upturn of f hot as it must approach unity if the
threshold maximum temperature falls much below 105 K.
The hot fraction therefore depends very much on the definition of the temperature threshold. Depending on the definition, gas accreted cold may in fact
have experienced a virial shock. For haloes with Tvir ≫ 105 K, however, we can
safely separate hot and cold accretion and trust the result that a larger fraction
of the gas goes through a virial shock for higher-mass haloes.
In the rest of this paper, we will define hot mode accretion using a fixed
maximum past temperature threshold of Tmax = 105.5 K.
2.6.2 Smooth accretion versus mergers
So far we have only looked at ‘smooth’ accretion, i.e. we excluded mergers with
a mass ratio greater than 1:10. We could have chosen not to exclude mergers,
because the gas reservoir of a halo can also grow through mergers. Even though
mergers with ratios greater than 1:10 contribute only ∼ 10% of the total gas
accretion for Mhalo < 1014 M⊙ (see Figure 2.3), it is interesting to investigate the
differences for hot and cold accretion.
Figure 2.11 compares the hot fraction of smooth accretion (solid curves) and
all accretion (dotted curves), which takes into account both smooth accretion
and mergers. The differences are negligibly small. Indeed, the hot fraction for
gas accreted in mergers (not shown) is nearly the same as that for gas accreted
smoothly.
2.6.3 Dependence on redshift
The fraction of gas that is accreted onto haloes in the hot mode also depends
on redshift, as can be seen from Figure 2.11 where the hot fraction is plotted
against halo mass for different redshifts. For a given halo mass, the hot fraction
increases with time between z = 5 and z = 1. Below z = 1 the rate of evolution
slows down, presumably because structure formation slows down, and the sign
of the evolution may reverse for low-mass haloes due to the decrease of Tvir with
time.
At high redshift the proper density of the Universe is higher and the cooling time is therefore shorter (tcool ∝ ρ−1 ∝ (1 + z)−3 ). The Hubble time is also
shorter, but its dependence on redshift is weaker (tH ∝ H −1 ∝ (Ωm (1 + z)3 +
ΩΛ )−1/2, so tH ∝ (1 + z)−3/2 at high redshift and tH is independent of redshift
at low redshift). The dynamical time at fixed overdensity has the same redshift
dependence as tH . Hence, cooling is more efficient at higher redshifts (e.g. Birnboim & Dekel, 2003) and the hot fraction will thus be lower for a fixed virial
temperature. For a fixed halo mass, the evolution in the hot fraction is smaller,
because Tvir is higher at higher redshifts. The environment can also play a role.
At high redshift (z > 2), 1012 M⊙ haloes are rare and they tend to reside in highly
overdense regions at the intersections of the filaments that make up the cosmic
43
Gas accretion onto galaxies and haloes
Figure 2.11: Hot fraction for accretion onto haloes just before z = 5, 4, 3, 2, 1, and 0
against halo mass at the same redshift. The curves at low halo masses are obtained from
simulation REF_L050N512. At the high-mass end we have added curves for simulation
REF_L100N512 to extend the dynamic range. Gas is considered to have been accreted hot
if it has Tmax ≥ 105.5 . The dotted curves show the hot fraction including both smooth
accretion and mergers. Each mass bin contains at least 10 haloes. For a fixed halo mass,
hot accretion tends to be more important at lower redshift.
web. Haloes of the same mass are, however, more common at low redshift and
form in single filaments, with more average densities. Hence, cold streams may
be able to feed massive haloes at high redshift, whereas this may not be possible
at low redshift (Kereš et al., 2005; Dekel & Birnboim, 2006).
The specific accretion rate of gas onto haloes increases mildly with halo mass
for 0 < z < 5, see Figure 2.3. Splitting this into hot and cold specific accretion
rates reveals a steep increase with halo mass for hot accretion, as shown in
Figure 2.12. The specific cold accretion rate decreases with halo mass for Mhalo &
1012 M⊙ .
From observations we know that the specific star formation rate, i.e. the SFR
divided by the stellar mass, declines with both time and stellar mass (e.g. Brinchmann et al., 2004; Bauer et al., 2005; Feulner et al., 2005; Chen et al., 2009). The
decline in the specific SFR may be related to the decline in the specific cold accretion rate. However, the decline is much stronger in the observations and present
for the entire stellar mass range probed.
2.6.4 Effects of physical processes
As discussed in Section 2.5, feedback from SNe and AGN decreases the halo
accretion rate, while metal-line cooling has very little effect. In this Section we
will discuss the influence of cooling and feedback on the hot and cold accretion
fractions at z = 2 and z = 0.
44
Accretion onto haloes
Figure 2.12: Specific smooth accretion rates of gas onto haloes against total halo mass just
before redshifts z = 5 (black, top curve) to z = 0 (green, bottom curve) for the simulation
REF_L050N512, with the highest mass bins from REF_L100N512. The solid and dashed
curves are the rates for hot (Tmax ≥ 105.5 K) and cold (Tmax < 105.5 K) accretion, respectively. Each mass bin contains at least 10 haloes. The specific hot accretion rate increases
with halo mass, whereas the specific cold accretion rate decreases for Mhalo > 1012 M⊙ .
To investigate the influence of galactic winds driven by SN feedback, we
ran simulations with no SN feedback at all and with more effective galactic
wind models, that can eject gas from more massive haloes. In other simulations,
cooling rates are computed assuming primordial abundances. We have also
included AGN feedback in one simulation.
To illustrate the effect these different processes have on an individual halo,
Figure 2.13 shows the same 1012 M⊙ halo as was shown in the middle panel
of Figure 2.7 for five different simulations. From top to bottom are shown: no
SN feedback and no metal-line cooling (NOSN_NOZCOOL); no metal-line cooling (NOZCOOL); reference SN feedback (REF); density dependent SN feedback
(WDENS); reference SN feedback and AGN feedback (AGN). The colour coding
shows gas overdensity in the left panels and temperature in the right panels. The
stronger the feedback (top row: weakest feedback, bottom row: strongest feedback) the more fragmented the streams become. All models predict the presence
of cold, dense gas throughout much of the halo. The diffuse halo gas is heated
to higher temperatures in simulations with strong SN or AGN feedback than
in the reference simulation. The radius out to which gas is heated increases for
strong feedback models.
Figure 2.14 shows how the fraction of the gas that accretes smoothly onto
haloes just before z = 2 (top panels) and z = 0 (bottom panels) in the hot mode,
i.e. with Tmax ≥ 105.5 K, depends on the physical processes that are modelled.
Even though the hot fractions are not completely converged at the low-mass end
45
Gas accretion onto galaxies and haloes
Figure 2.13: Gas overdensity (left) and temperature (right) in a 1 h−1 comoving Mpc box
centred on a halo of 1012 M⊙ at z = 2. We show the same halo as was shown in the middle
panel of Figure 2.7, but now for five different models. The white circles indicate the virial
radius of the halo. From top to bottom: no SN feedback and no metal-line cooling
(NOSN_NOZCOOL), no metal-line cooling (NOZCOOL), reference SN feedback (REF),
density dependent SN feedback (WDENS), reference SN feedback, and AGN feedback
(AGN). These simulations used 2 × 5123 particles in a 25 h−1 Mpc box. The structure of
the cold streams changes, but they exist in all simulations. The hot gas extends to larger
radii and has a higher temperature if feedback is more efficient. The structure inside the
halo is clearly different in different simulations, but cold gas is always present outside
the disc.
46
Accretion onto haloes
47
Figure 2.14: The average fraction of the gas that accreted smoothly onto haloes just before z = 2 (top panels) and z = 0 (bottom panels),
that reached maximum past temperatures above 105.5 K (by z = 2 and z = 0, respectively) is plotted as a function of total halo mass. The
line styles are identical to those used in Figure 2.4. The curves at the high-mass end are from simulations L100N512. At z = 2 the curves at
the low-mass end are from simulations L025N512, resulting in a factor 64 higher mass resolution. Each mass bin contains at least 10 haloes.
At z = 2, each halo contains at least 1000 dark matter particles. This is higher than our resolution limit for accretion onto haloes, but
it removes the overlap between simulations of different resolution. The differences between the simulations are small. Efficient feedback
generally reduces the hot fraction, indicating that hot gas is more vulnerable to feedback than cold gas.
Gas accretion onto galaxies and haloes
for some of the L100N512 runs, the trend with halo mass and the effect of the
variations in the simulations are robust. The haloes above Mhalo ≈ 1012 M⊙ in
the L025N512 runs (not plotted) show an increase in the hot fraction as steep
as the L100N512 runs. Before discussing the differences between the models,
we stress that these differences are small. The fraction of the gas that accretes
onto a halo of a given mass and at a given redshift in the hot mode can thus be
robustly estimated. It is insensitive to uncertainties in the baryonic physics, such
as radiative cooling and feedback from star formation and AGN.
We first focus on the left panels, which compare simulations with and without metal-line cooling and with and without SN feedback. For high-mass haloes
the fraction of gas accreting in the hot mode is a little bit higher without metalline cooling, because the gas will reach higher temperatures if the cooling rates
are lower. The effect is, however, small.
The hot fraction depends only slightly on the specific feedback model used
if the energy per unit stellar mass is kept fixed, as can be seen from the middle
panels of Figure 2.14. The hot fraction is a bit lower for the model with the most
effective feedback (WDENS).
The right panels show that AGN feedback decreases the hot fraction, though
the effect is not large and limited to high-mass (≫ 1011 M⊙ ) haloes. More
effective stellar feedback as a result of a top-heavy IMF in starbursts (DBLIMFCONTSFV1618) reduces the hot fraction more for low-mass . 1012 M⊙ haloes.
These results suggest that the hot accretion mode is slightly more affected by
feedback than the cold mode. Because the hot gas is less dense than the cold
gas and because it spans a greater fraction of the sky as seen by the galaxy, it is
more likely to be affected by feedback. It has been argued by several authors that
AGN feedback would therefore couple mostly to the hot gas (Kereš et al., 2005;
Dekel & Birnboim, 2006). Our results show that this effect is small, although
we will show below that it is important for accretion onto galaxies residing in
high-mass haloes at low redshift. The main conclusion is that the fraction of the
gas that accretes onto haloes in the hot mode is insensitive to feedback from SNe
and AGN.
2.7 Hot and cold accretion onto galaxies
A significant fraction of the gas that accretes onto haloes may remain in the
hot, low-density halo. This gas never cools and it will not get into the inner
galaxy and contribute to the SFR. This diffuse gas may be easily pushed out of
the halo by galactic winds. It is therefore of interest to look not only at the gas
that accretes onto haloes, but also at the gas that actually accretes onto galaxies.
After all, it is only the gas that is accreted onto galaxies that is available for star
formation.
Gas is by definition cold when it accretes onto a galaxy, because it must cool
below T = 105 K to be able to join the ISM. However, by using Tmax we are
probing the entire temperature history of the gas and not just the temperature at
48
Accretion onto galaxies
the time of accretion. Gas accreting onto a galaxy in the hot mode has been hot
in the past (usually when it accreted onto the halo), but was able to cool down
and reach the central galaxy. Gas accreting onto a galaxy in the cold mode has
never been hot in the past.
In Figure 2.15 we show the hot fraction for accretion onto haloes (dotted
curve), accretion onto the ISM (solid curve), and for stars formed (dashed curve)
just before z = 2 (top panel) and just before z = 0 (bottom panel) for the
50 h−1 Mpc reference simulation. To illustrate the convergence, we also show
the hot fraction for accretion onto the ISM for simulations with different resolutions. We show all results down to halo masses corresponding to 100 dark
matter particles, i.e. 1 dex below our resolution limit.
For high-mass haloes (Mhalo & 1012 M⊙ ) hot mode accretion is less important
for accretion onto the ISM, and therefore for star formation, than for accretion
onto haloes. For Tvir & 106 K the hot fraction remains approximately constant
with mass, even though the hot fraction for halo accretion becomes larger. The
lower hot fractions arise because the temperature of the hot gas increases with
the virial temperature and for these temperatures hotter gas has a longer cooling
time (e.g. Wiersma et al., 2009a), making it less likely to enter the galaxy. In reality, cold, dense clouds may be disrupted more easily than in SPH simulations,
which could push the hot fraction up (Agertz et al., 2007).
On the other hand, for low-mass haloes (Tvir . 105.5 K) the hot fraction for
accretion onto galaxies is higher than for accretion onto haloes. The virial temperature of these haloes is so low that the maximum temperature will only be
above 105.5 K if the gas was heated by SN feedback. This can happen after the
gas has accreted onto the halo, but before the gas joins the ISM, explaining the
higher hot fraction for accretion onto galaxies. Indeed, Oppenheimer et al. (2010)
have shown that the re-accretion of gas that has been ejected by galactic winds
can be important. The hot fraction for low-mass haloes is lower in simulations
without feedback, confirming our interpretation (see Figure 2.17).
As expected, for recently formed stars the hot fraction is comparable to that
for gas that recently accreted onto the ISM, although it is a bit lower. It is slightly
lower because of the time delay between accretion and star formation. The gas
from which the stars were formed was typically accreted at higher redshift and
onto lower-mass haloes, which corresponds to lower hot fractions.
Our lowest resolution simulations underestimate the hot fraction somewhat
at their low-mass ends, but this regime is excluded by our adopted resolution
limit, as indicated by the arrows. However, for z = 0 the results are also not fully
converged at the high-mass end (Mhalo > 1012 M⊙ ). For high-mass haloes the
hot fraction decreases with increasing resolution, as we also saw for accretion
onto haloes (see Figure 2.9), although the effect is much larger for accretion
onto galaxies. This is likely because higher densities can be reached with higher
resolution. Cold mode accretion may thus be somewhat more important for
fuelling massive galaxies than our simulations suggest.
The evolution of the hot fraction of gas accreted onto the ISM is shown in
49
Gas accretion onto galaxies and haloes
Figure 2.15: The dotted curve shows the average fraction of gas smoothly accreted onto
haloes at z = 2 (top panel) and z = 0 (bottom panel), that has maximum past temperatures above Tmax = 105.5 K. The solid curves show the average fraction of the gas
smoothly accreted onto the ISM with maximum past temperatures above Tmax = 105.5 K.
The dashed curves show the fraction of the stars formed in the same redshift intervals
from gas with maximum past temperatures above Tmax = 105.5 K. These reference simulations span a factor of 64 in mass resolution in each panel. Each mass bin contains
at least 10 haloes. Arrows correspond to the adopted resolution limit for accretion onto
galaxies. For high-mass haloes, the hot fractions for accretion onto haloes and galaxies
diverge. The hot fraction for recently formed stars follows the same trend as for accretion
onto the ISM.
50
Accretion onto galaxies
Figure 2.16: Hot fraction against halo mass for accretion onto the ISM just before z = 5,
4, 3, 2, 1, and 0 shown from bottom to top by the curves in black, blue, purple, orange,
red, and green, respectively. The curves at low halo masses are obtained from model
REF_L050N512. At the high-mass end we have added curves for REF_L100N512 to extend
the dynamic range. Each mass bin contains at least 10 haloes. The hot fraction increases
with redshift, except for haloes with virial temperatures which fall below 105.5 K, the
value we use to separate hot and cold accretion (Mhalo . 1011.5 M⊙ and z . 1). The hot
fraction varies less strongly with halo mass than for accretion onto haloes.
Figure 2.16 from z = 5 (bottom, black curve) to z = 0 (top, green curve) as
a function of halo mass. The trend with redshift is the same as for accretion
onto haloes (see Figure 2.11). The hot fraction increases with decreasing redshift
for all halo masses, except when the virial temperatures fall below 105.5 K, the
value we use to separate the hot and cold accretion modes, which happens for
Mhalo . 1011.5 M⊙ at z . 1. The hot fraction for accretion onto galaxies increases
less steeply with halo mass than for accretion onto haloes. This is due to the fact
that the cooling time of the hot gas increases for higher-mass haloes, making it
less likely that hot gas reaches the central galaxy.
For haloes with Tvir & 106 K, the hot fraction of gas that reaches the ISM is
much lower than the hot fraction of all the gas that accretes onto the halo. At
high redshift (z & 4) cold accretion is the dominant mode for feeding galaxies.
At lower redshift (z . 2) hot and cold accretion are comparable. Except for highmass haloes at low redshift (Mhalo > 1013 M⊙ at z = 0), hot mode accretion
is less important for feeding the central galaxy than cold mode accretion. It
is always less important for the growth of galaxies than it is for the growth
of haloes, though it is never negligible. We found the hot fraction of recently
formed stars to be slightly lower, because it takes some time to convert the gas
into stars. Cold mode accretion is most important for the total build-up of stellar
mass in galaxies.
51
Gas accretion onto galaxies and haloes
We have not included galaxy mergers. Including mergers preferentially brings
in gas accreted in the cold mode, because that gas was already part of the ISM.
This reduces the hot fraction slightly for high-mass haloes at low redshift. Cold
mode accretion is therefore also the main mode for galaxy growth in this case.
2.7.1 Effects of physical processes
We showed the effect of feedback, metal-line cooling, and cosmology on galaxy
accretion rates in Section 2.5. Feedback reduces these rates, while including
metal-line cooling increases them. In this Section we discuss their consequences
for the relative importance of hot and cold accretion.
Figure 2.17 shows the hot fraction of the gas that reaches the ISM between
z = 2.25 and z = 2 as a function of halo mass for the same simulations as were
shown for accretion onto haloes in Figure 2.14. Even though the hot fractions are
not completely converged for the L100N512 runs, the trend with halo mass and
the effect of the variations in the physics are robust. As was the case for accretion
onto haloes, the trends are the same for all simulations, although the differences
between models are larger for accretion onto the ISM than for accretion onto
haloes. At z = 2, the hot mode is less important for accretion onto the ISM,
and therefore less important for star formation, than the cold mode. For the
halo mass range shown at z = 0 (& 1012 M⊙ ), the hot mode is slightly more
important than the cold mode.
We can observe the difference between simulations with and without metalline cooling and with and without SN feedback in the left panels. The simulation
without metal-line cooling (NOZCOOL) has a slightly smaller hot fraction than
the simulation with metal-line cooling (REF) at z = 2 and for Mhalo . 1012.5 M⊙
at z = 0. Because the cooling times are longer in the absence of metal-line
cooling, less hot gas is able to reach the high densities that define the ISM. For
accretion onto haloes we found the opposite effect (see Figure 2.14), because the
lower cooling rate increases the maximum temperature reached by gas accreted
onto haloes and hence increases the corresponding hot fraction. For high mass
haloes (Mhalo & 1013 M⊙ ) at z = 0, the hot fraction is much higher in the absence
of metal-line cooling. In Figure 2.5 we have seen that metal-line cooling strongly
increases the accretion rates onto galaxies in lower mass galaxies. Thus, without
metal-line cooling, less hot gas accretes onto low-mass haloes, leaving more hot
gas to accrete onto their higher mass descendants.
We can compare the simulation without metal-line cooling (NOZCOOL) to
the one without SN feedback and without metal-line cooling (NOSN_NOZCOOL).
In the simulations with feedback a higher fraction of the gas accreted onto the
ISM has been hot, presumably because some of the gas accreted cold onto haloes
was heated by outflows before it joined the ISM (for the last time). At the highmass end at z = 0 the differences between the curves parallels those in the specific accretion rates (Figure 2.5). This suggests that here SN feedback increases
the hot fraction because it prevents the accretion of hot gas onto lower mass
52
53
Accretion onto galaxies
Figure 2.17: The average fraction of the gas accreting onto the ISM at z = 2 (top panels) and z = 0 (bottom panels), that has maximum past
temperatures Tmax ≥ 105.5 K. The line styles are identical to those used in Figure 2.14. The curves at the low and high-mass ends are from
simulations L025N512 and L100N512, respectively, which differ by a factor 64 in mass resolution. Each mass bin contains at least 10 haloes.
Differences in results from different simulations are mostly small, except for Mhalo > 1013 M⊙ at z = 0 if metal-line cooling is ignored or
AGN feedback is added.
Gas accretion onto galaxies and haloes
progenitors, leaving more gas available to cool in high-mass galaxies, where the
SN feedback is inefficient. The effect of SN feedback on the hot fraction at z = 2
is much smaller if metal-line cooling is included (NOSN). This may indicate that
the increase in the cooling rates due to the metals carried by the winds compensates for the extra shock heating.
The middle panels show the result for simulations with different values for
the SN feedback parameters, but the same amount of SN energy per unit stellar
mass formed. The hot fractions are similar, though slightly higher if the feedback model is more efficient (WML1V848 for Mhalo > 1011 M⊙ and WDENS for
Mhalo > 1012 M⊙ at z = 2).
Results for simulations with a prescription for SN feedback that use more
energy and for a model including AGN feedback are shown in the right panels.
Perhaps surprisingly, at z = 2 the simulation including AGN feedback (AGN)
gives results similar to the reference simulation. The accretion rate onto the
galaxy is suppressed by up to 1 dex, as can be seen in Figure 2.5, but the hot
fraction is almost the same. At z = 0 the hot fraction is somewhat lower, though
still above 40%.
In Figure 2.14 we showed that the hot fraction for the gas accreting onto
haloes does not change much if we vary the prescriptions for feedback and
radiative cooling. To first order, the same conclusion is true for the gas that
accretes onto the ISM and thus becomes star forming, although the differences
are larger. At z = 2 the hot fraction decreases significantly if both SN feedback
and metal-line cooling are turned off. For high-mass galaxies (Mhalo > 1013 M⊙ )
at z = 0 the importance of the hot mode increases substantially if metal-line
cooling is excluded and decreases significantly if AGN feedback is added. The
specific implementation of the SN feedback does not have a large effect on the
fraction of the gas accreting onto galaxies that has a maximum past temperature
Tmax ≥ 105.5 K.
2.8 Comparison with previous work
We can compare our results to the pioneering work of Kereš et al. (2005, 2009a),
and Ocvirk et al. (2008). All these studies used 250,000 K as the critical temperature to separate hot and cold accretion. We used 105.5 = 316, 228 K, but our
results would have been very similar if we had used 250,000 K.
Ocvirk et al. (2008) use an adaptive mesh refinement (AMR) code and include metal enrichment and cooling, but only weak SN feedback and no AGN
feedback. They use only a single simulation, whose resolution is similar to our
L025N512 runs. Their simulation was only run to z ≈ 1.5, so we can only compare to our high-redshift results. Their box size of 50 h−1 Mpc is too small to
sample haloes with mass & 1013 M⊙ . As their simulation is not Lagrangian, they
cannot trace the gas back in time, and were forced to separate the cold and hot
modes based on current temperatures.
54
Comparison
For z = 2 − 3 they predict that the hot fraction for accretion onto haloes
reaches 0.5 at Mhalo ∼ 1011.5 M⊙ , whereas we find Mhalo ∼ 1012 M⊙ . For
higher redshifts we predict somewhat higher hot fractions. We predict a gradual
increase in the transition mass with redshift, but see no sign of the sudden
change between z = 3 and 4 that they found.
For accretion onto galaxies, which they measure at 0.2 virial radii, Ocvirk
et al. (2008) also do not predict a sudden change with redshift. As the gas at
this radius is not necessarily star forming and has not necessarily cooled down
to T ≤ 105 K, it is not possible to make a completely fair comparison. They
find no change with redshift, whereas we find strong evolution. The hot fraction increases up to their highest halo mass, reaching values close to unity for
1012.5 M⊙ . In our simulations, however, the hot fraction for accretion onto galaxies is approximately constant and never exceeds 0.4 at z ≥ 2. As we are using the
SPH technique, it is possible that our simulations suffer from in-shock cooling,
which would lead to an underestimate of the hot fraction. However, we find
that the hot fraction in fact decreases with increasing resolution, the opposite
of what we would expect if this were an important effect. Perhaps the difference is due to the fact that we do not update the maximum past temperature
once the gas has become star forming. If the accretion shock onto the galaxy
happens after that time, we would underestimate the maximum temperature.
This is, however, consistent with our aims, as we are interested in the maximum
temperature reached before the gas entered the galaxy.
Kereš et al. (2005, 2009a) use SPH codes. They ignore metal-line cooling
and do not include feedback from SNe or AGN. The resolution of their main
simulation is comparable to our L100N512 runs, but their simulation volume
is more than eight times smaller. Their mass resolution is nearly two orders
of magnitudes worse than for our L025N512 runs. They identify galaxies using a different group finder, skid, which links bound stars and dense, cold gas
(ρ/hρbaryon i > 1000 and T < 30, 000 K). These groups are considered to be galaxies. In contrast to our work, they include accretion onto both central galaxies and
satellites, which could also lead to somewhat different results. Accretion onto
haloes was not investigated.
Contrary to our results and those of Kereš et al. (2009a), Kereš et al. (2005)
find that the hot fraction continues to increase with halo mass and that there is
no significant evolution. However, using the same method, Kereš et al. (2009a)
find much lower hot fractions than Kereš et al. (2005). They find that this difference is mostly due to the fact that they switched to the entropy conserving
formulation of SPH of Springel & Hernquist (2002), which prevents overcooling
due to artificial phase mixing and which we have used as well. We will therefore
only compare with Kereš et al. (2009a) (and only for accretion onto galaxies).
At high redshift (z = 4) we find similar results for the hot fractions as Kereš
et al. (2009a), although ours are slightly higher, which is due to the fact that we
include SN feedback. At z ≤ 2 they find that the hot fraction first increases,
reaches a maximum around Mhalo = 1012 M⊙ , after which it decreases. We
55
Gas accretion onto galaxies and haloes
find that the hot fraction varies less strongly with halo mass and that it remains
approximately constant at the high mass end.
Our results are also in qualitative agreement with Brooks et al. (2009), who
used SPH simulations (without metal-line cooling and AGN feedback) of a few
individual galaxies with Mhalo . 1012 M⊙ . A detailed comparison is difficult
as their sample is too small to obtain statistics and because they used a more
complicated criterion to separate the different accretion modes.
2.9 Conclusions
Before summarizing and discussing our findings, we list our main conclusions:
• To first order, the rate of gas accretion onto haloes follows that of dark
matter. Except for low-mass haloes (Mhalo ≪ 1011 M⊙ ), feedback changes
these rates only slightly.
• Except for groups and clusters, gas accretes mostly smoothly (i.e. not
through mergers with mass ratios greater than 1:10).
• The rate at which gas accretes onto galaxies is set by radiative cooling,
which is sensitive to the abundance of heavy elements, and by feedback
from SNe and AGN. Galactic winds driven by star formation increase the
halo mass at which the central galaxies grow the fastest by about two orders of magnitude to Mhalo ∼ 1012 M⊙ .
• The signs of the effects of feedback and metal-line cooling on gas accretion
can change with halo mass.
• Gas accretion is bimodal, with maximum past temperatures either of order
the virial temperature or . 105 K. Both modes can be present in a single
halo, the cold mode being most prominent in filaments.
• The fraction of gas accreted in the hot mode (i.e. maximum past temperature Tmax ≥ 105.5 K), increases with halo mass and with decreasing redshift.
• For accretion onto haloes, the relative importance of the hot and cold
modes is is robust to changes in the feedback prescriptions. Cold and
hot accretion dominate for Mhalo ≪ 1012 M⊙ and Mhalo ≫ 1012 M⊙ , respectively.
• For accretion onto galaxies the cold mode is always significant and the
relative importance of the two accretion modes is much more sensitive to
feedback and cooling than is the case for halo accretion.
• On average, most of the stars present in any mass halo at any redshift
were formed from gas accreted in the cold mode, although the hot mode
contributes typically over 10% for Mhalo & 1011 M⊙ (see Figure 2.18 below).
56
Conclusions
While the rate at which dark matter accretes onto haloes can be reliably calculated, the situation is rather more complicated for gas. Gas may be heated
through accretion shocks, but can also radiate away its thermal energy. This
cooling rate is, however, strongly affected by contamination with metals blown
out of galaxies. Such galactic winds driven by star formation or accreting supermassive black holes may also directly halt or reverse the accretion, which may
in turn cause gas elements to be recycled multiple times.
Pressing questions include: What fraction of the gas accreting onto haloes
experiences a shock near the virial radius? How does this fraction vary with
halo mass and redshift? What fraction of the gas that falls into a dark matter
halo accretes onto a galaxy and how does this vary with mass and redshift? How
do processes like metal-line cooling and feedback from star formation and AGN
affect gas accretion? We addressed these questions by analysing a large number
of cosmological, hydrodynamical simulations from the OWLS project (Schaye
et al., 2010). By repeating the simulations many times with varying parameters,
we investigated what physical processes drive the accretion of gas onto galaxies
and haloes. For each physical model we combined at least two 2 × 5123 particle
simulations in order to cover a dynamic range of about 4 orders of magnitude
in halo mass (Mhalo ∼ 1010 − 1014 M⊙ ). Schaye et al. (2010) have shown that
the simulation with AGN feedback is able to reproduce the steep slope of the
observed star formation rate density at z < 2. This is a significant improvement
over previous simulations. In a future paper we will discuss the contributions
of hot and cold accretion to the cosmic star formation history.
Except for Mhalo ≫ 1013 M⊙ at low redshift, mergers with mass ratios exceeding 1:10 contribute . 10% of the total accretion onto haloes. The growth
of haloes is thus dominated by smooth accretion. The specific rate of smooth
gas accretion onto haloes is close to that for dark matter accretion, particularly
at higher redshifts. It decreases with time and increases with halo mass. The
increase with halo mass is, however, gradual and the gradient decreases with
increasing halo mass. To first order, the halo accretion rate scales linearly with
the halo mass.
The rate of accretion onto haloes is relatively insensitive to the inclusion of
metal-line cooling. Efficient feedback can reduce the halo accretion rates by
factors of a few. In particular, for z = 2 we find that SN feedback reduces the
halo accretion rate of low-mass haloes (Mhalo ∼ 1010 M⊙ ) by a factor of about
four, but is typically not efficient for Mhalo & 1013 M⊙ .
As is the case for accretion onto haloes, accretion onto galaxies is mostly
smooth. Clumpy accretion, which in this case we defined as accretion of material
that already had densities nH ≥ 0.1 cm−3 at the previous snapshot, becomes of
comparable importance as smooth accretion only for Mhalo & 1013 M⊙ .
While the specific accretion rate onto haloes increases slowly with halo mass
over the full range spanned by our simulations, the specific accretion rate onto
galaxies increases rapidly for Mhalo ≪ 1012 M⊙ and drops quickly for Mhalo ≫
1012 M⊙ . The halo mass at which the specific accretion rate onto galaxies peaks
57
Gas accretion onto galaxies and haloes
is sensitive to feedback from SNe and AGN. Without SN feedback, the specific
accretion rate peaks at Mhalo ∼ 1010 M⊙ , where it exceeds the rate predicted
by runs that do include SN feedback by an order of magnitude. For higher
mass haloes (Mhalo ≫ 1011 M⊙ ), on the other hand, SN feedback tends to increase the specific accretion rates by about a factor of two, either because of the
increased importance of recycling (i.e. the same gas can be re-accreted after it
has been ejected, see Oppenheimer et al. 2010) or because without SN feedback
the accreted gas would already have been consumed in lower mass progenitor
galaxies. AGN feedback can strongly reduce the accretion rates onto galaxies.
This sensitivity to feedback is in contrast to accretion onto haloes. In the absence
of metal-line cooling, the peak in the specific accretion rate is less pronounced.
Hence, cooling and feedback set the efficiency of galaxy formation by controlling
what fraction of the gas that accretes onto haloes is able to accrete onto galaxies.
The rate of accretion onto galaxies is smaller than the accretion rate onto
haloes. The difference between the two rates increases with time and is minimal
for Mhalo ∼ 1012 M⊙ . For this mass the difference increases from a factor of two
at z = 2 to a factor of four at z = 0.
Tracing back in time, most gas particles that reside in haloes at z = 0 reached
their maximum temperature around, or shortly after, the time they were first accreted onto a halo. In the presence of a photo-ionising background, essentially all
gas accreting smoothly onto haloes has been heated to & 105 K. For haloes with
virial temperatures ≫ 105 K the probability distribution for the maximum past
temperature reached by gas accreted onto haloes is bimodal. The low temperature peak at ∼ 105 K represents gas that accreted predominantly through largescale filaments (but still smoothly). The higher densities in the filaments enable
efficient cooling which in turn prevents the establishment of a stable accretion
shock (e.g. Kereš et al., 2005; Dekel & Birnboim, 2006). The high-temperature
peak coincides with the virial temperature of the halo and is reached through
an accretion shock near the virial radius.
We separated these two modes of smooth gas accretion according to the maximum past temperature of the gas, which we updated for each particle at each
time step, and referred to them as cold (Tmax < 105.5 K) and hot (Tmax ≥ 105.5 K)
accretion, respectively. For high-mass haloes (virial temperatures & 106 K), the
hot fraction, i.e. the fraction of gas that is accreted in the hot mode, reflects the
fraction of the accreted gas that has experienced an accretion shock near the
virial radius. We emphasized, however, that for gas accreted onto haloes with
virial temperatures . 105.5 K (Mhalo . 1011.5 M⊙ at z = 2 and Mhalo . 1012 M⊙
at z = 0) gas accreted in the cold mode (according to our definition) may also
have gone through a virial shock.
The fraction of the gas that is accreted onto haloes and galaxies of a given
mass in the cold mode typically increases with redshift. This is because radiative
cooling is more efficient at high redshift, where the gas densities are higher (and
the cooling time is more sensitive to the density than the dynamical and Hubble
times).
58
Conclusions
For accretion onto haloes, the relative importance of the two modes is mostly
determined by the halo mass. At z = 0 the hot fraction increases from less than
0.1 at Mhalo ∼ 1011 M⊙ to more than 0.9 at Mhalo ∼ 1013 M⊙ . For all redshifts
for which we have sufficient statistics (z < 5), the hot fraction reaches 0.5 for
Mhalo ∼ 1012 M⊙ , in reasonable agreement with the predictions of Birnboim &
Dekel (2003) and Dekel & Birnboim (2006) for metal enriched gas at the virial
radius and with previous simulations (Kereš et al., 2005; Ocvirk et al., 2008;
Kereš et al., 2009a). Contrary to accretion onto haloes, the hot fraction for gas
accreted onto galaxies is only weakly dependent on halo mass. In particular, the
hot fraction for accretion onto galaxies is nearly constant for Mhalo & 1012 M⊙
and remains below 0.5, except at z ≈ 0.
For accretion onto haloes, the relative importance of the cold and hot modes
is mostly insensitive to the inclusion of metal-line cooling or feedback from SNe
and AGN. For accretion onto galaxies the effects are stronger, though generally still weak. The main exceptions are galaxies in high-mass haloes Mhalo >
1013 M⊙ at low redshift. For these systems the hot mode becomes much more
important in the absence of metal-line cooling (because less gas has cooled onto
their progenitors) and substantially less important if AGN feedback is considered (because it efficiently removes hot gas).
As expected, the hot fraction for the gas that is converted into stars is very
similar to that of the gas that accretes onto galaxies. As illustrated in Figure 2.18,
where we show the fraction of the total stellar mass formed from gas which has
reached Tmax ≥ 105.5 K in its past. For the full range of redshifts and halo masses
probed by our simulations, the majority of stars are formed from gas accreted in
the cold mode.
Both the comparison of our different models and the comparison with Ocvirk
et al. (2008) suggest that the conclusions regarding accretion onto haloes are robust, at least for z < 4. The gas accretion rate is similar to that of the dark matter
and dominated by smooth accretion. The hot mode changes from being negligible at Mhalo . 1011 M⊙ to strongly dominant at Mhalo & 1013 M⊙ . Contrary to
accretion onto haloes, the mode and particularly the rate of gas accretion onto
galaxies, and hence the provision of fuel for star formation, is affected by uncertain processes such as metal-line cooling and especially feedback from star
formation and AGN. This is reflected in the large differences in the predictions
by different groups. It seems clear, however, that the hot mode is much less
important for the growth of galaxies than it is for the growth of haloes.
We conclude that the rate and manner in which gas accretes onto haloes is
an important ingredient of models for the formation and evolution of galaxies
and that this process can be understood using simple physics. However, halo
accretion gives by itself little insight into the rate and mode through which gas
accretes onto galaxies. To understand galaxy formation, it is crucial to consider
feedback processes, such as metal enrichment and outflows driven by SNe and
AGN.
59
Gas accretion onto galaxies and haloes
Figure 2.18: Fraction of the stellar mass at the indicated redshifts, that formed from gas
that had earlier reached temperatures exceeding Tmax ≥ 105.5 K, as a function of the host
halo mass at the corresponding redshifts for the simulation REF_L050N512. We added
the highest mass bins from REF_L100N512 to extend the dynamic range. Each mass
bin contains at least 10 haloes. At any time and for any halo mass, hot mode accretion
contributed less than 40% to the total stellar mass.
Acknowledgements
We would like to thank Ben Oppenheimer and Volker Springel for comments
on an earlier version of the manuscript and all the members of the OWLS team
for valuable discussions. We would also like to thank the anonymous referee
for constructive comments. The simulations presented here were run on Stella,
the LOFAR BlueGene/L system in Groningen, on the Cosmology Machine at
the Institute for Computational Cosmology in Durham as part of the Virgo Consortium research programme, and on Darwin in Cambridge. This work was
sponsored by the National Computing Facilities Foundation (NCF) for the use
of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research (NWO), also through a VIDI grant, and from the
Marie Curie Initial Training Network CosmoComp (PITN-GA-2009-238356).
60
3
The drop in the cosmic star
formation rate below redshift 2 is
caused by a change in the mode of
gas accretion and by active
galactic nucleus feedback
The cosmic star formation rate is observed to drop sharply after redshift z = 2.
We use a large, cosmological, smoothed particle hydrodynamics simulation to
investigate how this decline is related to the evolution of gas accretion and to
outflows driven by active galactic nuclei (AGN). We find that the drop in the star
formation rate follows a corresponding decline in the global cold-mode accretion
rate density onto haloes, but with a delay of order the gas consumption time
scale in the interstellar medium. Here we define cold-mode (hot-mode) accretion
as gas that is accreted and whose temperature has never exceeded (did exceed)
105.5 K. In contrast to cold-mode accretion, which peaks at z ≈ 3, the hot mode
continues to increase to z ≈ 1 and remains roughly constant thereafter. By
the present time, the hot mode strongly dominates the global accretion rate
onto haloes. Star formation does not track hot-mode halo accretion because
most of the hot halo gas never accretes onto galaxies. AGN feedback plays a
crucial role by preferentially preventing gas that entered haloes in the hot mode
from accreting onto their central galaxies. Consequently, in the absence of AGN
feedback, gas accreted in the hot mode would become the dominant source of
fuel for star formation and the drop off in the cosmic star formation rate would
be much less steep.
Freeke van de Voort, Joop Schaye, C. M. Booth,
and Claudio Dalla Vecchia
Monthly Notices of the Royal Astronomical Society
Volume 415, Issue 3, pp. 2782-2789 (2011)
The drop in the cosmic SFR below z = 2
3.1 Introduction
The cosmic star formation rate (SFR) is observed to peak between redshifts z ≈ 3
and z ≈ 2 after which it decreases by an order of magnitude (e.g. Hopkins &
Beacom, 2006). Its evolution is thought to be determined by the combination of
the formation and growth of (dark matter) haloes, which depends on cosmology,
and the distribution of SFRs in haloes as a function of halo mass and redshift.
The latter depends on processes such as gas accretion, stellar mass loss, radiative
cooling, (re-)ionization, and feedback from star formation and active galactic
nuclei (AGN) (e.g. Schaye et al., 2010).
The observed rates of star formation in galaxies can only be sustained for
long periods of time if the galaxies are being fed continuously (e.g. Bauermeister
et al., 2010). This feeding happens through the accretion of gas from the intergalactic medium. In the simplest picture of spherical collapse, it is assumed that
all gas accreting onto a halo is shock-heated to the virial temperature of the halo,
reaching a quasi-static equilibrium supported by the pressure of the hot gas. If
the cooling time of the halo gas is sufficiently short, then it may subsequently
enter the central galaxy. Whether or not the halo gas can accrete onto the galaxy
therefore depends on both the temperature and the density of the gas (Rees &
Ostriker, 1977). However, if the cooling time of gas that has gone through a (hypothetical) accretion shock at the virial radius is short compared with the age
of the Universe, then there can be no hydrostatic halo and hence also no virial
shock. This will be the case for low-mass haloes (Rees & Ostriker, 1977; White
& Rees, 1978). The accretion rate onto the central galaxy then depends on the
infall rate, but not on the cooling rate (White & Frenk, 1991). Indeed, Birnboim
& Dekel (2003) showed that a virial shock is absent for low-mass haloes in a
spherically symmetric simulation.
However, cosmological simulations show significant deviations from spherical symmetry. Galaxies form inside the filaments that make up the cosmic web
and these filaments contribute significantly to, or even dominate, the gas supply
of galaxies (Dekel et al., 2009a). Because the density inside filaments is higher
than that of the ambient gas, the cooling time of the gas is much shorter and the
gas can accrete cold onto haloes of higher masses than predicted by spherically
symmetric models (e.g. Kereš et al., 2005; Dekel & Birnboim, 2006). This cold
gas can reach the high densities of the interstellar medium (ISM) much more
efficiently than the tenuous, hot gas in the halo. It is this ‘cold mode’ of accretion that predominantly feeds the galaxy and powers star formation (Kereš et al.,
2009a; Brooks et al., 2009; van de Voort et al., 2011a, hereafter V11).
The fraction of the accreted gas that is accreted cold, i.e. the fraction of the
gas that did not pass through a virial shock, depends on both halo mass and
redshift (Kereš et al. 2005; Dekel & Birnboim 2006; Ocvirk et al. 2008; Kereš et al.
2009a; Brooks et al. 2009; V11). In V11 we used simulations to show that the rate
at which gas accretes onto central galaxies is generally much lower than the rate
at which gas accretes onto their host haloes. Furthermore, we found that while
62
Simulations
halo accretion rates are determined by the depth of the gravitational potentials,
galaxy accretion rates are also sensitive to processes such as metal-line cooling
and feedback from star formation and AGN.
Here we use a large cosmological hydrodynamical simulation that includes
radiative cooling (computed element by element and thus including metal lines),
star formation, stellar mass loss, and outflows driven by both supernovae and
AGN, to determine how hot and cold accretion influence the global star formation history (SFH). We calculate global accretion rate densities, both for hotand cold-mode accretion, and for accretion onto haloes as well as accretion onto
galaxies. We will compare the evolution of these different global accretion rates
to the resulting global SFH and learn how they all link together. We will show
that the sharp drop in the global SFH after z ≈ 2 reflects the corresponding sharp
drop in the rate of cold-mode accretion onto haloes. Motivated by semi-analytic
models and simulations that have shown AGN feedback to be crucial for the suppression of star formation in high-mass haloes (e.g. Springel et al., 2005; Bower
et al., 2006; Croton et al., 2006; Lagos et al., 2008; Booth & Schaye, 2009; McCarthy
et al., 2010), we use an identical simulation, except for the omission of feedback
from AGN, to investigate the effect of AGN feedback on the global accretion
rates. We will show that the hot accretion mode is more strongly suppressed by
AGN feedback than the cold mode. Without AGN feedback, low-redshift star
formation would not be predominantly fuelled by the cold accretion mode and
the drop in the cosmic SFR would be much less strong.
The outline of this paper is as follows. In Section 3.2 we briefly describe the
simulations from which we derive our results and discuss our method for selecting recently accreted gas. In Section 3.3 we compare global accretion rates to the
cosmic SFR and show which haloes contribute most to the global accretion rates
and the cosmic SFH. In Section 3.4 we investigate the effect of AGN feedback on
the hot and cold accretion rate densities. Finally, we summarize and discuss our
results in Section 3.5.
3.2 Simulations
We use a modified version of gadget-3 (last described in Springel, 2005b), a
smoothed particle hydrodynamics (SPH) code that uses the entropy formulation
of SPH (Springel & Hernquist, 2002), which conserves both energy and entropy
where appropriate. This work is part of the OverWhelmingly Large Simulations (OWLS) project (Schaye et al., 2010), which consists of a large number of
cosmological simulations with varying (subgrid) physics. Here we make use of
the so-called ‘AGN’ and ‘reference’ models, which are identical except that only
model AGN includes supermassive black holes and AGN feedback. The AGN
simulation will be our fiducial model, but we will compare it with the OWLS
reference model in Section 3.4. As the simulations are fully described in Schaye
63
The drop in the cosmic SFR below z = 2
et al. (2010), we will only summarize their main properties here.
The simulations described here assume a ΛCDM cosmology with parameters
Ωm = 1 − ΩΛ = 0.238, Ωb = 0.0418, h = 0.73, σ8 = 0.74, n = 0.951. These values
are consistent1 with the WMAP 7-year data (Komatsu et al., 2011).
A cubic volume with periodic boundary conditions is defined, within which
the mass is distributed over N 3 dark matter and as many gas particles. The box
size (i.e. the length of a side of the simulation volume) of the simulations used in
this work is 100 h−1 comoving Mpc, with N = 512. The (initial) particle masses
for baryons and dark matter are 1.2 × 108 M⊙ and 5.6 × 108 M⊙ , respectively.
The gravitational softening length is 7.8 h−1 comoving kpc, i.e. 1/25 of the mean
dark matter particle separation, but we imposed a maximum of 2 h−1 proper kpc,
which is reached at z = 2.91.
The abundances of eleven elements released by massive stars and intermediate mass stars are followed as described in Wiersma et al. (2009b). We assume
the stellar initial mass function (IMF) of Chabrier (2003), ranging from 0.1 to
100 M⊙ . As described in Wiersma et al. (2009a), radiative cooling and heating are computed element by element in the presence of the cosmic microwave
background radiation and the Haardt & Madau (2001) model for the UV/X-ray
background from galaxies and quasars.
Star formation is modelled according to the recipe of Schaye & Dalla Vecchia
(2008). A polytropic equation of state Ptot ∝ ρ4/3
gas is imposed for densities ex−
3
ceeding nH = 0.1 cm , where Ptot is the total pressure and ρgas the density of
the gas. Gas particles with proper densities nH ≥ 0.1 cm−3 and temperatures
T ≤ 105 K are moved onto this equation of state and can be converted into star
particles. The star formation rate (SFR) per unit mass depends on the gas pressure and is set to reproduce the observed Kennicutt-Schmidt law (Kennicutt,
1998).
Feedback from star formation is implemented using the prescription of Dalla
Vecchia & Schaye (2008). About 40 per cent of the energy released by type II
SNe is injected locally in kinetic form. The rest of the energy is assumed to be
lost radiatively. The initial wind velocity is 600 km s−1 .
Our fiducial simulation includes AGN feedback. The model, which is a modified version of the model introduced by Springel et al. (2005), is fully described
and tested in Booth & Schaye (2009). In short, a seed mass black hole is placed
in every resolved halo. These black holes grow by accretion of gas, which results
in the injection of energy in the surrounding medium, and by mergers.
The accretion rate onto the black hole equals the so-called Bondi-Hoyle accretion rate (Bondi & Hoyle, 1944) if the gas density is low (nH < 10−1 cm−3 ).
However, in dense, star-forming gas, where the accretion rate would be severely
underestimated because the simulations do not include a cold, interstellar gas
phase and because the Jeans scales are unresolved, the accretion rate is mul1
The only significant discrepancy is in σ8 , which is 8 per cent, or 2.3σ, lower than the value
favoured by the WMAP 7-year data.
64
Simulations
∗ ) β , where n∗ =
tiplied by an efficiency parameter, α, given by α = (nH /nH
H
−
3
0.1 cm is the threshold density for star formation and β = 2. Note, however,
that our results are insensitive to the choice for β as long as it is chosen to be
large (see Booth & Schaye 2009). A fraction of 1.5 per cent of the rest-mass energy of the accreted gas is injected into the surrounding medium in the form
of heat, by increasing the temperature of at least one neighbouring gas particle
by at least 108 K. The minimum temperature increase ensures that the feedback
is effective, because the radiative cooling time of the heated gas is sufficiently
long, and results in fast outflows. When AGN feedback is included, the SFR is
reduced for haloes with Mhalo & 1012 M⊙ (Booth & Schaye, 2009). The AGN
simulation reproduces the observed mass density in black holes at z = 0 and the
black hole scaling relations (Booth & Schaye, 2009) and their evolution (Booth
& Schaye, 2010) as well as the observed optical and X-ray properties, stellar
mass fractions, SFRs, stellar age distributions and the thermodynamic profiles
of groups of galaxies (McCarthy et al., 2010).
The Lagrangian nature of the simulation is exploited by tracing each fluid
element back in time, which is particularly convenient for this work, as it allows
us to study the temperature history of accreted gas. During the simulations
the maximum past temperature, Tmax , was stored in a separate variable. The
variable was updated for each SPH particle at every time step for which the
temperature exceeded the previous maximum temperature. The artificial temperature the particles obtain when they are on the equation of state (i.e. when
they are part of the unresolved multiphase ISM) was ignored in this process.
This may cause us to underestimate the maximum past temperature of gas that
experienced an accretion shock at higher densities. Ignoring such shocks is, however, consistent with our aims, as we are interested in the maximum temperature
reached before the gas entered the galaxy.
Resolution tests are not included in this paper. However, Schaye et al. (2010)
have shown that the box size and resolution of the reference simulation used in
this paper suffice to obtain nearly converged results for the cosmic SFH at z < 3,
which changes by much less than a factor of 2 when changing the resolution
by a factor of 8. At higher redshifts the global SFR density is, however, underestimated as a result of the finite resolution. Because AGN feedback moves
the peak star formation activity to lower-mass haloes, the convergence of the
AGN simulation may be slightly worse. V11 tested the convergence of accretion rates and the fraction of the accretion due to the hot mode as a function of
halo mass. They found that increasing the resolution gives slightly higher cold
accretion fractions, which would only strengthen the conclusions of this work.
For quantities averaged over the entire simulation volume, we have to keep in
mind that the minimum halo mass that is included depends on the resolution.
The global fraction of gas accreted in the cold mode may therefore also depend
on the resolution, because the cold fraction increases with decreasing halo mass.
Increasing the resolution would allow us to include lower-mass haloes, thus increasing the global cold accretion fraction. Again, this would only strengthen
65
The drop in the cosmic SFR below z = 2
our conclusions.
3.2.1 Accretion and mergers
In this section we summarize our method for determining the gas accretion rates
onto haloes and galaxies and the amount of star formation within haloes. Our
method is described in more detail in V11. We use subfind (Dolag et al., 2009)
to identify gravitationally bound haloes and subhaloes. In this work we only
investigate accretion onto haloes that are not embedded inside larger haloes. In
other words, we do not consider subhaloes. The simulations are saved at discrete
output redshifts, called snapshots. The redshift intervals between snapshots are
∆z = 0.25 for 0 < z ≤ 4, and ∆z = 0.5 for 4 < z ≤ 6. This is the time
resolution for determining accretion rates. For all haloes, called descendants,
with more than 100 dark matter particles (i.e. with Mhalo & 1010.8 M⊙ ), we find
the progenitor at the previous output redshift. We do this by finding the group
containing most of the 25 most bound dark matter particles of the descendant.
Haloes without a well-defined progenitor are discarded from our analysis. All
gas entering a halo, both from accretion and from mergers, contributes to its
growth. We therefore identify all the gas and recently formed star particles that
are in the descendant, but not in its progenitor.
To participate in star formation, gas has to enter not only the halo, but also
the ISM of the galaxy. For the same haloes as we have selected above, we identify all particles entering the ISM (i.e. moving onto the equation of state) of the
descendant galaxy between the two consecutive output redshifts. Galaxy mergers are therefore automatically included. To make sure we are not looking at
accretion onto substructures within the main halo, we only consider accretion
taking place within the inner 15 per cent of the virial radius. This corresponds
to the growth of the central galaxy.
Finally, we identify all the stars formed in the same haloes and redshift bins
to calculate the corresponding SFRs. Again, unresolved haloes and satellites are
excluded.
We decided to include gas contributed by mergers, as well as smoother accretion flows, because both are mechanisms by which haloes and galaxies grow
and both can provide fuel for star formation. We note, however, that the contribution from mergers is much smaller than that from smooth accretion. Mergers
with mass ratios greater than 1:10 account for only . 10 per cent of the total halo
growth, except in groups and clusters at low redshift (see V11).
The simulations used for this study do not resolve haloes below Mhalo =
1010.8 M⊙ . We are therefore missing contributions to the global accretion rates
and SFR from lower mass haloes. Because we use a fixed maximum past temperature threshold of 105.5 K to distinguish hot from cold accretion (see below),
small haloes with virial temperatures below this threshold will by definition accrete almost all gas in the cold mode. The mass regime that we investigate here
66
Global accretion and star formation
is therefore the most interesting regime, where changes in accretion mode are
expected to occur (Dekel & Birnboim, 2006).
3.3 Global accretion and star formation
Schaye et al. (2010) showed that without feedback from supernovae and AGN,
the SFR density is overpredicted by a large factor at z . 2. By including supernova feedback they could lower the SFR density, but if the predicted SFR density
matched the observed peak at z ≈ 2, then it overpredicted the SFR density at
z = 0. The drop in the global SFR below z = 2 is much closer to the observed
slope if AGN feedback is included, but in that case the SFR density may be
slightly too low (Schaye et al., 2010). This discrepancy could be solved by decreasing the efficiency of feedback from star formation, which had been set to
reproduce the observed peak in the SFH using models without AGN feedback.
It is, however, not clear how seriously we should take the discrepancy, since the
AGN simulation does reproduce the observed masses and ages of the central
galaxies of groups (McCarthy et al., 2010). This would suggest that the problem may be solved by increasing σ8 from 0.74 to the currently favoured value of
0.81, which would have a relatively strong effect on global star formation rates
(see Schaye et al., 2010) while leaving the evolution of haloes of a given mass
nearly unchanged. Because, for the purposes of this work, the AGN simulation
is the most realistic run from the OWLS suite, we will adopt it as our fiducial
model. In Section 3.4 we will discuss how its predictions differ from those of a
simulation without AGN feedback.
The temperature of accreting gas has been found to follow a bimodal distribution (e.g. Kereš et al. 2005; V11). Therefore, two modes of accretion are
considered: the hot and the cold mode. The cooling function peaks at about
T = 105−5.5 K (e.g. Wiersma et al., 2009a), so there is little gas around this temperature. We therefore define hot (cold) accretion as accreted gas with maximum
past temperatures above (below) 105.5 K. Much of the gas that is shock-heated
to much higher temperatures is expected to stay hot for a long time, whilst gas
that is heated to lower temperatures can more easily cool and condense onto the
galaxy.
When considering accretion onto galaxies, it is important to note that the
terms ‘hot’ and ‘cold’ refer to the maximum past temperature rather than the
current temperature. In fact, gas that has been shock-heated to temperatures
in excess of 105.5 K must cool down before it can accrete onto a galaxy, as we
identify this type of accretion as gas joining the ISM, which in our simulations
means that the gas density crosses the threshold of nH = 0.1 cm−3 while the
temperature T ≤ 105 K. Thus, although gas that, according to our terminology
(which is consistent with that used in the literature), is accreted hot onto galaxies
has been hot in the past, it is cold at the time of accretion. In V11 we showed
that the maximum past temperature is usually reached around the time the gas
67
68
The drop in the cosmic SFR below z = 2
Figure 3.1: Evolution of global accretion rate and SFR densities in resolved haloes with well-defined progenitors. The left, middle, and
right panels show global accretion rate densities onto haloes, onto central galaxies, and global SFR densities, respectively. Red and blue
curves show accretion rate densities (left and middle panels) and SFR densities (right panel) resulting from hot- and cold-mode accretion,
respectively. In all panels, the black curve is the sum of the red and blue curves, the green curve shows the global SFR density in the
selected haloes, and the grey curve shows the global SFR density in the entire simulation box. The small ‘step’ visible at z ≈ 4 is caused
by the sudden increase in the time resolution for determining accretion, i.e. ∆z between snapshots decreases by a factor of two at z = 4.
Galaxies accrete most of their gas in the cold mode and this mode is responsible for an even larger fraction of the star formation. Because
of outflows driven by supernovae and AGN, the SFR density is generally lower than the galaxy accretion rate density. The global SFR
declines more rapidly than either the total and hot-mode accretion rate densities. This decline must therefore be caused by the drop in
global cold-mode accretion rate, though with a delay.
Global accretion and star formation
accreted onto the halo.
The global accretion rate density onto haloes, i.e. the gas mass accreting onto
resolved haloes per year and per comoving Mpc3 , is shown in the left panel of
Figure 3.1 by the solid, black curve. The solid, red and blue curves show global
accretion rates for hot- and cold-mode accretion, respectively. These global accretion rate densities are averaged over the time interval between two snapshots.
The SFR density in the haloes we consider is shown by the green curve. The
SFH in the entire box is shown by the dashed, grey curve. It is higher than the
dashed, green curve, because the latter excludes star formation in subhaloes and
unresolved haloes (i.e. Mhalo < 1010.8 M⊙ ).
The global accretion rate onto resolved main haloes (solid, black curve) peaks
at z ≈ 3. It is fairly constant, varying only by about a factor of two from z ≈ 4
down to z ≈ 0. The average accretion rate onto haloes of a given mass decreases
more strongly towards lower redshift (V11). However, the number of haloes at
a fixed mass increases and higher mass haloes form with decreasing redshift.
The combination of these effects results in an almost constant global accretion
rate density. We note, however, that the normalization and shape are not fully
converged with respect to resolution: higher resolution simulations may find
higher total and cold accretion rate densities. Increasing the resolution would
allow us to include haloes with lower masses, which would boost the cold accretion rate density by up to a factor of ∼ 2 − 3. The total accretion rate density
would therefore increase at z & 2, where cold accretion dominates. The global
accretion rate is an order of magnitude higher than the global SFR in the same
haloes (green, dashed curve), indicating that most of the gas that accretes onto
haloes never forms stars.
The global growth of haloes is dominated by cold accretion for z > 2, but
by z = 0 the contribution of the hot mode exceeds that of the cold mode by an
order of magnitude. The cold accretion rate density peaks around z = 3 and
falls rapidly thereafter, while the hot accretion rate density increases down to
z ≈ 2 and flattens off at lower redshifts. The global SFR peaks around z = 2
and declines by an order of magnitude to z = 0. An order of magnitude drop
is also visible for the global cold accretion rate from z = 3 to z = 0. Neither the
total nor the hot accretion rate histories can explain the drop in the cosmic SFH,
which must therefore be driven by the drop in the cold accretion rate.
The middle panel of Figure 3.1 shows the global accretion rates onto central
galaxies. The green and grey curves are identical to the ones shown in the left
panel. The black, red, and blue curves describe the total, hot, and cold accretion
rate densities, respectively. The total accretion rate shows the amount of gas that
joins the ISM. The gas can, however, be removed from the ISM by supernova
and AGN feedback, as well as by dynamical processes. This is why the overall
normalization of the SFR is generally lower than the ISM accretion rate. The
global SFR peaks later than the global galaxy accretion rate (z ≈ 2 versus z ≈ 3,
which corresponds to a difference of ∼ 1 Gyr in the age of the Universe). This
delay probably results from the time it takes to convert interstellar gas into stars.
69
The drop in the cosmic SFR below z = 2
The long gas consumption time scale implied by the assumed, Kennicutt star
formation law (∼ 1 Gyr for typical densities) allows the existence of reservoirs
of accreted gas. The SFR can therefore temporarily be higher than the galaxy
accretion rate, as happens for z < 0.5 (compare the dashed, green curve with
the solid, black curve, which include the same sample of resolved haloes). Gas
returned to the ISM by stellar mass loss, a process that is included in our simulations and that becomes important for z < 1 (Schaye et al., 2010; Leitner &
Kravtsov, 2010), also increases the SFR relative to the accretion rate.
As we did in the left panel of Figure 3.1 for accretion onto haloes, we split
the global accretion rate onto galaxies into separate contributions from the hot
and cold modes. The global hot accretion rate peaks around z = 2, as does the
SFR density. The hot accretion rate is, however, not nearly enough to account
for all the star formation in these galaxies, falling short by at least a factor of 2
at all redshifts. At z > 3, the global cold accretion rate is an order of magnitude
higher than the global hot accretion rate. This difference decreases to ∼ 0.25 dex
by z = 0. At all redshifts, it is mostly cold accretion that allows for the growth of
galaxies, even though hot accretion dominates the growth of haloes below z ≈ 2.
Comparing the middle panel to the left panel, we notice that the global cold
accretion rate onto galaxies is a factor of ∼ 3 − 4 lower than the cold accretion
rate onto haloes. Not all cold gas that accretes onto haloes makes it into the
central galaxy to form stars (see also V11). The shapes of the blue curves are,
however, similar, indicating that the fraction of the gas accreting cold onto the
halo that proceeds to accrete onto the galaxy is roughly constant with time.
The situation is very different for global hot accretion rates (red curves). Hot
accretion onto the ISM has already peaked at z ≈ 2.5, while hot accretion onto
haloes continues to increase down to z = 0. This can be explained by noting that
as the Universe evolves, gas is heated to higher temperatures, because haloes
become more massive. In addition, the average density of the Universe goes
down. The lower densities and higher temperatures gives rise to longer cooling
times. Moreover, winds from supernovae and AGN eject low-entropy gas at
high redshift, raising the entropy of the gas in haloes at low redshift (Crain
et al., 2010a; McCarthy et al., 2011). Hence, as time goes on, more of the halo gas
is unable to cool and reach the central galaxy. While the gravitational potential
is the most important factor for the growth of haloes, for the growth of galaxies,
the cooling function and feedback processes also come into play.
The right panel of Figure 3.1, which shows the global SFR densities due to
hot and cold accretion, confirms that the main fuel for star formation is gas accreted in the cold mode. The difference becomes smaller towards lower redshift.
However, even at z = 0 hot mode gas contributes 0.3 dex less than cold mode
gas.
To investigate which haloes contribute most to the global accretion rates and
SFHs, we show the same quantities as in Figure 3.1 for three different halo mass
bins in Figure 3.2. From top to bottom, the mass ranges are 1011 ≤ Mhalo <
1012 M⊙ , 1012 ≤ Mhalo < 1013 M⊙ , and Mhalo ≥ 1013 M⊙ , which contain 21813,
70
Global accretion and star formation
71
Figure 3.2: Evolution of global accretion rate densities onto haloes (left column), galaxies (middle column), and global SFR densities
(right column) for different halo mass bins. From top to bottom only haloes have been included with: 1011 ≤ Mhalo < 1012 M⊙ , 1012 ≤
Mhalo < 1013 M⊙ , and Mhalo ≥ 1013 M⊙ . The curves show the same quantities as in Figure 3.1. Above z ≈ 3.5 the highest mass bin
contains no haloes. At all redshifts most of the cold halo accretion, galaxy accretion, and star formation happens in low-mass haloes (i.e.
Mhalo < 1012 M⊙ ). At z & 2 low-mass haloes also dominate the global hot halo accretion rates. At z . 1 the total halo accretion rate is
dominated by high-mass haloes, but nearly all of the gas is accreted hot and unable to accrete onto galaxies.
The drop in the cosmic SFR below z = 2
2804, and 285 haloes at z = 0. The shape of the total halo accretion rate density in the lowest mass range is in agreement with that found by Bouché et al.
(2010) based on an extended Press-Schechter formalism and a fit to dark matter
accretion rates in N-body simulations.
For z > 2 the global accretion rate densities onto haloes (left column), galaxies (middle column), and the global star formation rate density (right column)
are all dominated by haloes with Mhalo < 1012 M⊙ (top row). At that time,
higher-mass haloes are still too rare to contribute significantly. Below z ≈ 2
haloes with Mhalo = 1012−13 M⊙ (middle row) begin to contribute significantly
and for accretion onto haloes, but not for accretion onto galaxies or star formation, their contribution is overtaken by Mhalo = 1013−14 M⊙ haloes (bottom row)
around z = 1.
Observe that the global halo accretion rate density starts to decline at z ≈ 3
and z ≈ 2 for the low and middle halo mass bins, respectively, and that it keeps
increasing down to z = 0 for Mhalo ≥ 1013 M⊙ . The global cold accretion rate
density decreases with time for z < 3, z < 2.5, and z < 1 for the low, middle,
and high halo mass bins, respectively.
Both the galaxy accretion rate density and the SFR density are dominated
by Mhalo < 1012 M⊙ haloes at all redshifts. Towards lower redshifts, high-mass
haloes account for larger fractions of the total galaxy accretion rate density and
SFR density, though they never dominate. High-mass haloes do dominate the
halo accretion rate at low redshift, but nearly all of the gas is accreted hot and
only a very small fraction of this gas is subsequently able to cool down onto
galaxies.
3.4 Effect of AGN feedback
It is interesting to see what the influence of AGN feedback is on our results.
Because AGN feedback is more important in higher-mass haloes, for which hotmode accretion is more important, we expect it to have a larger effect on the
hot-mode accretion rate density. Moreover, it has been hypothesized (e.g. Kereš
et al., 2005; Dekel & Birnboim, 2006) that hot, dilute gas may be more vulnerable to AGN feedback than cold streams and may therefore be preferentially
prevented from accreting onto galaxies. Indeed, Theuns et al. (2002) had already
demonstrated that supernova-driven outflows follow the path of least resistance,
leaving the cold filaments that produce HI absorption intact.
McCarthy et al. (2011) have shown that feedback from AGN at high redshift
increases the entropy of the halo gas at low redshift. The hot gas will therefore
be even hotter and less dense at low redshift than it would be in the absence of
AGN feedback, making it more susceptible to being heated or entrained in an
outflow, and thus to being prevented from accreting.
We compare our fiducial simulation, which includes AGN feedback, to the
OWLS ‘reference model’ which is identical to our fiducial run except that it does
72
73
Effect of AGN feedback
Figure 3.3: Evolution of global accretion rate densities onto haloes (left column), galaxies (middle column), and global SFR densities for
simulations with (solid curves, same as in Figure 3.1) and without (dashed curves) AGN feedback. The black, red, and blue curves show
the global accretion and SFR densities from all, hot-mode, and cold-mode accretion, respectively. AGN feedback suppresses halo accretion
only slightly, but the effect on galaxy accretion and star formation is large, up to an order of magnitude. AGN feedback preferentially
suppresses hot-mode galaxy accretion and star formation from gas accreted in the hot mode.
The drop in the cosmic SFR below z = 2
not include black holes and AGN feedback. This allows us to assess the effect
of AGN feedback on the global hot and cold accretion rates. Figure 3.3 shows
the same solid curves as were shown in Figure 3.1. They indicate the total,
hot, and cold accretion rate densities onto haloes (left panel) and onto galaxies
(middle panel) and the star formation rate density resulting from all, hot, and
cold accretion (right panel). The dashed curves show the same global accretion
rates and SFHs for the simulation without AGN feedback. For accretion onto
galaxies and for star formation the differences are striking. When AGN feedback
is excluded, late-time star formation is no longer predominantly fuelled by gas
accreted in the cold mode.
As expected, all accretion rate densities are reduced by the inclusion of AGN
feedback. The effect on halo accretion is, however, small, as was also shown
by V11. The hot and cold halo accretion rate densities are reduced by at most
0.2 and 0.1 dex, respectively. This reduction implies that AGN feedback also affects some gas outside of haloes. Even though the effect is small, AGN feedback
reduces hot halo accretion more than cold halo accretion.
The differential effect of AGN feedback on hot and cold accretion is much
more pronounced for accretion onto galaxies than for accretion onto haloes and
it increases towards lower redshift. At very high redshift (z = 9), Powell et al.
(2011) have shown that outflows (driven by supernova feedback) do not affect
the galaxy inflow rates. Our results indicate that this may change towards lower
redshifts, when densities are much lower. While AGN feedback reduces cold
accretion rate densities by up to 0.4 dex (at z = 0), the hot accretion rate densities
decrease by up to 0.8 dex (also at z = 0). The SFR densities are reduced by up to
0.6 dex for star formation powered by cold-mode accretion, but by 1 dex for hotmode accretion. The reduction due to AGN feedback is thus ∼ 0.4 dex greater
for the hot mode than for the cold mode, both for galaxy accretion and for
star formation. The larger reduction indicates that AGN feedback preferentially,
but not exclusively, prevents hot mode gas from accreting onto galaxies and
participating in star formation.
Hence, the inclusion of AGN feedback strongly boosts the size of the drop
in the cosmic SFR at late times. This preferential suppression of hot accretion
is the result of two effects, namely of the differential effect at a fixed halo mass,
indicating that hot-mode gas is more vulnerable to feedback than cold-mode
gas, and of the fact that AGN feedback is effective only in massive haloes (with
Mhalo & 1012), for which hot accretion is important. The latter is the dominant
effect.
3.5 Conclusions
We have investigated the evolution of the global gas accretion rate densities onto
haloes and onto their central galaxies and we have done so for both the hot
and cold accretion modes. In addition, we studied the contributions from gas
74
Conclusions
accreted through the cold and hot modes to the cosmic star formation history.
We made use of a 100 Mpc/h, 2 × 5123 particle SPH simulation from the OWLS
project that includes radiative cooling (computed element by element and thus
including metal lines), star formation, stellar mass loss, supernova feedback,
and AGN feedback. We isolated the effect of AGN feedback by comparing to a
second simulation that did not include AGN, but which was otherwise identical.
The hot and cold accretion modes were separated by using a fixed maximum
past temperature threshold of Tmax = 105.5 K.
The global gas accretion rate density onto haloes is much higher than that
onto galaxies and both rates exceed the cosmic SFR density. This confirms the
finding of V11 that most of the gas accreting onto haloes does not result in star
formation. This is the case for both accretion modes, but the differences are
larger for the hot mode.
The global SFR declines after z ≈ 2, whereas the global hot-mode accretion
rate onto haloes shows no such trend. From this, we conclude that the global
SFR follows the drop in the global cold-mode accretion rate onto haloes, which
sets in at z ≈ 3, but with a delay of order the gas consumption time scale in the
ISM. Star formation tracks cold-mode accretion rather than hot-mode accretion
because cold streams can reach the central galaxy, where star formation takes
place, much more easily than gas that is shock-heated to high temperatures near
the virial radius. Much of the hot gas cannot cool within a Hubble time and
therefore cannot accrete onto the central galaxy. In addition, we demonstrated
that it is very important that hot gas is more susceptible to removal by outflows
driven by feedback from AGN. Without AGN feedback, gas accreted in the hot
mode contributes significantly to the cosmic SFR below z = 1 and the drop in
the SFR below z = 2 would be much smaller.
For the hot mode the difference between the accretion rates onto haloes and
onto galaxies is larger at lower redshifts. While the hot accretion mode dominates the growth of haloes by an order of magnitude at z ≈ 0, it is still less
important than cold accretion for the growth of the central galaxies. At z > 2,
cold accretion even dominates the global accretion rate onto haloes.
We demonstrated that AGN feedback suppresses accretion onto galaxies and
that it does so much more efficiently for the hot mode than for the cold mode.
This happens because AGN feedback only becomes more efficient than feedback
from star formation in high-mass haloes, which are dominated by hot accretion,
and because hot-mode gas is more dilute and therefore more vulnerable to feedback. In addition, as demonstrated by McCarthy et al. (2011), by ejecting lowentropy halo gas at high redshift (z & 2), AGN feedback results in an increase
of the entropy, and thus a reduction of the cooling rates, of hot halo gas at low
redshift.
While Kereš et al. (2009a) did not investigate accretion onto haloes, they did
also find that cold accretion is most important for the growth of galaxies, with
hot accretion becoming increasingly important towards lower redshifts (see also
Kereš et al. 2005; Ocvirk et al. 2008; Brooks et al. 2009; V11). However, their
75
The drop in the cosmic SFR below z = 2
simulation included neither winds from supernovae nor feedback from AGN.
AGN feedback was in fact ignored by all previous cosmological simulations
investigating gas accretion except for Khalatyan et al. (2008), who simulated a
single object, and except for V11. Our results suggest that the neglect of this
important process leads to a strong overestimate of the global accretion rate
and SFR densities and of the importance of the hot accretion mode for galaxy
accretion and star formation.
In summary, the rapid decline in the cosmic SFR density below z = 2 is
driven by the corresponding drop in the cold accretion rate density onto haloes.
The total accretion rate onto haloes falls off much less rapidly because the hot
mode becomes increasingly important. AGN feedback, which acts preferentially
on gas accreted in the hot mode, prevents the hot halo gas from accreting onto
galaxies and forming stars and is therefore a crucial factor in the steep decline
of the cosmic SFR density.
Acknowledgements
We would like to thank Avishai Dekel and all the members of the OWLS team for
valuable discussions and the anonymous referee for useful comments. The simulations presented here were run on Stella, the LOFAR BlueGene/L system in
Groningen, on the Cosmology Machine at the Institute for Computational Cosmology in Durham as part of the Virgo Consortium research programme, and
on Darwin in Cambridge. This work was sponsored by the National Computing
Facilities Foundation (NCF) for the use of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research (NWO),
also through a VIDI grant, and from the Marie Curie Initial Training Network
CosmoComp (PITN-GA-2009-238356).
76
4
Properties of gas in and around
galaxy haloes
We study the properties of gas inside and around galaxy haloes as a function
of radius and halo mass, focusing mostly on z = 2, but also showing some
results for z = 0. For this purpose, we use a suite of large cosmological, hydrodynamical simulations from the OverWhelmingly Large Simulations project.
The properties of cold- and hot-mode gas, which we separate depending on
whether the temperature has been higher than 105.5 K while it was extragalactic,
are clearly distinguishable in the outer parts of massive haloes (virial temperatures ≫ 105 K). The differences between cold- and hot-mode gas resemble those
between inflowing and outflowing gas. The cold-mode gas is mostly confined to
clumpy filaments that are approximately in pressure equilibrium with the diffuse, hot-mode gas. Besides being colder and denser, cold-mode gas typically
has a much lower metallicity and is much more likely to be infalling. However,
the spread in the properties of the gas is large, even for a given mode and a
fixed radius and halo mass, which makes it impossible to make strong statements about individual gas clouds. Metal-line cooling causes a strong cooling
flow near the central galaxy, which makes it hard to distinguish gas accreted
through the cold and hot modes in the inner halo. Stronger feedback results in
larger outflow velocities and pushes hot-mode gas to larger radii. The gas properties evolve as expected from virial arguments, which can also account for the
dependence of many gas properties on halo mass. We argue that cold streams
penetrating hot haloes are observable as high-column density H i Lyman-α absorption systems in sightlines near massive foreground galaxies.
Freeke van de Voort & Joop Schaye
Monthly Notices of the Royal Astronomical Society
Submitted (2012), arXiv:1111.5039
Gas properties in and around haloes
4.1 Introduction
The gaseous haloes around galaxies grow by accreting gas from their surroundings, the intergalactic medium, which is the main reservoir for baryons. The
galaxies themselves grow by accreting gas from their haloes, from which they
can form stars. Some of the gas is, however, returned to the circumgalactic
medium by galactic winds driven by supernovae (SNe) or active galactic nuclei
(AGN) and by dynamical processes such as tidal or ram pressure forces. Such
interactions between the different gas phases are essential for galaxy formation
and evolution.
The physical state of the gas in and around haloes will determine how fast
galaxies grow. Quantifying and understanding the properties of the gas is therefore vital for theories of galaxy formation. It is also crucial for making predictions and for the interpretation of observations as the physical state of the gas
determines how much light is absorbed and emitted.
Theoretical and computational studies of the accretion of gas onto galaxies
have revealed the existence of two distinct modes. In the first mode the inflowing
gas experiences an accretion shock as it collides with the hot, hydrostatic halo
near the virial radius. At that point it is shock-heated to temperatures similar
to the virial value and typically remains part of the hot halo for longer than a
dynamical time. If it reaches a sufficiently high density, it can cool radiatively
and settle into a disc (e.g. Rees & Ostriker, 1977; White & Rees, 1978; Fall &
Efstathiou, 1980). This mode is referred to as ‘hot-mode accretion’ (Katz et al.,
2003; Kereš et al., 2005). If, on the other hand, the cooling time of the gas is short
compared to the dynamical time, which is the case for haloes of sufficiently low
mass, a hot halo is unable to form and the accreting gas will not go through a
shock near the virial radius. The accretion rate then depends on the infall rate
instead of on the cooling rate (White & Frenk, 1991; Birnboim & Dekel, 2003;
Dekel & Birnboim, 2006). Additionally, simulations have shown that much of
the gas enters the halo along dense filaments or in clumps, which gives rise
to short cooling times, even in the presence of a hot, hydrostatic halo. This
denser gas does not go through an accretion shock near the virial radius and
will therefore remain cold until it accretes onto the central galaxy or is hit by an
outflow (e.g. Kereš et al., 2005; Dekel et al., 2009a; van de Voort et al., 2011a). We
refer to this mode as ‘cold-mode accretion’ (Katz et al., 2003; Kereš et al., 2005).
Hot- and cold-mode accretion play very different roles in the formation of
galaxies and their gaseous haloes (Kereš et al., 2005; Ocvirk et al., 2008; Kereš
et al., 2009a,b; Brooks et al., 2009; Dekel et al., 2009a; Crain et al., 2010a; van de
Voort et al., 2011a,b; Powell et al., 2011; Faucher-Giguère et al., 2011). It has been
shown that cold-mode accretion is more important at high redshift, when the
density of the Universe is higher. Hot-mode accretion dominates the fuelling
of the gaseous haloes of high-mass systems (halo mass > 1012 M⊙ ; e.g. Ocvirk
et al., 2008; van de Voort et al., 2011a). The importance of hot-mode accretion is
much reduced when considering accretion onto galaxies (as opposed to haloes)
78
Introduction
(Kereš et al., 2009a; van de Voort et al., 2011a). At z ≥ 1 all galaxies accrete
more than half of their material in the cold mode, although the contribution of
hot-mode accretion is not negligible for high-mass haloes. Cold-mode accretion
provides most of the fuel for star formation and shapes the cosmic star formation
rate density (van de Voort et al., 2011b).
van de Voort et al. (2011a,b) investigated the roles of feedback mechanisms
on the gas accretion. They found that while the inclusion of metal-line cooling
has no effect on the accretion onto haloes, it does increase the accretion rate onto
galaxies, because it decreases the cooling time of the hot halo gas. Feedback
from SNe and AGN can reduce the accretion rates onto haloes by factors of a
few, but accretion onto galaxies is suppressed by up to an order of magnitude.
The inclusion of AGN feedback is particularly important for suppressing hotmode accretion onto galaxies, because it is mainly effective in high-mass haloes
and because diffuse gas is more susceptible to outflows.
Hot, hydrostatic halo gas is routinely studied using X-ray observations of
galaxy groups and clusters and has perhaps even been detected around individual galaxies (e.g. Crain et al., 2010a,b; Anderson & Bregman, 2011). As of yet,
there is no direct observational evidence for cold-mode accretion, even though
there are claims of individual detections in H i absorption based on the low
metallicity and proximity to a galaxy of the absorption system (Ribaudo et al.,
2011; Giavalisco et al., 2011). Cosmological simulations can reproduce the observed H i column density distribution (Altay et al., 2011). They show that coldmode accretion is responsible for much of the observed high column density H i
absorption at z ∼ 3. In particular, most of the detected Lyman limit and low column density damped Lyman-α absorption may arise in cold accretion streams
(Fumagalli et al., 2011a; van de Voort et al., 2012).
It has also been claimed that the diffuse Lyman-α emission detected around
some high-redshift galaxies is powered by cold accretion (e.g. Fardal et al., 2001;
Dijkstra & Loeb, 2009; Goerdt et al., 2010; Rosdahl & Blaizot, 2011), but both
simulations and observations indicate that the emission is more likely scattered
light from central H ii regions (e.g. Furlanetto et al., 2005; Faucher-Giguère et al.,
2010; Steidel et al., 2010; Hayes et al., 2011; Rauch et al., 2011).
The temperature is, however, not the only difference between the two accretion modes. In this paper we use the suite of cosmological hydrodynamical simulations from the OverWhelmingly Large Simulations project (OWLS; Schaye
et al., 2010) to investigate other physical properties, such as the gas density,
pressure, entropy, metallicity, radial peculiar velocity, and accretion rate of the
gas in the two modes. We will study the dependence of gas properties on radius
for haloes of total mass ∼ 1012 M⊙ and the dependence on halo mass of the
properties of gas just inside the virial radius. Besides contrasting the hot and
cold accretion modes, we will also distinguish between inflowing and outflowing gas. While most of our results will be presented for z = 2, when both hotand cold-mode accretion are important for haloes of mass ∼ 1012 M⊙ , we will
also present some results for z = 0, which are therefore directly relevant for ob79
Gas properties in and around haloes
servations of gas around the Milky Way. We will make use of the different OWLS
runs to investigate how the results vary with the efficiency of the feedback and
the cooling.
This paper is organized as follows. The simulations are described in Section 4.2, including the model variations, the way in which haloes are identified,
and our method for distinguishing gas accreting in the hot and cold modes. In
Sections 4.3 and 4.4 we study the radial profiles and the dependence on halo
mass, respectively. In Section 4.5 we discuss the difference in physical properties between inflowing and outflowing gas. We assess the effect of metal-line
cooling and feedback from SNe and AGN on the gas properties in Section 4.6.
In Section 4.7 we study the properties of gas around Milky Way-sized galaxies
at z = 0. Finally, we discuss and summarize our conclusions in Section 4.8.
4.2 Simulations
To investigate the gas properties in and around haloes, we make use of simulations taken from the OWLS project (Schaye et al., 2010), which consists of a large
number of cosmological simulations, with varying (subgrid) physics. Here, we
make use of a subset of these simulations. We first summarize the reference
simulation, from which we derive our main results. The other simulations are
described in Section 4.2.1. For a full description of the simulations, we refer
the reader to Schaye et al. (2010). Here, we will only summarize their main
properties.
We use a modified version of gadget-3 (last described in Springel, 2005b), a
smoothed particle hydrodynamics (SPH) code that uses the entropy formulation
of SPH (Springel & Hernquist, 2002), which conserves both energy and entropy
where appropriate.
All the cosmological simulations used in this work assume a ΛCDM cosmology with parameters derived from the WMAP year 3 data, Ωm = 1 − ΩΛ =
0.238, Ωb = 0.0418, h = 0.73, σ8 = 0.74, n = 0.951 (Spergel et al., 2007). These
values are consistent1 with the WMAP year 7 data (Komatsu et al., 2011). The
primordial abundances are X = 0.752 and Y = 0.248, where X and Y are the
mass fractions of hydrogen and helium, respectively.
A cubic volume with periodic boundary conditions is defined, within which
the mass is distributed over N 3 dark matter and as many gas particles. The
box size (i.e. the length of a side of the simulation volume) of the simulations
used in this work are 25, 50, and 100 h−1 Mpc, with N = 512. The (initial)
3
particle masses for baryons and dark matter are 1.5 × 107 ( 50 hL−box
1 Mpc ) M⊙ and
3
7.0 × 107 ( 50 hL−box
1 Mpc ) M⊙ , respectively, and are listed in Table 4.1. We use the
notation L***N###, where *** indicates the box size in comoving Mpc/h and
1
The most significant discrepancy is in σ8 , which is 8 per cent, or 2.3σ, lower than the value
favoured by the WMAP 7-year data.
80
Table 4.1: Simulation parameters: simulation identifier, comoving box size (Lbox ), number of dark matter particles (N, the number of
baryonic particles is equal to the number of dark matter particles), mass of dark matter particles (mDM ), initial mass of gas particles
11.5 M < M
12.5 M , and number of haloes with more than 100 dark matter particles.
(minitial
⊙
⊙
halo < 10
gas ), number of haloes with 10
simulation
L100N512
L050N512
L025N512
Lbox
−
1
(h Mpc)
100
50
25
N
5123
5123
5123
mDM
(M⊙ )
5.56 × 108
6.95 × 107
8.68 × 106
minitial
gas
(M⊙ )
1.19 × 108
1.48 × 107
1.85 × 106
1011.5
number of haloes with
M⊙ < Mhalo < 1012.5 M⊙
4407 (z = 2)
518 (z = 2); 1033 (z = 0)
59 (z = 2)
number of resolved haloes
at z = 2
32167
32663
25813
Simulations
81
Gas properties in and around haloes
### the number of particles per dimension. The gravitational softening length
−1 comoving kpc, i.e. 1/25 of the mean dark matter
is initially 3.9 ( 50 hL−box
1 Mpc ) h
−1 kpc proper.
particle separation, but we imposed a maximum of 1 ( 50 hL−box
1 Mpc ) h
We use simulation REF_L050N512 for our main results. The L025N512 simulations are used for images, for comparisons between simulations with different
subgrid physics, and for resolution tests. The L100N512 run is only used for the
convergence tests shown in the Appendix.
The abundances of eleven elements (hydrogen, helium, carbon, nitrogen,
oxygen, neon, magnesium, silicon, sulphur, calcium, and iron) released by massive stars (type II SNe and stellar winds) and intermediate mass stars (type Ia
SNe and asymptotic giant branch stars) are followed as described in Wiersma
et al. (2009b). We assume the stellar initial mass function (IMF) of Chabrier
(2003), ranging from 0.1 to 100 M⊙ . As described in Wiersma et al. (2009a), radiative cooling and heating are computed element-by-element in the presence
of the cosmic microwave background radiation and the Haardt & Madau (2001)
model for the UV/X-ray background from galaxies and quasars. The gas is
assumed to be optically thin and in (photo)ionization equilibrium.
Star formation is modelled according to the recipe of Schaye & Dalla Vecchia (2008). The Jeans mass cannot be resolved in the cold, interstellar medium
(ISM), which could lead to artificial fragmentation (e.g. Bate & Burkert, 1997).
Therefore, a polytropic equation of state Ptot ∝ ρ4/3
gas is implemented for densities
exceeding nH = 0.1 cm−3 , where Ptot is the total pressure and ρgas the density
of the gas. This equation of state makes the Jeans mass, as well as the ratio of
the Jeans length and the SPH smoothing kernel, independent of the density. Gas
particles whose proper density exceeds nH ≥ 0.1 cm−3 while they have temperatures T ≤ 105 K are moved on to this equation of state and can be converted into
star particles. The star formation rate per unit mass depends on the gas pressure
and is set to reproduce the observed Kennicutt-Schmidt law (Kennicutt, 1998).
Feedback from star formation is implemented using the prescription of Dalla
Vecchia & Schaye (2008). About 40 per cent of the energy released by type II
SNe is injected locally in kinetic form. The rest of the energy is assumed to be
lost radiatively. Each gas particle within the SPH smoothing kernel of the newly
formed star particle has a probability of being kicked. For the reference model,
the mass loading parameter η = 2, meaning that, on average, the total mass of
the particles being kicked is twice the mass of the star particle formed. Because
the winds sweep up surrounding material, the effective mass loading can be
much higher. The initial wind velocity is 600 km s−1 for the reference model.
Schaye et al. (2010) showed that these parameter values yield a peak global star
formation rate density that agrees with observations.
82
Simulations
Table 4.2: Simulation parameters: simulation identifier, cooling including metals (Z
cool), initial wind velocity (vwind ), initial wind mass loading (η), AGN feedback included
(AGN). Differences from the reference model are indicated in bold face.
simulation
REF
NOSN_NOZCOOL
NOZCOOL
WDENS
AGN
Z cool
yes
no
no
yes
yes
vwind
η
(km s−1 )
600
2
0
0
600
2
density dependent
600
2
AGN
no
no
no
no
yes
4.2.1 Variations
To investigate the effect of feedback and metal-line cooling, we have performed
a suite of simulations in which the subgrid prescriptions are varied. These are
listed in Table 4.2.
The importance of metal-line cooling can be demonstated by comparing the
reference simulation (REF) to a simulation in which primordial abundances are
assumed when calculating the cooling rates (NOZCOOL). We also performed a
simulation in which both cooling by metals and feedback from SNe were omitted
(NOSN_NOZCOOL). To study the effect of SN feedback, this simulation can be
compared to (NOZCOOL).
In massive haloes the pressure of the ISM is too high for winds with velocities
of 600 km s−1 to blow the gas out of the galaxy (Dalla Vecchia & Schaye, 2008).
To make the winds effective at higher halo masses, the velocity can be scaled
with the local sound speed, while adjusting the mass loading so as to keep the
energy injected per unit stellar mass constant at ≈ 40 per cent (WDENS).
Finally, we have included AGN feedback (AGN). Black holes grow via mergers and gas accretion and inject 1.5 per cent of the rest-mass energy of the accreted gas into the surrounding matter in the form of heat. The model is based
on the one introduced by Springel et al. (2005) and is described and tested in
Booth & Schaye (2009), who also demonstrate that the simulation reproduces
the observed mass density in black holes and the observed scaling relations between black hole mass and central stellar velocity dispersion and between black
hole mass and stellar mass. McCarthy et al. (2010) have shown that model AGN
reproduces the observed stellar mass fractions, star formation rates, and stellar
age distributions in galaxy groups, as well as the thermodynamic properties of
the intragroup medium.
83
Gas properties in and around haloes
4.2.2 Identifying haloes
The first step towards finding gravitationally bound structures is to identify dark
matter haloes. These can be found using a Friends-of-Friends (FoF) algorithm.
If the separation between two dark matter particles is less than 20 per cent of
the average separation (the linking length b = 0.2), they are placed in the same
group. Baryonic particles are linked to a FoF halo if their nearest dark matter
neighbour is in that halo. We then use subfind (Dolag et al., 2009) to find the
most bound particle of a FoF halo, which serves as the halo centre. In this
work we use a spherical overdensity criterion, considering all the particles in the
simulation. We compute the virial radius, Rvir , within which the average density
agrees with the prediction of the top-hat spherical collapse model in a ΛCDM
cosmology (Bryan & Norman, 1998). At z = 2 this corresponds to a density of
ρ = 169hρi.
We include only haloes containing more than 100 dark matter particles in our
analysis, corresponding to a minimum dark matter halo mass of Mhalo = 1010.7,
109.8, and 108.9 M⊙ in the 100, 50, and 25 h−1 Mpc box, respectively. For these
limits our mass functions agree very well with the Sheth & Tormen (1999) fit.
Table 4.1 lists, for each simulation of the reference model, the number of haloes
with mass 1011.5 M⊙ < Mhalo < 1012.5 M⊙ and the number of haloes with more
than 100 dark matter particles.
4.2.3 Hot- and cold-mode gas
During the simulations the maximum past temperature, Tmax, was stored in a
separate variable. The variable was updated for each SPH particle at every time
step for which the temperature was higher than the previous maximum past
temperature. The artificial temperature the particles obtain when they are on
the equation of state (i.e. when they are part of the unresolved multiphase ISM)
was ignored in this process. This may cause us to underestimate the maximum
past temperature of gas that experienced an accretion shock at densities nH >
0.1 cm−3 . Ignoring such shocks is, however, consistent with our aims, as we
are interested in the maximum temperature reached before the gas entered the
galaxy. Note, however, that the maximum past temperature of some particles
may reflect shocks in outflowing rather than accreting gas.
Another reason why Tmax may underestimate the true maximum past temperature, is that in SPH simulations a shock is smeared out over a few smoothing
lengths, leading to in-shock cooling (Hutchings & Thomas, 2000). If the cooling
time is of the order of, or smaller than, the time step, then the maximum temperature will be underestimated. Creasey et al. (2011) have shown that a particle
mass of 106 M⊙ is sufficient to avoid numerical overcooling of accretion shocks
onto haloes, like in our high-resolution simulations (L025N512). The Appendix
shows that our lower-resolution simulations give very similar results.
Even with infinite resolution, the post-shock temperatures may, however, not
84
Dependence on radius
be well defined. Because electrons and protons have different masses, they will
have different temperatures in the post-shock gas and it may take some time
before they equilibrate through collisions or plasma effects. We have ignored this
complication. Another effect, which was also not included in our simulation, is
that shocks may be preceded by the radiation from the shock, which may affect
the temperature evolution. Disregarding these issues, van de Voort et al. (2011a)
showed that the distribution of Tmax is bimodal and that a cut at Tmax = 105.5 K
naturally divides the gas into cold- and hot-mode accretion and that it produces
similar results as studies based on adaptive mesh refinement simulations (Ocvirk
et al., 2008). This Tmax threshold was chosen because the cooling function peaks
at 105−5.5 K (e.g. Wiersma et al., 2009a), which results in a minimum in the
temperature distribution. Additionally, the UV background can only heat gas
to about 105 K, which is therefore characteristic for cold-mode accretion. In this
work we use the same Tmax = 105.5 K threshold to separate the cold and hot
modes.
4.3 Physical properties: dependence on radius
The gas in the Universe is distributed in a cosmic web of sheets, filaments, and
haloes. The filaments also affect the structure of the haloes that reside inside
them or at their intersections. At high redshift, cold, narrow streams penetrate
hot haloes and feed galaxies efficiently (e.g. Kereš et al., 2005; Dekel & Birnboim,
2006; Agertz et al., 2009; Ceverino et al., 2010; van de Voort et al., 2011a). The
middle row of Figure 4.1 shows the overdensity in several haloes with different
masses, ranging from Mhalo = 1012.5 (left panel) to 1010.5 M⊙ (right panel), taken
from the high-resolution reference simulation (REF_L025N512) at z = 2. Each
image is four virial radii on a side, so the physical scale decreases with decreasing halo mass, as indicated in the middle panels. To illustrate the morphologies
of gas that was accreted in the different modes, we show the density of the coldand hot-mode gas separately in the top and bottom panels, respectively. The
spatial distribution is clearly different. Whereas the cold-mode gas shows clear
filaments and many clumps, the hot-mode gas is much more spherically symmetric and smooth, particularly for the higher halo masses. The filaments become broader, relative to the size of the halo, for lower mass haloes. In high-mass
haloes, the streams look disturbed and some fragment into small, dense clumps,
whereas they are broad and smooth in low-mass haloes. Cold-mode accretion is
clearly possible in haloes that are massive enough to have well-developed virial
shocks if the density of the accreting gas is high, which is the case when the gas
accretes along filaments or in clumps.
Figure 4.2 shows several physical quantities for the gas in a cubic 1 h−1 comoving Mpc region, which is about four times the virial radius, centred on the
1012 M⊙ halo from Figure 4.1. These properties are (from the top-left to the
bottom-right): gas overdensity, temperature, maximum past temperature, pres85
86
Gas properties in and around haloes
Figure 4.1: Gas overdensity at z = 2 in and around haloes with, from left to right, Mhalo = 1012.5 , 1012 , 1011.5 , 1011 , and 1010.5 M⊙ taken
from the simulation REF_L025N512. All images show projections of the gas density in cubes of 4 virial radii on a side. The proper sizes of
the images are indicated in the panels of the middle row. In the middle column all gas was included. In the top (bottom) row we have only
included cold- (hot-)mode gas, i.e. gas with Tmax < 105.5 K (Tmax ≥ 105.5 K). The filaments, streams, and dense clumps consist of gas that
has never been heated to temperatures greater than 105.5 K.
Dependence on radius
87
Figure 4.2: From the top-left to the bottom-right: gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity,
radial peculiar velocity, radial mass flux (in solar mass per year per proper Mpc2 ), and hot fraction in a cubic 1 h−1 comoving Mpc region
centred on a halo of Mhalo ≈ 1012 M⊙ at z = 2 taken from the REF_L025N512 simulation. The white circles indicate the virial radius.
Gas properties in and around haloes
sure, entropy, metallicity, radial peculiar velocity, radial mass flux, and finally the
“hot fraction” which we define as the mass fraction of the gas that was accreted
in the hot mode (i.e. that has Tmax ≥ 105.5 K). The properties are mass-weighted
and projected along the line of sight. The virial radius is 264 h−1 comoving kpc
and is indicated by the white circles.
In Figure 4.3 we show the same quantities as in Figure 4.2 as a function of
radius for the haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 2 in simulation
REF_L050N512. The black curves show the median values for all gas, except for
the last two panels which show the mean values. The red (blue) curves show the
median or mean values for hot- (cold-)mode gas, i.e. gas with maximum past
temperatures above (below) 105.5 K. The shaded regions show values within the
16th and 84th percentiles. Hot-mode gas at radii larger than 2Rvir is dominated
by gas associated with other haloes and/or large-scale filaments.
All the results we show are weighted by mass. In other words, we stacked all
518 haloes in the selected mass range using R/Rvir as the radial coordinate. The
black curves in Figure 4.3 (except for the last two panels) then show the values
of the corresponding property (e.g. the gas overdensity in the top-left panel)
that divide the total mass in each radial bin in half, i.e. half the mass lies above
the curve. We have done the same analysis for volume-weighted quantities by
computing, as a function of radius, the values of each property that divides the
total volume, i.e. the sum of mgas /ρ, in half but we do not show the results.
The volume is completely dominated by hot-mode gas out to twice the virial
radius, reaching 50 per cent at 3Rvir . Even though the volume-weighted hot
fraction is very different, the properties of the gas and the differences between
the properties of hot- and cold-mode gas are similar if we weigh by volume
rather than mass.
We find that the median density of cold-mode gas is higher, by up to 1 dex,
than that of hot-mode gas and that its current temperature is lower, by up to
2 dex, at least beyond 0.2Rvir . The hot-mode maximum past temperature is on
average about an order of magnitude higher than the cold-mode maximum past
temperature. The median pressure of the hot-mode gas only exceeds that of the
cold mode by a factor of a few, but for the entropy the difference reaches 2.5 dex.
For R & Rvir the gas metallicity in the cold mode is lower and has a much larger
spread (four times larger at Rvir ) than in the hot mode. Cold-mode gas is flowing
in at much higher velocities, by up to 150 km s−1 , and dominates the accretion
rate at all radii. Below, we will discuss these gas properties individually and in
more detail.
4.3.1 Density
The halo shown in Figure 4.2 is being fed by dense, clumpy filaments as well as
by cooling diffuse gas. The filaments are overdense for their radius, both inside
and outside the halo. The top-left panel of Figure 4.3 shows that the overdensity
of both hot- and cold-mode gas increases with decreasing radius, from ∼ 10 at
88
Dependence on radius
89
Figure 4.3: Properties of gas in haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 2 as a function of radius for all (black curves), hot-mode
(red curves), and cold-mode (blue curves) gas. Results are shown for the simulation REF_L050N512. Shaded regions show values within
the 16th and 84th percentiles, i.e., the ±1σ scatter around the median. From the top-left to the bottom-right, the different panels show the
mass-weighted median gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity, radial peculiar velocity,
the mean accretion rate, and the mean mass fraction of hot-mode gas, respectively.
Gas properties in and around haloes
10Rvir to ∼ 102 at Rvir and to 104 at 0.1Rvir . The median density of cold-mode gas
is higher by up to an order of magnitude than that of hot-mode gas for all radii
0.1Rvir < R < 4Rvir . The cold-mode gas densities exhibit a significant scatter of
about 2 dex, as opposed to about 0.4 dex for hot-mode gas at Rvir , which implies
that the cold-mode gas is much clumpier. Beyond 4Rvir the median hot-mode
density becomes higher than for the cold mode, because there the hot-mode gas
is associated with different haloes and/or large-scale filaments, which are also
responsible for heating the gas.
4.3.2 Temperature
Hot gas, heated either by accretion shocks or by SN feedback, extends far beyond
the virial radius (top-middle of Figure 4.2). Most of the volume is filled with hot
gas. The location of cold gas overlaps with that of dense gas, so the temperature
and density are anti-correlated. This anti-correlation is a result of the fact that
the cooling time deceases with the gas density.
For R & 0.2Rvir the temperatures of the hot- and cold-mode gas do not vary
strongly with radius (top middle panel of Figure 4.3). Note that this panel shows
the current temperature and not the maximum past temperature. Gas accreted
in the hot mode has a temperature ∼ 106 K at R > 0.2Rvir , which is similar to
the virial temperature. The median temperature of the hot-mode gas increases
slightly from ≈ 2Rvir to ≈ 0.2Rvir because the hot gas is compressed as it falls in.
Within 0.5Rvir the scatter increases and around 0.2Rvir the median temperature
drops sharply to ∼ 104 K. The dramatic decrease in the temperature of the hotmode gas is a manifestation of the strong cooling flow that results when the
gas has become sufficiently dense to radiate away its thermal energy within a
dynamical time. The median temperature of cold-mode gas peaks at slightly
below 105 K around 2Rvir and decreases to ∼ 104 K at 0.1 Rvir . The peak in
the temperature of the cold-mode gas is determined by the interplay between
photo-heating by the UV background and radiative cooling. The temperature
difference between the two accretion modes reaches a maximum of about 2 dex
at 0.3Rvir and vanishes around 0.1Rvir .
4.3.3 Maximum past temperature
The maximum past temperature (top-right panel of Figure 4.2) is by definition
at least as high as the current temperature, but its spatial distribution correlates
well with that of the current temperature. As shown by Figure 4.3, the difference
between maximum past temperature and current temperature is small at R &
Rvir , but increases towards smaller radii and becomes 1 dex for cold-mode gas
and 2 dex for hot-mode gas at 0.1Rvir .
While the temperature of the cold-mode gas decreases with decreasing radius, its maximum past temperature stays constant at Tmax ≈ 105 K. This value
of Tmax is reached around 2Rvir as a result of heating by the UV background.
90
Dependence on radius
Both the current and the maximum past temperature of the hot-mode gas increase with decreasing radius for R > 0.3Rvir . The fact that Tmax decreases
below 0.3Rvir shows that it is, on average, the colder part of the hot-mode gas
that can reach these inner radii. If it were a random subset of all the hot-mode
gas, then Tmax would have stayed constant.
4.3.4 Pressure
As required by hydrostatic equilibrium, the gas pressure generally increases
with decreasing radius (middle-left panels of Figures 4.2 and 4.3). However, the
median pressure profile (Figure 4.3) does show a dip around 0.2 − 0.3Rvir that
reflects the sharp drop in the temperature profiles. Here catastrophic cooling
leads to a strong cooling flow and thus a breakdown of hydrostatic equilibrium.
Comparing the pressure map with those of the density and temperature,
the most striking difference is that the filaments become nearly invisible inside
the virial radius, whereas they stood out in the density and temperature maps.
However, beyond the virial radius the filaments do have a higher pressure than
the diffuse gas. This suggests that pressure equilibrium is quickly established
after the gas accretes onto the haloes.
Figure 4.3 shows that the difference between the pressures of the hot- and
cold-mode gas increases beyond 2Rvir . This is because at these large radii the
hot-mode gas is associated with other haloes and/or large-scale filaments, while
the cold-mode gas is intergalactic, so we do not expect them to be in pressure
equilibrium. Moving inwards from the virial radius, the median pressure difference increases until it reaches about an order of magnitude at 0.3Rvir . At
smaller radii the pressures become nearly the same because the hot-mode gas
cools down to the same temperature as the cold-mode gas.
Although it takes some time to reach pressure equilibrium if the hot gas is
suddenly heated, we expect the hot and cold gas to be approximately in equilibrium inside the halo, because a phase with a higher pressure will expand,
lowering its pressure, and compressing the phase with the lower pressure, until
equilibrium is reached. While the pressure distributions do overlap, there is still
a significant difference between the two. This difference decreases somewhat
with increasing resolution, because the cold gas reaches higher densities and
thus higher pressures, as is shown in the Appendix. From the example pressure
map (Figure 4.2) we can see that the filaments inside the halo are in fact approximately in pressure equilibrium with the diffuse gas around them. At first sight
this seems at odds with the fact that the median pressure profiles are different.
However, the pressure map also reveals an asymmetry in the pressure inside
the halo, with the gas to the left of the centre having a higher pressure than the
gas to the right of the centre. Because there is also more hot-mode gas to the
left, this leads to a pressure difference between the two modes when averaged
over spherical shells, even though the two phases are locally in equilibrium. The
asymmetry arises because the hot-mode gas is a space-filling gas and the flow
91
Gas properties in and around haloes
has to converge towards the centre of the halo, which increases its pressure. The
cold-mode gas is not space filling and therefore does not need to compress as
much.
4.3.5 Entropy
We define the entropy as
S≡
P(µmH )5/3
,
kB ρ5/3
(4.1)
where µ is the mean molecular weight, mH is the mass of a hydrogen atom,
and kB is Boltzmann’s constant. Note that the entropy remains invariant for
adiabatic processes. In the central panel of Figure 4.2 we clearly see that the
filaments have much lower entropies than the diffuse gas around them. This is
expected for cold, dense gas.
For R > Rvir the median entropy of hot-mode gas is always higher than that
of cold-mode gas (Figure 4.3). While the entropy of the cold-mode gas decreases
smoothly and strongly towards the centre of the halo, the entropy of the hotmode gas decreases only slightly down to 0.2Rvir after which it drops steeply.
Cold-mode gas cools gradually, but hot-mode gas cannot cool until it reaches
high enough densities, which results in a strong cooling flow.
4.3.6 Metallicity
The middle-right panels of Figures 4.2 and 4.3 show that the cold-mode streams
have much lower metallicities than the diffuse, hot-mode gas, at least for R &
Rvir . The cold-mode gas also has a much larger spread in metallicity, four orders
of magnitude at Rvir , as opposed to only one order of magnitude for hot-mode
gas.
The gas in the filaments tends to have a lower metallicity, because most of it
has never been close to a star-forming region, nor has it been affected by galactic
winds, which tend to avoid the filaments (Theuns et al., 2002). The radial velocity
image in the bottom-left panel of Figure 4.2 confirms that the winds take the
path of least resistance. The cold mode also includes dense clumps, which show
a wide range of metallicities. If the density is high enough for embedded star
formation to occur, then this can quickly enrich the entire clump. The enhanced
metallicity will increase its cooling rate, making it even more likely to accrete
in the cold mode (recall that our definition of the maximum past temperature
ignores shocks in the ISM). On the other hand, clumps that have not formed stars
remain metal-poor. The metallicity spread is thus caused by a combination of
being shielded from winds driven by the central galaxy and exposure to internal
star formation.
At Rvir the median metallicity of the gas is subsolar, Z ∼ 10−1 Z⊙ for hotmode gas and Z ∼ 10−2 Z⊙ for cold-mode gas. However, we caution the reader
92
Dependence on radius
that the median cold-mode metallicity is not converged with numerical resolution (see the Appendix) and could in fact be much lower. The metallicity increases towards the centre of the halo and this increase is steeper for cold-mode
gas. The metallicity difference between the two modes disappears at R ≈ 0.5Rvir ,
but we find this radius to move inwards with increasing resolution (see the Appendix). Close to the centre the hot gas cools down and ongoing star formation
in the disc enriches all the gas. The scatter in the metallicity decreases, especially
for cold-mode gas, to ∼ 0.7 dex.
As discussed in detail by Wiersma et al. (2009b), there is no unique definition of metallicity in SPH. The metallicity that we assign to each particle is the
ratio of the metal mass density and the total gas density at the position of the
particle. These “SPH-smoothed abundances” were also used during the simulation for the calculation of the cooling rates. Instead of using SPH-smoothed
metallicities, we could, however, also have chosen to compute the metallicity as
the ratio of the metal mass and the total gas mass of each particle. Using these
so-called particle metallicities would sharpen the metallicity gradients at the interfaces of different gas phases. Indeed, we find that using particle metallicities
decreases the median metallicity of the metal-poor cold mode. For the hot mode
the median particle metallicity is also lower than the median smoothed metallicity, but it increases with resolution, whereas the cold-mode particle metallicities
decrease with resolution.
While high-metallicity gas may belong to either mode, gas with metallicity .
10−3 Z⊙ is highly likely to be part of a cold flow. This conclusion is strengthened
when we increase the resolution of the simulation or when we use particle rather
than SPH-smoothed metallicities. Thus, a very low metallicity appears to be a
robust way of identifying cold-mode gas.
4.3.7 Radial velocity
The radial peculiar velocity is calculated with respect to the halo centre after
subtracting the peculiar velocity of the halo. The peculiar velocity of the halo is
calculated by taking the mass-weighted average velocity of all the gas particles
within 10 per cent of virial radius. Note that the Hubble flow is not included in
the radial velocities shown. It is unimportant inside haloes, but is about a factor
of two larger than the peculiar velocity at 10Rvir .
The bottom-left panel of Figure 4.2 shows that gas outside the haloes is, in
general, moving towards the halo (i.e. it has a negative radial velocity). Within
the virial radius, however, more than half of the projected area is covered by
outflowing gas. These outflows are not only caused by SN feedback. In fact,
simulations without feedback also show significant outflows (see Figures 4.7
and 4.8). A comparison with the pressure map shows that the outflows occur in
the regions where the pressure is relatively high for its radius (by 0.1 − 0.4 dex,
see Figures 4.5 and 4.6). The inflowing gas is associated with the dense, cold
streams, but the regions of infall are broader than the cold filaments. Some of
93
Gas properties in and around haloes
the hot-mode gas is also flowing in along with the cold-mode gas. These fast
streams can penetrate the halo and feed the central disc. At the same time, some
of the high temperature gas will expand, causing mild outflows in high pressure
regions and these outflows are strengthened by SN-driven winds.
The hot-mode gas is falling in more slowly than the cold-mode gas or is
even outflowing (bottom-left panel of Figure 4.3). This is expected, because
the gas converts its kinetic energy into thermal energy when it goes through
an accretion shock and because a significant fraction of the hot-mode gas may
have been affected by feedback. For hot-mode gas the median radial velocity is
closest to zero between 0.3Rvir < R < 1Rvir . Most of it is inflowing at smaller
radii, where the gas temperature drops dramatically, and also at larger radii.
The cold-mode gas appears to accelerate to −150 km s−1 towards Rvir (i.e.
radial velocities becoming more negative) and to decelerate to −30 km s−1 from
Rvir towards the disc. We stress, however, that the behaviour of individual gas
elements is likely to differ significantly from the median profiles. Individual,
cold gas parcels will likely accelerate until they go through an accretion shock
or are hit by an outflow, at which point the radial velocity may suddenly vanish
or change sign. If this is more likely to happen at smaller radii, then the median
profiles will show a smoothly decelerating inflow. Finally, observe that while
there is almost no outflowing cold-mode gas around the virial radius, close to
the central galaxy (R . 0.3Rvir ) a significant fraction is outflowing.
4.3.8 Accretion rate
The appropriate definition of the accretion rate in an expanding Universe depends on the question of interest. Here we are interested in the mass growth of
haloes in a comoving frame, where the haloes are defined using a criterion that
would keep halo masses constant in time if there were no peculiar velocities. An
example of such a halo definition is the spherical overdensity criterion, which
we use here, because the virial radius is in that case defined as the radius within
which the mean internal density is a fixed multiple of some fixed comoving
density.
The net amount of gas mass that is accreted per unit time through a spherical
shell S with comoving radius x = R/a, where a is the expansion factor, is then
given by the surface integral
Ṁgas ( x )
= −
= −
Z
ZS
S
a3 ρ ẋ
dS
a2
ρvrad dS,
(4.2)
(4.3)
where a3 ρ and dS/a2 are a comoving density and a comoving area, respectively,
and the radial peculiar velocity is vrad ≡ a ẋ. We evaluate this integral as follows,
Ṁgas ( R) = −
94
mgas,i vrad,i
Ashell ,
Vshell
R ≤r < R +dR
∑
i
(4.4)
Dependence on radius
where
4π
(( R + dR)3 − R3 ),
(4.5)
3
1
(4.6)
Ashell = 4π ( R + dR)2 ,
2
ri is the radius of particle i, and dR is the bin size. Note that a negative accretion
rate corresponds to net outflow.
The mass flux map shown in the bottom-middle panel of Figure 4.2 is computed per unit area for each pixel as Σi mgas,i vrad,i /Vpix , where Vpix is the proper
volume of the pixel. The absolute mass flux is highest in the dense filaments and
in the other galaxies outside Rvir , because they contain a lot of mass and have
high inflow velocities.
The gas accretion rate Ṁgas ( R/Rvir ) computed using equation (4.4) is shown
as the black curve in the bottom-middle panel of Figure 4.3. The accretion rate
is averaged over all haloes in the mass bin we are considering here (1011.5 M⊙ <
Mhalo < 1012.5 M⊙ ). Similarly, the red and blue curves are computed by including only hot- and cold-mode particles, respectively. The accretion rate is positive
at all radii, indicating net accretion for both modes. The inflow rate is higher
for the cold mode even though the hot-mode gas dominates the mass budget
around the virial radius (see Section 4.3.9). The hot-mode gas accretion rate is a
combination of the density and the radial velocity of the hot-mode gas, as well
as the amount of mass in the hot mode. Gas belonging to the cold mode at
R > Rvir may later become part of the hot mode after it has reached R < Rvir .
The extended halo is not in a steady state, because the accretion rate varies
with radius. Moving inwards from 10Rvir to Rvir , the net rate of infall drops by
about an order of magnitude. This implies that the (extended) halo is growing:
the flux of mass that enters a shell from larger radii exceeds the flux of mass
that leaves the same shell in the direction of the halo centre. This sharp drop in
the accretion rate with decreasing radius is in part due to the fact that some of
the gas at R > Rvir is falling towards other haloes that trace the same large-scale
structure.
Within the virial radius the rate of infall of all gas and of cold-mode gas continues to drop with decreasing radius, but the gradient becomes much less steep
(d ln Ṁ/d ln R ≈ 0.4), indicating that the cold streams are efficient in transporting mass to the central galaxy. For the hot mode the accretion rate only flattens at
R . 0.4Rvir around the onset of catastrophic cooling. Hence, once the hot-mode
gas reaches small enough radii, its density becomes sufficiently high for cooling
to become efficient, and the hot-mode accretion becomes efficient too. However,
even at 0.1Rvir its accretion rate is still much lower than that of cold-mode gas.
Vshell =
4.3.9 Hot fraction
Even though the average hot fraction, i.e. the mean fraction of the gas mass that
has a maximum past temperature greater than 105.5 K, of the halo in the image
95
Gas properties in and around haloes
is close to 0.5, few of the pixels actually have this value. For most pixels f hot
is either close to one or zero (bottom-right panel of Figure 4.2), confirming the
bimodal nature of the accretion.
The bottom-right panel of Figure 4.3 shows that the hot fraction peaks around
the virial radius, where it is about 70 per cent. Although the hot fraction decreases beyond the virial radius, it is still 30 per cent around 10Rvir . The hotmode gas at very large radii is associated with other haloes and/or large-scale
filaments. Within the halo the hot fraction decreases from 70 per cent at Rvir to
35 per cent at 0.1Rvir . While hot-mode accretion dominates the growth of haloes,
most of the hot-mode gas does not reach the centre. Cold-mode accretion thus
dominates the growth of galaxies.
4.4 Dependence on halo mass
In Figure 4.4 we plot the same properties as in Figure 4.3 as a function of halo
mass for gas at radii 0.8Rvir < R < Rvir , where differences between hot- and
cold-mode gas are large. Grey, dashed lines show analytic estimates and are
discussed below. The dotted, grey line in the top-left panel indicates the star
formation threshold, i.e. nH = 0.1 cm−3 . The differences between the density
and temperature of the hot- and cold-mode gas increase with the mass of the
halo. The average temperature, maximum past temperature, pressure, entropy,
metallicity, absolute radial peculiar velocity, absolute accretion rate, and the hot
fraction all increase with halo mass.
We can compare the gas overdensity at the virial radius to the density that we
would expect if baryons were to trace the dark matter, ρvir . We assume an NFW
profile (Navarro et al., 1996), take the mean internal density, ∆hρi, from spherical
collapse calculations (Bryan & Norman, 1998) and the halo mass-concentration
relation from Duffy et al. (2008) and calculate the mean overdensity at Rvir . This
is plotted as the dashed, grey line in the top-left panel of Figure 4.4. It varies very
weakly with halo mass, because the concentration depends on halo mass, but
this is invisible on the scale of the plot. For all halo masses the median density
is indeed close to this analytic estimate. While the same is true for the hotmode gas, for high-mass haloes (Mhalo & 1012 M⊙ ) the median density of coldmode gas is significantly higher than the estimated density and the difference
reaches two orders of magnitude for Mhalo ∼ 1013 M⊙ . A significant fraction
of the cold-mode gas in these most massive haloes is star forming and hence
part of the ISM of satellite galaxies. The fact that cold-mode gas becomes denser
and thus clumpier with halo mass could have important consequences for the
formation of clumpy galaxies at high redshift (Dekel et al., 2009b; Agertz et al.,
2009; Ceverino et al., 2010).
The blue curve in the top-middle panel shows that the median temperature
of the cold-mode gas at Rvir decreases slightly with halo mass, from 40,000 K to
15,000 K. This reflects the increase in the median density of cold-mode gas with
96
Dependence on mass
97
Figure 4.4: Properties of gas at 0.8Rvir < R < Rvir at z = 2 as a function of halo mass for all (black curves), hot-mode (red curves), and
cold-mode (blue curves) gas. Results are shown for the simulation REF_L050N512. Shaded regions show values within the 16th and 84th
percentiles, i.e., the ±1σ scatter around the median. From the top-left to the bottom-right, the different panels show the mass-weighted
median gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity, radial peculiar velocity, the mean accretion
rate, and the mean mass fraction of hot-mode gas, respectively. The horizontal, dotted line in the first panel indicates the threshold for star
formation (nH = 0.1 cm−3 ). The dashed, grey curves show analytic estimates from virial arguments.
Gas properties in and around haloes
halo mass, which results in shorter cooling times. The median temperature of
the hot-mode gas increases with halo mass and is approximately equal to the
virial temperature for Mhalo & 1011.5 M⊙ . The virial temperature is plotted as
the dashed, grey line and is given by
!1/3
G2 H02 Ωm ∆
µmH 2/3
Mhalo (1 + z),
(4.7)
Tvir =
54
kB
2/3 1+z
Mhalo
5
≈ 9.1 × 10 K
,
(4.8)
3
1012 M⊙
where G is the gravitational constant, H0 the Hubble constant and µ is assumed
to be equal to 0.59.
While much of the gas accreted onto low-mass haloes in the hot mode has
a temperature smaller than 105.5 K and has therefore already cooled down substantially2 , there is very little overlap in the current temperatures of gas accreted
in the two modes for haloes with Tvir & 106 K. Because the cooling rates decrease
with temperature for T > 105.5 K (e.g. Wiersma et al., 2009a), most of the hotmode gas in haloes with higher temperatures stays hot. For the same reason, the
median temperature of all gas rises sharply at M ≈ 1011.5 M⊙ (Tvir ≈ 105.5 K)
and is roughly equal to Tvir for Mhalo > 1012 M⊙ .
The top-right panel shows that the median maximum past temperature of
gas at the virial radius is close to the virial temperature, which is again shown
as the grey dashed curve, for the full range of halo masses shown. Some of
the gas does, however, have a maximum past temperatures that differs strongly
from the virial temperature. The largest difference is found for cold-mode gas
in high-mass haloes. Because of its high density, its cooling time is short and
the gas does not shock to the virial temperature. The maximum past temperature of gas accreted in the cold mode is close to 105 K for all halo masses. For
Mhalo < 1010.5 M⊙ this temperature is higher than the virial temperature. The
gas in low-mass haloes has not been heated to its maximum temperature by
a virial shock, but by the UV background radiation or by shocks from galactic winds. Heating by the UV background is the dominant process, because
simulations without supernova feedback show the same result (see Figure 4.8).
The maximum past temperature of hot-mode gas follows the virial temperature
closely for high-mass haloes. For Tvir < 105.5 K (Mhalo . 1011.5 M⊙ ) the maximum past temperature of the hot-mode gas remains approximately constant, at
around 105.7 K, because of our definition of hot-mode gas (Tmax ≥ 105.5 K).
2/3
(middle-left panel). We
The pressure of the gas increases roughly as Mhalo
can estimate the pressure at the virial radius from the virial temperature and the
density at the virial radius.
T ρ
Pvir
= vir vir ,
(4.9)
kB
µmH
2
Note that for haloes with Tvir . 105.5 K the median hot-mode temperature is affected by the
requirement Tmax > 105.5 K (our definition of hot-mode gas).
98
Dependence on mass
where µ is assumed to be equal to 0.59. This pressure is shown by the dashed,
grey line. The actual pressure is very close to this simple estimate. It scales
with mass as the virial temperature because the density at the virial radius is
nearly independent of the mass. For all halo masses the median pressure of the
gas accreted in the hot-mode is about a factor of two higher than the median
pressure of the cold-mode gas.
The central panel shows that the entropy difference between hot- and coldmode gas increases with halo mass, because the entropy of hot-mode gas increases with halo mass, whereas the cold-mode entropy decreases. The hotmode gas follows the slope of the relation expected from virial arguments,
Svir =
Pvir (µmH )5/3
kB ρ5/3
vir
,
(4.10)
where µ is assumed to be equal to 0.59. Svir is shown as the dashed, grey line.
The middle-right panel shows that the median gas metallicity at the virial
radius increases from ∼ 10−2 Z⊙ for Mhalo ∼ 1010 M⊙ to ∼ 10−1 Z⊙ for 1013 M⊙ .
This increase reflects the increased fraction of hot-mode gas (see the bottom-right
panel) and an increase in the median metallicity of the cold-mode gas, which is
probably due to the fact that a greater fraction of the gas resides in the ISM of
satellite galaxies for more massive haloes (see the top-left panel). The scatter
in the metallicity of the cold-mode gas is always very large. The hot-mode gas
has a median metallicity ∼ 10−1 Z⊙ for all halo masses, which is similar to
the predicted metallicity of the warm-hot intergalactic medium (Wiersma et al.,
2011).
The black curve in the bottom-left panel shows that for all halo masses more
mass is falling into the halo than is flowing out. The radial velocity distributions are, however, very broad. A substantial fraction of the hot-mode gas, more
than half for Mhalo < 1011.5 M⊙ , is outflowing at Rvir . Cold-mode gas is predominantly inflowing for all masses, but the fraction of outflowing gas becomes
significant for Mhalo < 1011.5 M⊙ .
As expected, the gas at the virial radius falls in faster for higher-mass haloes
and the absolute velocities are larger for cold-mode gas. We can compare the
radial peculiar velocity to the escape velocity,
vesc
=
≈
s
2GMhalo
,
Rvir
1/3 Mhalo
1 + z 1/2
,
275 km s−1
3
1012 M⊙
(4.11)
(4.12)
99
Gas properties in and around haloes
where we used
Rvir
=
≈
!1/3
2GM
1
,
2
1+z
H0 Ωm ∆
1/3 1 + z −1
Mhalo
114 kpc
.
3
1012 M⊙
(4.13)
(4.14)
We show −vesc by the dashed, grey curve. We only expect the gas to have a
velocity close to this estimate if it fell in freely from very large distances and
if the Hubble expansion, which damps peculiar velocities, were unimportant.
However, we do expect the scaling with mass to be more generally applicable.
For the cold mode the trend with halo mass is indeed well reproduced by the
escape velocity.
On average, for halo masses above 1011 M⊙ , the net accretion rate is positive, which means that more mass is flowing in than is flowing out (bottommiddle panel). Therefore, unsurprisingly, the haloes are growing. For haloes
with 1010 M⊙ < Mhalo < 1011 M⊙ the mean accretion rate is negative (indicating
net outflow), but small (∼ 0.1 M⊙ yr−1 ). The mean accretion rate of cold-mode
gas is positive for all halo masses, but for hot-mode gas there is net outflow
for Mhalo < 1011.5 M⊙ . Although these haloes are losing gas that is currently
hot-mode, their hot-mode gas reservoir may still be increasing if cold-mode gas
is converted into hot-mode gas. For higher-mass haloes, the hot-mode accretion
rate is also positive and it increases approximately linearly with halo mass. This
is the regime where the implemented supernova feedback is not strong enough
to blow gas out of the halo. This transition mass is increased by more than an
order of magnitude when more effective supernova feedback or AGN feedback
is included (not shown). For Mhalo > 1012.5 M⊙ the hot-mode inflow rate is
slightly stronger than the cold-mode inflow rate.
The grey, dashed curve indicates the accretion rate a halo with a baryon
fraction Ωb /Ωm would need to have to grow to its current baryonic mass in a
time equal to the age of the Universe at z = 2,
Ṁ =
Ωb Mhalo
.
Ωm tUniverse
(4.15)
Comparing this analytic estimate with the actual mean accretion rate, we see
that they are equal for Mhalo > 1011.5 M⊙ , indicating that these haloes are in
a regime of efficient growth. For lower-mass haloes, the infall rates are much
lower, indicating that the growth of these haloes has halted, or that their baryon
fractions are much smaller than Ωb /Ωm .
The bottom-right panel of Figure 4.4 shows that, at the virial radius, hotmode gas dominates the gas mass for high-mass haloes. The hot fraction at Rvir
increases from 10 per cent in haloes of ∼ 1010 M⊙ to 90 per cent for Mhalo ∼
1013 M⊙ . Note that for haloes with Mhalo < 1011.3 M⊙ the virial temperatures are
lower than our adopted threshold for hot-mode gas. The hot fraction would have
100
Inflow and outflow
been much lower without supernova feedback ( f hot < 5 per cent for Mhalo <
1010.5 M⊙ ).
4.5 Inflow and outflow
Figures 4.5 and 4.6 show the physical properties of the gas, weighted by the
radial mass flux, for all, inflowing, and outflowing gas (black, blue, and red
curves, respectively). Except for the last two panels, the curves indicate the
medians, i.e. half the mass flux is due to gas above the curves. Similarly, the
shaded regions indicate the 16th and 84th percentiles. Note that we do not plot
this separately for hot- and cold-mode gas. The differences between the blue
and red curves arise purely from the different radial peculiar velocity directions.
We can immediately see that separating gas according to its radial velocity
direction yields similar results as when the gas is separated according to its
maximum past temperature (compare to Figures 4.3 and 4.4). Like cold-mode
gas, inflowing gas has, on average, a higher density, a lower temperature, a lower
entropy, and a lower metallicity than outflowing gas.
Comparing Figures 4.3 and 4.5, we notice that the differences in density, temperature, pressure, entropy, and metallicity between in- and outflowing gas tend
to be slightly smaller than between cold- and hot-mode gas. This is particularly
true outside the haloes (at R > 3Rvir ), where there is a clear upturn in the density and pressure of outflowing gas that is accompanied by a marked decrease
in the temperature. These features are due to gas that is flowing towards other
haloes and/or large-scale filaments. Although such gas is outflowing from the
perspective of the selected halo, it is actually infalling gas and hence more likely
to be cold-mode.
Unsurprisingly, the radial peculiar velocities (bottom-left panels) are clearly
very different when we separate the gas into in- and outflowing components
than when we divide it into cold and hot modes. Low values of the radial
velocity are avoided because the plot is weighted by the mass flux. While the
radial velocity of cold-mode gas decreases from the virial radius towards the
centre, the mass flux-weighted median radial velocity of inflowing gas is roughly
constant. Within the haloes, the mass flux-weighted median radial velocity of
outflowing gas decreases with radius.
Both the inflow and the outflow mass flux (bottom-middle panel of Figure 4.5) are approximately constant inside 0.7Rvir , which implies that the fraction of the gas that is outflowing is also constant (last panel of Figure 4.5). A
mass flux that is independent of radius implies efficient mass transport, as the
same amount of mass passes through each shell per unit of time. The inflowing
mass flux decreases from 10Rvir to ∼ Rvir because the overdensity of the region
is increasing and because some of the gas that is infalling at distances ≫ Rvir
is falling towards neighbouring haloes. At R & Rvir the outflowing mass flux
decreases somewhat, indicating that the transportation of outflowing material
101
102
Gas properties in and around haloes
Figure 4.5: Properties of gas in haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 2 as a function of radius for all (black curves), outflowing
(red curves), and inflowing (blue curves) gas. Results are shown for the simulation REF_L050N512. Shaded regions show values within
the 16th and 84th percentiles, i.e., the ±1σ scatter around the median. From the top-left to the bottom-right, the different panels show
the mass flux-weighted median gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity, radial peculiar
velocity, the mean accretion rate, and the mean mass fraction of outflowing gas, respectively. Most of the trends with radius for inflowing
and outflowing gas are similar to those for cold-mode and hot-mode gas, respectively, as shown in Figure 4.3.
Inflow and outflow
103
Figure 4.6: Properties of gas at 0.8Rvir < R < Rvir at z = 2 as a function of halo mass for all (black curves), outflowing (red curves), and
inflowing (blue curves) gas. Results are shown for the simulation REF_L050N512. Shaded regions show values within the 16th and 84th
percentile, i.e., the ±1σ scatter around the median. From the top-left to the bottom-right, the different panels show the mass flux-weighted
median gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity, radial peculiar velocity, the mean accretion
rate, and the mean mass fraction of outflowing gas, respectively. The horizontal, dotted line in the first panel indicates the threshold for
star formation (nH = 0.1 cm−3 ). The dashed, grey curves show analytic estimates from virial arguments. Most of the trends with mass for
inflowing and outflowing gas are similar to those for cold-mode and hot-mode gas, respectively, as shown in Figure 4.4.
Gas properties in and around haloes
slows down and that the galactic winds are becoming less efficient. This can
also be seen by the drop in outflow fraction around the virial radius in the last
panel of Figure 4.5. (The small decrease in outflow fraction below 1010.5 M⊙
is a resolution effect.) The outflowing mass flux increases again at large radii,
because the hot-mode gas is falling towards unrelated haloes.
Comparing Figures 4.4 and 4.6, we see again that, to first order, inflowing and
outflowing gas behave similarly as cold-mode and hot-mode gas, respectively.
There are, however, some clear differences, although we do need to keep in mind
that some are due to the fact that Figure 4.4 is mass-weighted while Figure 4.6 is
mass flux-weighted. The mass flux-weighted median temperature of outflowing
gas is always close to the virial temperature. For Mhalo . 1011 M⊙ this is much
lower than the median temperature of hot-mode gas, but that merely reflects
the fact that for these haloes the virial temperature is lower than the value of
105.5 K that we use to separate the cold and hot modes. The mass flux-weighted
maximum past temperature is about 0.5 dex higher than Tvir .
Another clear difference is visible at the high-mass end (Mhalo & 1012.5 M⊙ ).
While the cold-mode density increases rapidly with mass, the overdensity of
infalling gas remains ∼ 102 , and while the cold-mode temperature remains ∼
104 K, the temperature of infalling gas increases with halo mass. Both of these
differences can be explained by noting that, around the virial radius, hot-mode
gas accounts for a greater fraction of the infall in higher mass haloes (see the
bottom-middle panel of Figure 4.4).
As was the case for the cold-mode gas, the radial peculiar velocity of infalling
gas scales like the escape velocity (bottom-middle panel). Interestingly, although
the mass flux-weighted median outflowing velocity is almost independent of
halo mass, the high-velocity tail is much more prominent for low-mass haloes.
Because the potential wells in these haloes are shallow and because the gas
pressure is lower, the outflows are not slowed down as much before they reach
the virial radius. The flux-weighted outflow velocities are larger than the inflow
velocities for Mhalo < 1011.5 M⊙ , whereas the opposite is the case for higher-mass
haloes.
Finally, the last panel of Figure 4.6 shows that the fraction of the gas that is
outflowing around Rvir is relatively stable at about 30–40 per cent. Although the
accretion rate is negative for 1010 M⊙ < Mhalo < 1011 M⊙ , which indicates net
outflow, less than half of the gas is outflowing.
4.6 Effect of metal-line cooling and outflows driven
by supernovae and AGN
Figure 4.7 shows images of the same 1012 M⊙ halo as Figure 4.2 for five different
high-resolution (L025N512) simulations at z = 2. Each row shows a different
property, in the same order as the panels in the previous figures. Different
columns show different simulations, with the strength of galactic winds increas104
Metal-line cooling and outflows
Figure 4.7: As Figure 4.2, but comparing the different simulations listed in Table 4.2. The
images show a cubic 1 h−1 comoving Mpc region centred on a halo of Mhalo ≈ 1012 M⊙
at z = 2 taken from the L025N512 simulations. From left to right, the different columns
show the simulation with neither SN feedback nor metal-line cooling, the simulation
without metal-line cooling, the reference simulation (which includes SN feedback and
metal-line cooling), the simulation for which the wind speed scales with the effective
sound speed of the ISM, and the simulation with AGN feedback. Note that the images
shown in the middle column are identical to those shown in Figure 4.2.
105
106
Gas properties in and around haloes
Figure 4.8: Properties of gas in haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 2 as a function of radius for hot-mode (red curves) and
cold-mode (blue curves) gas for the five different L025N112 simulations listed in Table 4.2, as indicated in the legend. From the top-left to
the bottom-right, the different panels show the mass-weighted median gas overdensity, temperature, maximum past temperature, pressure,
entropy, metallicity, radial peculiar velocity, the mean accretion rate, and the mean mass fraction of hot-mode gas, respectively.
Metal-line cooling and outflows
ing from left to right (although the winds are somewhat stronger in NOZCOOL
than in REF). The first column shows the simulation without SN feedback and
without metal-line cooling. The second column shows the simulation with SN
feedback, but without metal-line cooling. The third column shows our reference
simulation, which includes both SN feedback and metal-line cooling. The fourth
column shows the simulation with density-dependent SN feedback, which is
more effective at creating galactic winds for this halo mass. The last column
shows the simulation that includes both SN and AGN feedback.
The images show substantial and systematic differences. More efficient feedback results in lower densities and higher temperatures of diffuse gas and in
the case of AGN feedback, even some of the cold filaments are partially destroyed. Although the images reveal some striking differences, Figure 4.8 shows
that the trends in the profiles of the gas properties, including the differences
between hot and cold modes, are very similar in the different simulations. This
is partly because the profiles are mass-weighted, whereas the images are only
mass-weighted along the projected dimension. We would have seen larger differences if we had shown volume-weighted profiles, because the low-density,
high-temperature regions, which are most affected by the outflows, carry very
little mass, but dominate the volume. Although the conclusions of the previous
sections are to first order independent of the particular simulation that we use,
there are some interesting and clear differences, which we shall discuss below.
We can isolate the effect of turning off SN-driven outflows by comparing
models NOSN_NOZCOOL and NOZCOOL. Without galactic winds, the coldmode densities and pressures are about an order of magnitude higher within
0.5Rvir . On the other hand, turning off winds decreases the density of hot-mode
gas by nearly the same factor around 0.1Rvir . Galactic winds thus limit the
build up of cold-mode gas in the halo center, which they accomplish in part by
converting cold-mode gas into hot-mode gas (i.e. by shock-heating cold-mode
gas to temperatures above 105.5 K). We can see that this must be the case by
noting that the hot-mode accretion rate is negative inside the haloes for model
NOZCOOL. The absence of SN-driven outflows also has a large effect on the
distribution of metals. Without winds, the metallicities of both hot- and coldmode gas outside the halo are much lower, because there is no mechanism to
transport metals to large distances. On the other hand, the metallicity of the
cold-mode gas is higher within the halo, because the star formation rates, and
thus the rates of metal production, are higher. This suggests that the metals in
cold-mode gas are associated with locally formed stars, e.g. infalling companion
galaxies.
Increasing the efficiency of the feedback, as in models WDENS and particularly AGN, the cold-mode median radial velocity becomes less negative and the
accretion rate of cold-mode gas inside haloes decreases. At the same time, the
radial velocity and the outflow rate of the hot-mode increase. In other words,
more efficient feedback hinders the inflow rate of cold-mode gas and boosts
the outflows of hot-mode gas. The differences are particularly large outside the
107
Gas properties in and around haloes
haloes. Whereas the moderate feedback implemented in model REF predicts
net infall of hot-mode gas, the net accretion rate of hot-mode gas is negative
out to about 4Rvir when AGN feedback is included. Beyond the virial radius,
stronger winds substantially increase the mass fraction of hot-mode gas. This
comes at the expense of the hot-mode gas inside the haloes, which decreases if
the feedback is more efficient, at least for 0.2Rvir < R < Rvir .
The effect of metal-line cooling can be isolated by comparing models NOZCOOL and REF. Without metal-line cooling, the cooling times are much longer.
Consequently, the median temperature of the hot-mode gas remains above 106 K
(at least for R > 0.1Rvir ), whereas it suddenly drops to below 105 K around
0.2Rvir when metal-line cooling is included. Thus, the catastrophic cooling flow
of the diffuse, hot component in the inner haloes is due to metals. Indeed, while
the median hot-mode radial peculiar velocity within 0.2Rvir is positive without
metal-line cooling, it becomes negative (i.e. infalling) when metal-line cooling is
included.
4.7 Evolution: Milky Way-sized haloes at z = 0
Figure 4.9 is identical to Figure 4.3 except that it shows profiles for z = 0 rather
than z = 2. For comparison, the dotted curves in Figure 4.9 show the corresponding z = 2 results. As we are again focusing on 1011.5 M⊙ < Mhalo <
1012.5 M⊙ , the results are directly relevant for the Milky Way galaxy.
Comparing Figure 4.3 to Figure 4.9 (or comparing solid and dotted curves
in Figure 4.9), we see that the picture for z = 0 looks much the same as it
did for z = 2. There are, however, a few notable differences. The overdensity
profiles hardly evolve, although the difference between the cold and hot modes
is slightly smaller at lower redshift. However, a constant overdensity implies a
strongly evolving proper density (ρ ∝ (1 + z)3) and thus also a strongly evolving
cooling rate. The large decrease in the proper density caused by the expansion
of the Universe also results in a large drop in the pressure and a large increase
in the entropy.
The lower cooling rate shifts the peak of the cold-mode temperature profile
from about 2Rvir to about Rvir . While there is only a small drop in the temperature of the hot-mode gas, consistent with the mild evolution of the virial
temperature of a halo of fixed mass (Tvir ∝ (1 + z); eq. [4.7]), the evolution in
the median temperature for all gas is much stronger than for the individual accretion modes. While at z = 2 the overall median temperature only tracks the
median hot-mode temperature around 0.5Rvir < R < 2Rvir , at z = 0 the two
profiles are similar at all radii.
The metallicity profiles do not evolve much, except for a strong increase in
the median metallicity of cold-mode gas at R ≫ Rvir . Both the weak evolution
of the metallicity of dense gas and the stronger evolution of the metallicity of
the cold, low-density intergalactic gas far away from galaxies are consistent with
108
Milky Way-sized haloes at z = 0
109
Figure 4.9: Properties of gas in haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 0 as a function of radius for all (black curves), hot-mode
(red curves), and cold-mode (blue curves) gas. Results are shown for the simulation REF_L050N512. Most z = 2 curves from Figure 4.3
have also been included, for comparison, as dotted curves. Shaded regions show values within the 16th and 84th percentiles, i.e., the ±1σ
scatter around the median. From the top-left to the bottom-right, the different panels show the mass-weighted median gas overdensity,
temperature, maximum past temperature, pressure, entropy, metallicity, radial peculiar velocity, the mean accretion rate, and the mean
mass fraction of hot-mode gas, respectively. The radial profiles at z = 0 follow the same trends as at z = 2 (compare Figure 4.3), although
the pressure, the infall velocity and the accretion rates are lower, the entropy is higher, and the hot mode accounts for a greater mass
fraction.
Gas properties in and around haloes
the findings of Wiersma et al. (2011), who found these trends to be robust to
changes in the subgrid physics.
The absolute, net radial velocities of both the hot- and cold-mode components are smaller at lower redshift, as expected from the scaling of the characteristic velocity (vesc ∝ (1 + z)1/2; eq. [4.11]).
While at z = 2 the net accretion rate was higher for the cold mode at all
radii, at z = 0 the hot mode dominates beyond 3Rvir . At low redshift the rates
are about an order of magnitude lower than at z = 2. For R < 0.4Rvir the net
accretion rate is of order 1 M⊙ yr−1 , which is dominated by the cold mode, even
though most of the mass is in the hot mode. Since a substantial fraction of both
the cold- and hot-mode gas inside this radius is outflowing, the actual accretion
rates will be a bit higher.
At z = 0 the fraction of the mass that has been hotter than 105.5 K exceeds
50 per cent at all radii and the profile show a broad peak of around 80 per cent
at 0.3 < R < Rvir . Thus, hot-mode gas is more important at z = 0 than at
z = 2, where cold-mode gas accounts for most of the mass for R . 0.3Rvir and
R & 2Rvir . This is consistent with van de Voort et al. (2011a), who investigated
the evolution of the hot fraction in more detail using the same simulations.
4.8 Conclusions and discussion
We have used cosmological hydrodynamical simulations from the OWLS project
to investigate the physical properties of gas in and around haloes. We paid particular attention to the differences in the properties of gas accreted in the cold
and hot modes, where we classified gas that has remained colder (has been hotter) than 105.5 K while it was extragalactic as cold-mode (hot-mode) gas. Note
that our definition allows hot-mode gas to be cold, but that cold-mode gas cannot be hotter than 105.5 K. We focused on haloes of 1012 M⊙ at z = 2 drawn
from the OWLS reference model, which includes radiative cooling (also from
heavy elements), star formation, and galactic winds driven by SNe. However,
we also investigated how the properties of gas near the virial radius change with
halo mass, we compared z = 2 to z = 0, we measured properties separately for
inflowing and outflowing gas, and we studied the effects of metal-line cooling
and feedback from star formation and AGN. We focused on mass-weighted median gas properties, but noted that volume-weighted properties are similar to
the mass-weighted properties of the hot-mode gas, because most of the volume
is filled by dilute, hot gas, at least for haloes with Tvir & 105.5 K (see Figures 4.1
and 4.2).
Let us first consider the properties of gas just inside the virial radius of haloes
drawn from the reference model at z = 2 (see Figure 4.4). The fraction of the
gas accreted in the hot mode increases from 10 per cent for halo masses Mhalo ∼
1010 M⊙ to 90 per cent for Mhalo ∼ 1013 M⊙ . Hence, 1012 M⊙ is a particularly
interesting mass scale, as it marks the transition between systems dominated by
110
Conclusions and discussion
cold and hot mode gas.
Although the cold streams are in local pressure equilibrium with the surrounding hot gas, cold-mode gas is physically distinct from gas accreted in the
hot mode. It is colder (T < 105 K vs. T & Tvir ) and denser, particularly for highmass haloes. While hot-mode gas at the virial radius has a density ∼ 102 hρi for
all halo masses, the median density of cold-mode gas increases steeply with the
halo mass.
While the radial peculiar velocity of cold-mode gas is negative (indicating infall) and scales with halo mass like the escape velocity, the median hot-mode
velocities are positive (i.e. outflowing) for Mhalo . 1011.5 M⊙ and for larger
masses they are much less negative than for cold-mode gas. Except for Mhalo ∼
1010.5 M⊙ , the net accretion rate is positive. For 1012 < Mhalo < 1013 M⊙ the
cold- and hot-mode accretion rates are comparable.
While hot-mode gas has a metallicity ∼ 10−1 Z⊙ , the metallicity of coldmode gas is typically significantly smaller and displays a much larger spread.
The scatter in the local metallicity of cold-mode gas is large because the cold
filaments contain low-mass galaxies that have enriched some of the surrounding
cold gas. We emphasized that we may have overestimated the median metallicity
of cold-mode gas because we find it to decrease with increasing resolution. It is
therefore quite possible that most of the cold-mode gas in the outer halo still has
a primordial composition.
The radial profiles of the gas properties of haloes with 1011.5 < Mhalo <
12.5
10
M⊙ revealed that the differences between gas accreted in the cold and hot
modes vanishes around 0.1Rvir (see Figure 4.3), although the radius at which
this happens decreases slightly with the resolution. The convergence of the
properties of the two modes at small radii is due to catastrophic cooling of the
hot gas at R . 0.2Rvir . Interestingly, in the absence of metal-line cooling the hotmode gas remains hot down to much smaller radii, which suggests that it is very
important to model the small-scale chemical enrichment of the circumgalactic
gas. While stronger winds do move large amounts of hot-mode gas beyond the
virial radius, even AGN feedback is unable to prevent the dramatic drop in the
temperature of hot-mode gas inside 0.2Rvir , at least at z = 2.
While the density and pressure decrease steeply with radius, the mass-weighted median temperature peaks around 0.5 − 1.0Rvir . This peak is, however, not
due to a change in the temperature of either the cold- or hot-mode gas, but
due to the radial dependence of the mass fraction of gas accreted in the hot
mode. The hot-mode fraction increases towards the halo, then peaks around
0.5 − 1.0Rvir and decreases moving further towards the centre. Even outside the
halo there is a significant amount of hot-mode gas (e.g. ∼ 30 per cent at 10Rvir ).
Beyond the cooling radius, i.e. the radius where the cooling time equals the
Hubble time, the temperature of the hot-mode gas decreases slowly outwards,
but the temperature of cold-mode gas only peaks around 2Rvir at values just
below 105 K. The density for which this peak temperature is reached depends on
the interplay between cooling (both adiabatic and radiative) and photo-heating.
111
Gas properties in and around haloes
The metallicity decreases with radius and does so more strongly for cold-mode
gas. Near 0.1Rvir the scatter in the metallicity of cold-mode gas is much reduced,
although this could be partly a resolution effect.
The median radial peculiar velocity of cold-mode gas is most negative around
0.5 − 1.0Rvir . For the hot mode, on the other hand, it is close to zero around that
same radius. Hence, the infall velocity of the cold streams peaks where the hotmode gas is nearly static, or outflowing if the feedback is very efficient. We note,
however, that the scatter in the peculiar velocities is large. For R . Rvir much
of the hot-mode gas is outflowing and the same is true for cold-mode gas at
R ∼ 0.1Rvir .
Inside the halo the cold-mode accretion rate increases only slightly with radius (d ln Ṁ/d ln R ≈ 0.4), indicating that most of the mass is transported to
the central galaxy. For the hot-mode, on the other hand, the accretion rate only
flattens at R . 0.4Rvir . This implies that the hot accretion mode mostly feeds
the hot halo. However, hot-mode gas that reaches radii ∼ 0.1Rvir is efficiently
transported to the centre as a result of the strong cooling flow. Nevertheless,
cold-mode accretion dominates the accretion rate at all radii.
Dividing the gas into inflowing and outflowing components yields results
that are very similar to classifying the gas on the basis of its maximum past
temperature. This is because inflowing gas is mostly cold-mode and outflowing
gas is mostly hot-mode. The situation is, however, different for high-mass haloes
(Mhalo & 1012.5 M⊙ ). Because the two accretion modes bring similar amounts
of mass into these haloes, the properties of the infalling gas are intermediate
between those of the cold and hot accretion modes.
When expressed in units of the mean density of the universe, the z = 0 density profiles (with radius expressed in units of the virial radius) are very similar
to the ones at z = 2. The same is true for the metallicities and temperatures,
although the peak temperatures shift to slightly smaller radii (again normalized
to the virial radius) with time. A fixed overdensity does imply that the proper
density evolves as ρ ∝ (1 + z)3 , so the pressure (entropy) are much lower (higher)
at low redshift. Infall velocities and accretion rates are also significantly lower,
while the fraction of gas accreted in the hot mode is higher. The difference in
the behaviour of the two accretion modes is, however, very similar at z = 0 and
z = 2.
Although there are some important differences, the overall properties of the
two gas modes are very similar between our different simulations, and are therefore insensitive to the inclusion of metal-line cooling and galactic winds. Without SN feedback, the already dense cold-mode gas reaches even higher densities,
the metallicity of hot-mode gas in the outer halo is much lower. Without metalline cooling, the temperature at radii smaller than 0.2Rvir is much higher. With
strong SN feedback or AGN feedback, a larger fraction of the gas is outflowing,
the outflows are faster, and the peak in the fraction of the gas that is accreted in
the hot mode peaks at a much larger radius (about 3Rvir instead of 0.5 − 1.0Rvir ).
Kereš et al. (2011) have recently shown that some of the hot gas properties
112
Conclusions and discussion
depend on the numerical technique used to solve the hydrodynamics. They did,
however, not include metal-line cooling and feedback. They find that the temperatures of hot gas (i.e. T > 105 K) around 1012−13 M⊙ haloes are the same
between the two methods, but that the median density and entropy of 1012 M⊙
haloes is somewhat different, by less than a factor of two. These differences are
comparable to the ones we find when using different feedback models. They also
show that the radial velocities are different at small radii. Our results show that
including metal-line cooling decreases the radial velocities, whereas including
supernova or AGN feedback increases the radial velocities significantly. Even
though there are some differences, the main conclusions of this work are unchanged. The uncertainties associated with the subgrid implementation of feedback and the numerical method are therefore unlikely to be important for our
main conclusions.
Cold (i.e. T ≪ 105 K) outflows are routinely detected in the form of blueshifted interstellar absorption lines in the rest-frame UV spectra of star-forming
galaxies (e.g. Weiner et al., 2009; Steidel et al., 2010; Rubin et al., 2010; Rakic et al.,
2011a). This is not in conflict with our results, because we found that the outflowing gas spans a very wide range of temperatures and because the detectable
UV absorption lines are biased towards colder, denser gas. Additionally, the
results we showed are mass-weighted, but if we had shown volume-weighted
quantities, the outflow fractions would have been larger. The inflowing material has smaller cross-sections and is therefore less likely to be detected (e.g.
Faucher-Giguère & Kereš, 2011; Stewart et al., 2011a).
How can we identify cold-mode accretion observationally? The two modes
only differ clearly in haloes with Tvir ≫ 105 K (Mhalo ≫ 1010.5 M⊙ ((1 + z)/3)−3/2),
because photo-ionization by the UV background radiation ensures that all accreted gas is heated to temperatures up to ∼ 105 K near the virial radius. Near
the central galaxy, R . 0.1Rvir , it is also difficult to distinguish the two modes,
because gas accreted in the hot mode is able to cool.
In the outer parts of sufficiently massive haloes the properties of the gas
accreted in the two modes do differ strongly. The cold-mode gas is confined
to clumpy filaments that are approximately in pressure equilibrium with the
diffuse, hot-mode gas. Besides being colder and denser, cold-mode gas typically
has a much lower metallicity and is much more likely to be infalling. However,
the spread in the properties of the gas is large, even for a given mode and a fixed
radius and halo mass, which makes it impossible to make strong statements
about individual gas clouds. Nevertheless, it is clear that most of the dense
(ρ ≫ 102 hρi) gas in high-mass haloes (Tvir & 106 K) is infalling, has a very low
metallicity and was accreted in the cold-mode.
Cold-mode gas could be observed in UV line emission if we are able to detect
it in the outer halo of massive galaxies. Diffuse Lyman-α emission has already
been detected (e.g. Steidel et al., 2000; Matsuda et al., 2004), but its interpretation is complicated by radiative transfer effects and the detected emission is
more likely scattered light from central H ii regions (e.g. Furlanetto et al. 2005;
113
Gas properties in and around haloes
Faucher-Giguère et al. 2010; Steidel et al. 2011; Hayes et al. 2011; Rauch et al.
2011, but see also Dijkstra & Loeb 2009; Rosdahl & Blaizot 2011). Metal-line
emission from ions such as C iii, C iv, Si iii, and Si iv could potentially reveal
cold streams, but current facilities do not probe down to the expected surface
brightnesses (Bertone et al., 2010b; Bertone & Schaye, 2012).
The typical temperatures (T ∼ 104 K) and densities (ρ & 102 hρi) correspond
to those of strong quasar absorption lines systems. For example, at z = 2 the
typical H i column density is3 NH i ∼ 1016 cm−2 (ρ/[102 hρi])3/2 (Schaye, 2001a)
with higher column density gas more likely to have been accreted in the cold
mode. At low redshift the H i column densities corresponding to a fixed overdensity are about 1–2 orders of magnitude lower (Schaye, 2001a).
Indeed, simulations show that Lyman limit systems (i.e. NH i > 1017.2 cm−2 )
may be used to trace cold flows (Faucher-Giguère & Kereš, 2011; Fumagalli et al.,
2011a; van de Voort et al., 2012) and van de Voort et al. (2012) have demonstrated
that cold-mode accretion is required to match the observed rate of incidence of
strong absorbers at z = 3. Many strong QSO absorbers also tend to have low
metallicities (e.g. Ribaudo et al., 2011; Giavalisco et al., 2011; Fumagalli et al.,
2011b), although it should be noted that metallicity measurements along one
dimension may underestimate the mean metallicities of three-dimensional gas
clouds due to the expected poor small-scale metal mixing (Schaye et al., 2007).
We also note that most Lyman limit systems are predicted to arise in or around
haloes with masses that are much lower than required for the presence of stable
accretion shocks near the virial radius, so that they will generally not correspond
to cold streams penetrating hot, hydrostatic haloes (van de Voort et al., 2012). To
study those, it is therefore more efficient to target sight lines to QSOs close to
massive foreground galaxies (e.g. Rakic et al., 2011b; Faucher-Giguère & Kereš,
2011; Stewart et al., 2011a; Kimm et al., 2011).
A Resolution tests
We have checked (but do not show) that the results presented in this work are
converged with respect to the size of the simulation volume if we keep the resolution fixed. The only exception is hot-mode gas at R > 5Rvir , for which the
radial velocities and accretion rate require a box of at least 50h −1Mpc on a side
(which implies that our fiducial simulation is sufficiently large).
Convergence with resolution is, however, more difficult to achieve. In Figures 10 and 11 we show again the radial profiles and mass dependence of the
halo properties for the hot- and cold-mode components at z = 2. Shown are
three different simulations of the reference model, which vary by a factor of 64
(8) in mass (spatial) resolution. All trends with radius and halo mass are very
similar in all runs, proving that most of our conclusions are robust to changes
3
For NH i & 1018 cm−2 the relation is modified by self-shielding, see e.g. Schaye 2001b; Altay et al.
2011.
114
Resolution tests
115
Figure 10: Convergence of gas profiles with resolution. All profiles are for haloes with 1011.5 M⊙ < Mhalo < 1012.5 M⊙ at z = 2. Results
are shown for simulations REF_L025N512 (solid), REF_L050N512 (dotted), and REF_L050N512 (dashed) and for both the hot (red) and
cold (blue) modes. The three simulations vary by a factor of 64 (8) in mass (spatial) resolution. From the top-left to the bottom-right, the
different panels show the mass-weighted median gas overdensity, temperature, maximum past temperature, pressure, entropy, metallicity,
radial peculiar velocity, the mean accretion rate, and the mean mass fraction of hot-mode gas, respectively.
116
Gas properties in and around haloes
Figure 11: Convergence of the properties of gas at 0.8Rvir < R < 1Rvir as a function of halo mass with resolution. Panels and curves as in
Figure 10.
Acknowledgements
in the resolution. Below we will discuss the convergence of hot- and cold-mode
gas separately and in more detail.
The convergence is generally excellent for hot mode gas. As the resolution
is increased, the density of hot-mode gas decreases slightly and the temperature
drop close to the halo centre shifts to slightly smaller radii, which also affects
the pressure and entropy. There is a small upturn in the density of hot-mode gas
at the virial radius as we approach the halo mass corresponding to the imposed
minimum of 100 dark matter particles, showing that we may have to choose a
minimum halo mass that is a factor of 5 higher for complete convergence. The
radial peculiar velocity increases slightly with resolution, causing the hot-mode
accretion rate to decrease.
Convergence is more difficult to achieve for cold-mode gas. The density of
cold-mode gas inside haloes, and thereby also the difference between the two
modes, increases with the resolution. The pressure of the cold-mode gas also
increases somewhat with resolution, which leads to a smaller difference with
the pressure of hot-mode gas. The cold-mode radial velocity becomes more
negative, increasing the difference between the two modes.
The median metallicity of the cold-mode gas decreases strongly with increasing resolution for R > 0.3Rvir . The metallicity difference between the two modes
therefore increases, although the distributions still overlap (not shown), and the
radius at which the metallicities of the two modes converge decreases. In fact,
the convergence of the median metallicity of cold-mode gas is so poor that we
cannot rule out that it would tend to zero at all radii if we keep increasing the
resolution.
If we use particle metallicities rather than SPH smoothed metallicities (see
Section 4.3.6), then the median metallicity of both modes is lower and the median
cold-mode metallicity plummets to zero around the virial radius (not shown).
The decrease in metallicity with increasing resolution is in that case less strong,
but still present. The unsmoothed hot-mode metallicities are also not converged
and lower than the (converged) smoothed hot-mode metallicities, but they increase with increasing resolution. The difference between the two modes therefore increases with resolution.
With increasing resolution, the radial velocities of cold-mode gas become
slightly more negative within the halo. The net accretion rates and hot fractions
are converged.
Even though some properties are slightly resolution dependent, or strongly
so for the case of the metallicity of cold-mode gas, all our conclusions are robust
to increases in the numerical resolution.
Acknowledgements
We would like to thank the referee, Daniel Ceverino, for helpful comments and
Robert Crain, Alireza Rahmati and all the members of the OWLS team for valu117
Gas properties in and around haloes
able discussions. The simulations presented here were run on Stella, the LOFAR
BlueGene/L system in Groningen, on the Cosmology Machine at the Institute
for Computational Cosmology in Durham as part of the Virgo Consortium research programme, and on Darwin in Cambridge. This work was sponsored by
the National Computing Facilities Foundation (NCF) for the use of supercomputer facilities, with financial support from the Netherlands Organization for
Scientific Research (NWO), also through a VIDI grant, and from the Marie Curie
Initial Training Network CosmoComp (PITN-GA-2009-238356).
118
5
Cold accretion flows and the
nature of high column density H i
absorption at redshift 3
Simulations predict that galaxies grow primarily through the accretion of gas
that has not gone through an accretion shock near the virial radius and that this
cold gas flows towards the central galaxy along dense filaments and streams.
There is, however, little observational evidence for the existence of these cold
flows. We use a large, cosmological, hydrodynamical simulation that has been
post-processed with radiative transfer to study the contribution of cold flows to
the observed z = 3 column density distribution of neutral hydrogen, which our
simulation reproduces. We find that nearly all of the H i absorption arises in
gas that has remained colder than 105.5 K, at least while it was extragalactic. In
addition, the majority of the H i is falling rapidly towards a nearby galaxy, with
non-negligible contributions from outflowing and static gas. Above a column
density of NH i = 1017 cm−2 , most of the absorbers reside inside haloes, but the
interstellar medium only dominates for NH i > 1021 cm−2 . Haloes with total
mass below 1010 M⊙ dominate the absorption for 1017 < NH i < 1021 cm−2 , but
the average halo mass increases sharply for higher column densities. Although
very little of the H i in absorbers with NH i . 1020 cm−2 resides inside galaxies,
systems with NH i > 1017 cm−2 are closely related to star formation: most of
their H i either will become part of the interstellar medium before z = 2 or
has been ejected from a galaxy at z > 3. Cold accretion flows are critical for
the success of our simulation in reproducing the observed rate of incidence of
damped Lyman-α and particularly that of Lyman limit systems. We therefore
conclude that cold accretion flows exist and have already been detected in the
form of high column density H i absorbers.
Freeke van de Voort, Joop Schaye, Gabriel Altay,
and Tom Theuns
Monthly Notices of the Royal Astronomical Society
In press (2012), arXiv:1109.5700
Cold flows as H i absorption systems
5.1 Introduction
Galaxies grow by accreting gas from their haloes and their haloes grow by accreting gas from the intergalactic medium (IGM). Feedback from star formation
and active galactic nuclei returns a significant fraction of the interstellar medium
(ISM) to the halo and may even blow it out of the halo into the IGM. This cycle of inflow and outflow makes the circumgalactic medium and the IGM vital
ingredients for our understanding of the formation and evolution of galaxies.
Theoretically we expect that gas accreting onto haloes with sufficiently low
circular velocities will not shock-heat to the virial temperature of the halo, but
will instead flow in cold (i.e. T ∼ 104 K) and relatively unimpeded. This socalled “cold accretion” will happen if the cooling time of virialized gas is too
short to maintain a hot, hydrostatic halo (e.g. White & Frenk, 1991; Birnboim
& Dekel, 2003; Dekel & Birnboim, 2006). The existence of such a cold accretion
mode has been confirmed by simulations, which have furthermore demonstrated
that cold-mode accretion can also be important for haloes sufficiently massive
to contain hot, hydrostatic gas. Because gas accretes preferentially along the
filaments of the cosmic web, the streams of infalling gas have relatively high gas
densities and correspondingly low cooling times. This allows the cold streams to
penetrate the hot, hydrostatic haloes surrounding massive galaxies, particularly
at high redshift (e.g. Kereš et al., 2005; Ocvirk et al., 2008; Dekel et al., 2009a;
Kereš et al., 2009a; Brooks et al., 2009; van de Voort et al., 2011a,b; van de Voort
& Schaye, 2012; Fumagalli et al., 2011a; Faucher-Giguère et al., 2011).
Although the dilute halo gas that has been shock-heated to the virial temperature is routinely detected in X-ray observations of clusters and groups of
galaxies, and has perhaps even been seen around individual galaxies (e.g. Crain
et al., 2010a,b; Anderson & Bregman, 2011), there is no clear, direct observational
evidence for cold-mode accretion. However, Rauch et al. (2011) have observed
cold, filamentary, infalling gas which could be cold-mode accretion. It has been
claimed that the diffuse Lyman-α emission detected around some high-redshift
galaxies is due to cold accretion (e.g. Dijkstra & Loeb, 2009; Goerdt et al., 2010),
but both simulations and observations indicate that the emission is more likely
scattered light from central H ii regions (e.g. Furlanetto et al., 2005; FaucherGiguère et al., 2010; Steidel et al., 2010; Hayes et al., 2011; Rauch et al., 2011).
Individual H i absorbers have also been suggested to be evidence for cold accretion based on their proximity to a galaxy and their low metallicity (Ribaudo
et al., 2011; Giavalisco et al., 2011), but it is difficult to make strong statements
for an individual gas cloud, particularly since H i near galaxies does not need to
be inflowing, even if it has a low metallicity. Given that outflows are routinely
detected in the form of blueshifted interstellar absorption lines in the spectra
of star-forming galaxies (e.g. Steidel et al., 2010; Rubin et al., 2010; Rakic et al.,
2011a), one may wonder why inflowing gas is not commonly seen in the form
of redshifted absorption lines. It is, however, quite possible that the inflowing
material has such small cross-sections that the signal is completely swamped by
120
Introduction
outflowing material (e.g. Faucher-Giguère & Kereš, 2011; Stewart et al., 2011a).
It is challenging to observe cold gas around distant galaxies in emission, because it typically has densities that are low compared to that of the cold ISM.
Absorption line measurements are therefore very important, with the Lyman-α
line of neutral hydrogen being the most sensitive probe. Indeed, H i absorption
can be detected both within and outside of galaxies and at z ∼ 3 the column density distribution has been measured over ten orders of magnitude in NH i (e.g.
Tytler, 1987; Kim et al., 2002; Péroux et al., 2005; O’Meara et al., 2007; Prochaska
& Wolfe, 2009; Noterdaeme et al., 2009; Prochaska et al., 2010). By correlating
the H i absorption in the spectra of background quasars with both the transverse
and line of sight separations from foreground galaxies, Rakic et al. (2011b) have
recently presented strong evidence for infall of cold gas on scales of ∼ 1.4 − 2.0
proper Mpc at z ∼ 2.4.
The low column density (NH i < 1017.2 cm−2 ) material is known as the
Lyman-α forest and originates mostly in the photo-ionized IGM (e.g. Bi et al.,
1992; Cen et al., 1994; Hernquist et al., 1996; Theuns et al., 1998; Schaye, 2001a).
Because these systems are optically thin, they are relatively easy to model in simulations. Lyman Limit Systems (LLSs; 1017.2 < NH i < 1020.3 cm−2 ) and Damped
Lyman-α Systems (DLAs; NH i > 1020.3 cm−2 ) are optically thick to Lyman limit
photons. Because the gas comprising these strong absorbers is partially shielded
from the ambient UV radiation, it will be more neutral, and will also be colder,
than if it were optically thin. These high column density systems are harder to
model, because in order to know which gas is self-shielded, one needs to perform a radiative transfer calculation. Additionally, at the highest gas densities a
fraction of the hydrogen will be converted into molecules, reducing the atomic
hydrogen fraction1 (e.g. Schaye, 2001b; Krumholz et al., 2009).
The difficulty with interpreting absorption-line studies is that they only allow us to study the gas along the line-of-sight direction. It is therefore hard
to determine what kind of objects are causing the absorption. Simulations that
reproduce the observed absorption-line statistics can be employed to study the
three-dimensional distribution of the absorbing gas and to guide the interpretation of the observations.
A lot of progress has been made in understanding and modelling the H i column density distribution function (e.g. Katz et al., 1996; Schaye, 2001a,b; Zheng
& Miralda-Escudé, 2002; Altay et al., 2011; McQuinn et al., 2011; Fumagalli et al.,
2011a). Building on previous work, we ask what kind of gas is causing the H i
absorption. Altay et al. (2011) have post-processed the reference model of the
OWLS suite of cosmological simulations (see Section 5.2) with radiative transfer
and found that the predicted z = 3 H i column density distribution agreed with
observations over the full range of observed column densities. We analyse their
simulation, selecting different subsets of the gas to see what fraction of the high
column density absorption is due to what kind of gas. The selections are based
1 In
this work we mean atomic hydrogen when we write “neutral hydrogen” or “H i”.
121
Cold flows as H i absorption systems
on the maximum past temperature, membership of haloes and the ISM, and the
radial velocity towards the nearest galaxy. These properties are all important to
determine whether or not the gas is accreting in the cold mode. We find that
almost all high column density absorption arises in gas that has never been hotter than 105.5 K, at least not while it was extragalactic, and that resides inside of
haloes. Most of this gas is strongly linked to star formation because it is either
currently in the ISM, has been part of the ISM, or will become part of the ISM
before z = 2. Inflowing gas provides the largest contribution to the H i column
density distribution function, but outflowing and static gas cannot be neglected.
In Section 5.2 we describe the simulation we used. The different gas samples
are listed and described in Section 5.3. In Section 5.4 we determine the contribution of the different gas samples to the total amount of gas and H i and to the
H i column density distribution function. We discuss our results and conclude
in Section 5.5.
5.2 Simulations
We use a modified version of gadget-3 (last described in Springel, 2005b), a
smoothed particle hydrodynamics (SPH) code that uses the entropy formulation
of SPH (Springel & Hernquist, 2002), which conserves both energy and entropy
where appropriate. This work is part of the OverWhelmingly Large Simulations
(OWLS) project (Schaye et al., 2010), which consists of a large number of cosmological simulations with varying (subgrid) physics. Here we make use of the
so-called ‘reference’ model, with the difference that it was run with updated cosmological parameters. We have tested runs with different supernova feedback
and with AGN feedback and we found our conclusions to be robust to changes
in the model. The model is fully described in Schaye et al. (2010) and we will
only summarize its main properties here.
The simulation assumes a ΛCDM cosmology with parameters Ωm = 1 −
ΩΛ = 0.272, Ωb = 0.0455, h = 0.704, σ8 = 0.81, n = 0.967. These values are
taken from the WMAP year 7 data (Komatsu et al., 2011). In the present work,
we use the simulation output at redshifts 3 and 2.
A cubic volume with periodic boundary conditions is defined, within which
the mass is distributed over 5123 dark matter and as many gas particles. The box
size (i.e. the length of a side of the simulation volume) of the simulation used in
this work is 25 h−1 comoving Mpc. The (initial) particle masses for baryons and
dark matter are 2.1 × 106 M⊙ and 1.0 × 107 M⊙ , respectively. The gravitational
softening length is 1.95 h−1 comoving kpc, i.e. 1/25 of the mean dark matter
particle separation, with a maximum of 0.5 h−1 proper kpc.
Star formation is modelled according to the recipe of Schaye & Dalla Vecchia
(2008). A polytropic equation of state Ptot ∝ ρ4/3
gas is imposed for densities exceeding nH = 0.1 cm−3 , where Ptot is the total pressure and ρgas the density of
the gas. Gas particles with proper densities nH ≥ 0.1 cm−3 and temperatures
122
Simulations
T ≤ 105 K are moved onto this equation of state and can be converted into star
particles. The star formation rate (SFR) per unit mass depends on the gas pressure and reproduces the observed Kennicutt-Schmidt law (Kennicutt, 1998) by
construction.
Feedback from star formation is implemented using the prescription of Dalla
Vecchia & Schaye (2008). About 40 per cent of the energy released by type
II supernovae is injected locally in kinetic form, while the rest of the energy
is assumed to be lost radiatively. The initial wind velocity is 600 km s−1 and
the initial mass loading is two, meaning that, on average, a newly formed star
particle kicks twice its own mass in neighbouring gas particles.
The abundances of eleven elements released by massive stars and intermediate mass stars are followed as described in Wiersma et al. (2009b). We assume
the stellar initial mass function (IMF) of Chabrier (2003), ranging from 0.1 to
100 M⊙ . As described in Wiersma et al. (2009a), radiative cooling and heating are computed element by element in the presence of the cosmic microwave
background radiation and the Haardt & Madau (2001) model for the UV/X-ray
background from galaxies and quasars in the optically thin limit.
We apply a self-shielding correction in post-processing by using the radiative
transfer calculations described in Altay et al. (2011) and Altay et al. (in preparation). This is an iterative method that uses reverse ray-tracing (i.e. shooting
rays starting from the gas element) to compute the optical depth and to calculate a new neutral fraction until the results converge. The method assumes
that the radiation field is dominated by the UV background radiation. Altay
et al. (2011) have shown that this provides a good match to the observed H i
column density distribution function. The temperature of the ISM gas in the
simulation is determined by the imposed effective pressure and therefore not
realistic, so we set it to 104 K, typical of the warm neutral medium. Gas with
lower densities (nH < 0.1 cm−3 ) was assumed to be optically thin during the
simulation, whereas this may not be the case because of self-shielding. We use
the temperatures that were calculated in the presence of the UV background to
be self-consistent with the simulation, even though the actual gas temperatures
will be lower in the self-shielded case. These choices do not affect the results described here. Hydrogen is converted into molecules with a prescription based on
observations by Blitz & Rosolowsky (2006), who provide the molecular fraction
as a function of the gas pressure.
Recently Kereš et al. (2011) have shown that the sizes of galaxy discs depend
on the computational method used (but see also Hummels & Bryan (2011)).
However, Sales et al. (2010) have shown that changes in the feedback model lead
to dramatic variations in the morphology of discs, as well as to variations of up
to an order of magnitude in disc masses. Indeed, Scannapieco et al. (2011) have
shown explicitly that variations in the feedback prescription are much more important than the numerical scheme used to solve the hydrodynamics. To assess
the robustness of our conclusions, we have redone our analysis using simulations
with different feedback prescriptions, but do not show the results. The simula123
Cold flows as H i absorption systems
#
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
name
all
Tmax<5p5
inhalo
inmainhalo
insubhalo
inhalo9to10
inhalo10to11
inhalo11to12
inhalo12to13
inflowing
11. static
12. outflowing
13. inhalo_inflowing
14. inhalo_static
15. inhalo_outflowing
16.
17.
18.
19.
inISM
pastISM
futureISM
futurefirstISM
selection
all gas
gas with Tmax ≤ 105.5 K
halo gas (with Mhalo ≥ 109 M⊙ )
gas in main haloes (with Mmain halo ≥ 109 M⊙ )
gas in satellites (with Msatellite ≥ 108 M⊙ )
gas in haloes with 109 ≤ Mhalo < 1010 M⊙
gas in haloes with 1010 ≤ Mhalo < 1011 M⊙
gas in haloes with 1011 ≤ Mhalo < 1012 M⊙
gas in haloes with 1012 ≤ Mhalo < 1013 M⊙
gas that is moving towards the nearest (nearest in units of Rvir ) halo
centre with a peculiar velocity greater than a quarter of its circular
velocity
gas that is neither inflowing (#10) nor outflowing (#12)
gas that is moving away from the nearest (nearest in units of Rvir ) halo
centre with a peculiar velocity greater than a quarter of its circular
velocity
halo gas that is moving towards the halo centre with a peculiar velocity
greater than a quarter of its circular velocity
halo gas that is neither inflowing (#10) nor outflowing (#12)
halo gas that is moving away from the halo centre with a peculiar
velocity greater than a quarter of its circular velocity
gas which is in the ISM at z = 3
gas which is not in the ISM at z = 3, but was at some redshift z > 3
gas which is not in the ISM at z = 3, but will be before z = 2.
gas which is not in the ISM at z ≥ 3, but will be before z = 2.
124
Table 5.1: List of selection criteria for the various gas samples in the same order as in Figures 5.1 and 5.4.
Gas samples
tions reproduce the observed H i column density distribution function independent of the feedback scheme (Altay et al. in preparation). Although the relative
contributions of the different gas selections to the H i absorption vary somewhat between different simulations, the general conclusions are unchanged. We
therefore conclude that the uncertainties associated with the feedback and the
numerical method are unlikely to be important for our conclusions.
5.3 Gas samples
We compute the z = 3 contribution of gas with different properties to the H i
column density distribution function. The gas selections that we consider are
listed in Table 5.1. They are based on the maximum past temperature, Tmax ,
membership of haloes, the peculiar velocity towards the nearest halo, vrad , and
on whether the gas is part of the ISM. These properties are all important to
determine whether or not this gas is accreting in the cold mode. Cold-mode gas
should have a low temperature at least until it becomes part of the ISM. Gas
has only been accreted if it is inside a halo. It is likely to accrete onto a halo or
its central galaxy if its radial peculiar velocity towards the halo centre is high,
but note that gas orbiting around the central galaxy can also be built up by cold
flows and could be viewed as evidence for cold accretion (Stewart et al., 2011b).
The gas is certainly accreting onto a galaxy if it enters the ISM of a galaxy and
becomes star forming in the near future. Below, we describe the selections in
detail.
The maximum past temperature, Tmax , is the maximum value that the temperature of a gas element has reached over the entire past simulation history.
High time resolution is achieved by storing a separate variable during the simulation which is updated every time-step if the gas reaches a higher temperature
than the previous value of Tmax. The artificial temperature that a gas particle has
while it is on the imposed equation of state, and thus star forming, is ignored.
Because we are interested in the temperature history before the gas accretes onto
a galaxy, this is consistent with our aims. Cold-mode gas does not experience a
shock at the virial radius and reaches a maximum temperature of ∼ 105 K just
before accretion onto a halo due to heating by the UV background (van de Voort
et al., 2011a). We therefore select cold-mode gas by using Tmax ≤ 105.5 K (sample
Tmax<5p5 of Table 5.1). While hot-mode gas has by definition been hotter than
105.5 K, its current temperature can be much lower (e.g. van de Voort & Schaye,
2012).
We note that Tmax may underestimate the true maximum past temperature.
In SPH simulations a shock is smeared out over a few smoothing lengths, leading to in-shock cooling (Hutchings & Thomas, 2000). If the cooling time is of
the order of or smaller than the time step, then the maximum temperature will
be underestimated. Creasey et al. (2011) have shown that a particle mass of
106 M⊙ is sufficient to avoid numerical overcooling of accretion shocks onto
125
Cold flows as H i absorption systems
haloes, which is very close to the resolution used in this simulation. Interpolating their results indicates that our mass resolution is indeed sufficient. Even
with infinite resolution, the post-shock temperatures may, however, not be well
defined. Because they have different masses, electrons and protons will have
different temperatures in the post-shock gas and it may take some time before
they equilibrate through collisions or plasma effects. We have ignored this complication. Another effect, which was also not included in our simulation, is that
shocks may be preceded by the radiation from the shock, which may affect the
temperature evolution. Ignoring these issues, van de Voort et al. (2011a) showed
that the distribution of Tmax is bimodal and that a cut at Tmax = 105.5 K naturally divides the gas into filamentary cold- and diffuse hot-mode accretion and
that it produces similar results as studies based on adaptive mesh refinement
simulations.
Haloes are found by using a Friends-of-Friends (FoF) algorithm. If the separation between two dark matter particles is less than 20 per cent of the average
separation (the linking length b = 0.2), they are placed in the same group. Assuming a radial density profile ρ(r ) ∝ r −2 , corresponding to a flat rotation curve,
such a group has an average overdensity of hρhalo i/hρi ≈ 180 (e.g. Lacey & Cole,
1994), which is close to the value for a virialized object predicted by the top-hat
spherical collapse model. Baryonic particles are placed in a halo if their nearest dark matter neighbour is part of the halo. Haloes can contain both bound
and unbound particles. The selections are made by using haloes with total mass
Mhalo ≥ 109 M⊙ , corresponding to approximately 100 dark matter particles. A
gas particle is considered to be in a halo if it is a member of a Friends-of-Friends
group (inhalo).
We use subfind (Springel et al., 2001; Dolag et al., 2009) on the FoF output
to identify gravitationally bound subhaloes. The main halo is the most massive
subhalo in a FoF halo and the remaining subhaloes are classified as satellites.
Because only bound particles are included in this definition, some unbound
particles are not attached to any subhalo, although they are part of the FoF halo.
The gas is in a main halo if it is a member of the most massive subhalo, with
Mmain halo ≥ 109 M⊙ (inmainhalo) and the gas is in a satellite if it is a member of
a subhalo, with Msatellite ≥ 108 M⊙ , that is not a main halo (insubhalo).
The halo gas (inhalo) is subdivided into four mass bins, 109 ≤ Mhalo <
10
10 M⊙ (inhalo9to10), 1010 ≤ Mhalo < 1011 M⊙ (inhalo10to11), 1011 ≤ Mhalo <
1012 M⊙ (inhalo11to12), and 1012 ≤ Mhalo < 1013 M⊙ (inhalo12to13), containing
38 504, 3626, 275, and 17 haloes, respectively.
The radial peculiar velocity of every gas particle is calculated with respect
to the nearest halo. The position (and the centre) of the halo is defined as the
position of its most bound particle. The virial radius, Rvir , is the radius around
this centre which encloses an average density that agrees with the prediction
from top-hat spherical collapse calculations in a ΛCDM cosmology (Bryan &
Norman, 1998). Distances towards a halo, d, are normalized by Rvir of that halo.
The nearest halo is the one for which d/Rvir is minimum. The halo’s peculiar
126
Results
velocity is defined to be the centre of mass velocity of its main subhalo and is
subtracted from the gas peculiar velocity to determine the relative radial peculiar
velocity. If the gas is located inside a halo, its radial velocity is calculated with
respect to the centre of that halo, even if it is also in a satellite. The selections
are made by comparing
the radial velocity of the gas to a quarter of the circular
√
velocity, vcirc = GMvir /Rvir , of the nearest halo, where Mvir is the total mass
inside Rvir . The gas is inflowing when vrad ≤ −0.25vcirc (inflowing), static when
−0.25vcirc < vrad < 0.25vcirc (static), and outflowing when vrad ≥ 0.25vcirc (outflowing). Note that gas near or inside a small halo embedded in a filament may
be classified as outflowing with respect to its nearest halo, whereas it might be
inflowing with respect to a much larger halo that is being fed by this filament. It
is hard to unambiguously identify this gas, so we just caution the reader that the
amount of inflowing gas may be an underestimate. This would only strengthen
our conclusions.
The definition of the nearest halo is somewhat arbitrary and the gas may be
many virial radii away and unrelated to the nearest halo. This is why we make
the same radial velocity cuts for all gas (samples 10–12 of Table 5.1) also for gas
that is already inside a (FoF) halo, so that we know it has already been accreted
by the halo (samples 13–15 of Table 5.1). Halo gas which is inflowing is in the
process of accreting onto the central galaxy (inhalo_inflowing).
In our simulation gas becomes star forming when its density exceeds nH =
0.1 cm−3 while its temperature T ≤ 105 K. Because of supernova feedback, the
gas can leave the ISM and re-enter it (e.g. Oppenheimer et al., 2010). We will
call this recycled gas even though it may not have been part of a star before it
was ejected from the ISM. We keep track of the time a gas particle last reached
or left the ISM. We select all the gas that is star forming at z = 3, i.e. the ISM
(inISM), star forming before but not at z = 3, i.e. recycled gas (pastISM), star
forming before z = 2 but not at z = 3, i.e. gas that will accrete onto a galaxy
before z = 2 (futureISM), or star forming before z = 2 but not at z ≥ 3, i.e. gas
that will accrete onto the galaxy before z = 2 for the first time (futurefirstISM).
The time elapsed between z = 3 and z = 2 is about 1.2 Gyr, which is similar
to the gas consumption time scale implied by the observed Kennicutt-Schmidt
star formation law for typical ISM densities and indicates whether the gas will
accrete onto a galaxy in the near future.
5.4 Results
5.4.1 Gas and H i fractions
Many of the gas samples listed in Table 5.1 contain a much larger fraction of the
total H i mass than of the total gas mass. This is illustrated in Figure 5.1, which
shows the fraction of the total amount of gas (left panel) and the fraction of the
total amount of neutral hydrogen (right panel) accounted for by the samples
127
128
Cold flows as H i absorption systems
Figure 5.1: Fraction of the total amount of gas (left) and H i (right) at z = 3 accounted for by the selections listed in Table 5.1. Many
samples (#3–9 and #13–19) contain a much larger fraction of the H i mass than of the total gas mass.
Results
listed in Table 5.1. The density parameter of all the gas Ωgas = 0.15787 and of
neutral hydrogen ΩH i = 0.00178, so at z = 3 only about one per cent of the
gas mass consists of neural hydrogen. Selections based on halo membership
(samples 3–9 and 13–15) and on participation in star formation (samples 16–19)
account for little of the gas mass, but a significant part of the H i mass.
The maximum past temperature selection (Tmax<5p5) contains almost all
gas in the simulation. This is not so surprising, because most of the mass in the
Universe is in the IGM and the UV background can only heat this gas to temperatures . 105 K. The same selection also contains almost all neutral hydrogen
gas. Gas that shocked to T > 105.5 K while it was extragalactic, either through
accretion shocks or shocks caused by galactic winds, accounts for only about 10
per cent of both the gas and H i. This already tells us that most gas and most
neutral hydrogen is cold-mode gas.
Note that this is not a trivial result. While it is true that gas with temperatures
above 105.5 K will be collisionally ionized and therefore difficult to see in H i
absorption, we distinguish cold- and hot-mode gas based on the maximum past
temperature rather than the current temperature. Gas parcels accreted in the hot
mode can cool down, reach temperatures similar to those of cold-mode gas, and
show up in H i absorption.
Haloes contain less than 10 per cent of the gas, but more than 90 per cent
of the neutral hydrogen (inhalo). Gas outside haloes contributes little to the
H i content, because the neutral fraction increases with density and the highest
densities are found inside haloes. Combining this with the finding that sample
Tmax<5p5 accounts for nearly 90 per cent of the neutral hydrogen, proves that
most H i absorption arises from gas that has been accreted onto haloes in the
cold-mode. All main haloes contain seven times more gas and four times more
H i than all satellites (compare inmainhalo and insubhalo).
Haloes from the entire mass range contain a significant part of the H i mass
(samples 6–9). Haloes in the highest mass bin are very rare and their total
contribution is the smallest (15 per cent; inhalo12to13). Haloes below Mhalo =
109 M⊙ , and therefore below our resolution limit, are not expected to contain
a large amount of H i, because we already account for the vast majority of H i
with higher mass haloes (inhalo) and our simulations reproduce the observed H i
distribution (Altay et al., 2011).
Approximately 40 per cent of the gas and half of the neutral hydrogen is
inflowing faster than a quarter of the circular velocity of the nearest (nearest
in units of Rvir ) halo (inflowing). The contribution is even larger for all inflowing gas, without a minimum radial velocity threshold (about 65 per cent; not
shown). Outflows always account for less than 25 per cent of the gas and H i
mass (outflowing). The contribution of outflowing gas and of static gas (i.e. gas
moving either in or out at velocities below 0.25vcirc ; static) is lower for H i than
for all gas, whereas the contribution of inflowing gas is higher.
Within haloes, the importance of inflows (inhalo_inflowing), with respect to
outflows (inhalo_outflowing) and static gas (inhalo_static), increases slightly. This
129
Cold flows as H i absorption systems
is not visible in Figure 5.1, because the bars are too small. The H i inside haloes
is distributed over the inflowing, static, and outflowing components in the same
way as all H i (i.e. both inside and outside of haloes), because haloes account for
nearly all the H i. Thus, about half of the H i can be accounted for by gas inside
the virial radius that is falling towards the halo centre with a velocity greater
than 25 per cent of the halo’s circular velocity.
Very little gas is contained in the ISM of galaxies, but almost half of the H i
mass is (inISM). The amount of gas that has been ejected from galaxies at z > 3
(pastISM) is greater than the amount that is in the ISM at z = 3 (inISM), but the
situation is reversed for H i. Similarly, more gas has been ejected from galaxies at
z > 3 (pastISM) than will accrete onto galaxies at 2 ≤ z < 3 (futureISM), but it is
the other way around for neutral hydrogen. Taken together, gas that is currently
in the ISM and gas that will enter the ISM within 1.2 Gyr (inISM + futureISM)
account for most of the H i in the Universe. Gas/H i that will accrete onto a
galaxy at 2 ≤ z < 3 for the first time (futurefirstISM) accounts for most/less than
half of the total amount of gas/H i that will accrete at 2 ≤ z < 3 (futureISM).
5.4.2 Spatial distribution: A visual impression
To gain insight into the spatial distribution of the neutral hydrogen, Figure 5.2
shows the H i column densities at z = 3 in a 2 by 2 comoving h−1 Mpc region
centred on a 1012.4 M⊙ halo, one of the most massive objects in the simulation.
The Figure is meant to illustrate the spatial distribution of the H i corresponding
to some of the samples listed in Table 5.1. Some gas samples trace only a subset
of the high column density sightlines, while others trace the full morphology of
the H i.
In the top row, the column densities are shown when including all gas (left),
only gas with Tmax ≤ 105.5 K (middle), and only gas inside haloes (right). The
vast majority of neutral gas inside and outside haloes satisfies Tmax ≤ 105.5 K, so
even for the 1012.4 M⊙ halo with Tvir = 106.2 K, most of the H i is contributed by
gas that has Tmax ≤ 105.5 and that has thus not gone through an accretion shock
near the virial radius. When we exclude gas outside haloes (top right panel), we
lose the filamentary material connecting different haloes, as well as most of the
NH i < 1017 cm−2 sightlines.
The middle row shows the column density when including only gas that is
inflowing towards the nearest (nearest in units of Rvir ) halo faster than a quarter of the circular velocity of that halo (left), only gas outflowing faster than a
quarter of the circular velocity (right), and the remaining and hence “static” gas
(middle). The morphologies of the H i gas are very different. The inflowing gas
traces most of the extended and filamentary structure of the total H i distribution, while the static and outflowing gas are concentrated in the centres of the
haloes.
The images shown in the bottom row include only gas that is not part of the
ISM at z = 3. Additionally, the panels include only gas that was part of the ISM
130
Results
Figure 5.2: H i column density images for a cubic region of 2 comoving h−1 Mpc on a side
centred on a 1012.4 M⊙ halo at z = 3, one of the most massive haloes in this simulation.
For reference, the virial radius of this halo is 268 comoving h−1 kpc and indicated with
black circles. For all but the first panel, the H i column densities were computed including
only gas selected to be part of the samples indicated in each panel and listed in Table 5.1.
Some gas samples trace the full H i morphology, whereas others only trace a subset of
the high column density sightlines.
131
Cold flows as H i absorption systems
for some redshift z > 3 (i.e. ejected gas; left panel), only gas that becomes part
of the ISM at 2 ≤ z < 3 (middle), and only gas that joins the ISM at 2 ≤ z < 3
for the first time (right). The ejected gas that is not currently part of the ISM
(bottom left panel) is located relatively close to the centres of haloes, where star
formation is taking place, but it is more spread out than the actual ISM (not
shown). Comparing it to the middle row, with inflowing (left), static (centre),
and outflowing (right) gas, we immediately see that some of the ejected gas is
already inflowing and thus recycling. Note that it may have been ejected from
a different halo than the one it is in now. Most of the lower column density
filamentary gas, especially the gas outside the halo, is missing. Even though
ejected gas contributes significantly to NH i & 1018 cm−2 gas, it is unimportant
for lower column densities.
If we include all the gas that will reach the ISM between 2 ≤ z < 3, i.e. within
1.2 Gyr from the redshift at which we are studying the H i column densities (bottom middle panel), we leave the morphology of the NH i > 1016 cm−2 sightlines
intact, including the filaments in between haloes, although they become somewhat weaker. Most, but not all, H i gas in filaments close to a halo will accrete
onto a galaxy before z = 2.
The last panel shows a subset of the gas in the previous panel, because it
only includes gas that reaches the ISM between 2 ≤ z < 3 for the first time. The
general morphology of H i is the same, apart from some extra holes in the central
region of the halo, which are dominated by ejected gas. The column densities
above 1018 cm−2 are lower for a given pixel.
We conclude that the large-scale H i filaments that feed massive haloes consist
mostly of gas that has never gone through a virial shock, that is inflowing and
that will join the ISM, and hence participate in star formation, in the near future.
This gas typically has H i column densities similar to those of LLSs or higher for
embedded clumps. Within haloes, the infalling cold-mode gas has higher H i
column densities and tends to have a more clumpy morphology than the H i in
filaments outside haloes.
5.4.3 The column density distribution function
The H i column density distribution function is defined as the number of absorption lines N , per unit column density dNH i , per unit absorption distance
dX.
d2 N
d2 N dz
f ( NH i , z) ≡
≡
(5.1)
dNH i dX
dNH i dz dX
Absorbers with a fixed proper size and a constant comoving number density are
distributed uniformly, in a statistical sense, per unit absorption distance along
a line-of-sight (Bahcall & Peebles, 1969). The absorption distance is related to
the redshift path dz as dX/dz = H0 (1 + z)2 /H (z), where H (z) is the Hubble
parameter.
132
Results
Figure 5.3: Predicted H i column density distribution function at z = 3 (black curve)
and a compilation of observations around the same redshift (data points: Péroux et al.,
2005; O’Meara et al., 2007; Noterdaeme et al., 2009; Prochaska et al., 2010) and powerlaw constraints (dashed curve: Prochaska & Wolfe, 2009). The black curve is obtained by
collapsing the full three-dimensional H i distribution onto a plane. The observations are
matched well (see also Altay et al., 2011).
The predicted H i column density distribution function is shown in Figure 5.3
as the black curve. It was calculated by projecting the full three-dimensional
gas distribution onto a two-dimensional grid with 16 3842 pixels, which is sufficient to achieve convergence. Observationally determined power-law slopes at
NH i < 1019 cm−2 (Prochaska & Wolfe, 2009) and data points at NH i > 1019 cm−2
(Péroux et al., 2005; O’Meara et al., 2007; Noterdaeme et al., 2009; Prochaska
et al., 2010) have been converted to the cosmology assumed in our simulation
and are shown as red, dashed lines and red data points, respectively. The observations of the H i column density distribution function are matched well, also at
column densities lower than shown here (Altay et al., 2011). The match would
have been even better if we had corrected the gas temperatures for the effect of
self-shielding (see Altay et al., 2011). Including the radiation from local sources
might worsen the agreement, although Nagamine et al. (2010) have shown this
effect to be unimportant.
For NH i & 1017 cm−2 nearly all sightlines are dominated by a single absorption system, because they are very rare (Prochaska et al., 2010; Altay et al.,
2011). For column densities . 1016 cm−2 our method of projecting the entire
25 comoving h−1 Mpc simulation box does not recover the true column density distribution due to the projection of unrelated lower column density absorbers. Altay et al. (2011) therefore determine the column density distribution
in this regime by decomposing H i absorption spectra into Voigt profiles. Above
NH i ∼ 1018 cm−2 the column density distribution function flattens, because self133
Cold flows as H i absorption systems
shielding becomes important (Katz et al., 1996; Zheng & Miralda-Escudé, 2002;
Altay et al., 2011). It steepens again at NH i & 1020.3 cm−2 , because the neutral
hydrogen fraction saturates (Altay et al., 2011), and at NH i & 1021.5 m−2 due to
the formation of molecules (Schaye, 2001b; Zwaan & Prochaska, 2006; Krumholz
et al., 2009; Noterdaeme et al., 2009).
We can quantify the contribution of different gas samples by calculating the
mean fraction of the H i column density that is due to each gas selection as a
function of the total H i column density. This is shown in Figure 5.4 for all
the samples listed in Table 5.1. Note that the mean fraction would be 0.5 for a
′ if the selection includes all N ′ absorbers, but only half of
column density NH
i
Hi
their H i. However, a mean fraction of 0.5 would also be obtained if the selection
′ , but all the H i of the
includes half of the absorbers with column density NH
i
selected absorbers. Samples based on cuts in halo mass are best described by
the second case, but most other samples combine the two types of possibilities.
Figure 5.4 shows that most of the H i absorption is due to cold-mode gas that
is flowing towards the centre of the nearest halo. Above NH i = 1017 cm−2 this
gas is primarily inside haloes. Most of the H i gas at these column densities is
currently in the ISM or will become part of the ISM within the next 1.2 Gyr. We
discuss this in more detail below.
For absorbers with NH i < 1021 cm−2 more than 90 per cent of the H i column
density is due to gas that has never gone through a virial shock, i.e. cold-mode
gas (top left panel). For higher column densities, which arise mostly in the ISM
of galaxies residing in haloes with Mhalo > 1011 M⊙ , this cold-mode fraction
drops to 70 per cent. We do not know what caused the remaining gas to be
heated above 105.5 K (note that the same gas had a much smaller neutral fraction
at the time when it was this hot). It could have been a virial shock, an accretion
shock at a smaller radius, or a shock associated with a galactic wind. Note that
the gas that has Tmax > 105.5 K because it has been shocked in an outflow, may
have been accreted in the cold mode.
Most high column density gas resides in haloes, but the halo fraction drops
below 50 per cent for NH i < 1017 cm−2 (top middle panel). Combining this with
the fact that most gas has Tmax < 105.5 K, we conclude that most LLSs and most
DLAs arise from gas inside haloes that has been accreted in the cold mode. Most
of the H i absorption occurs in main haloes. Satellites contribute less than 20 per
cent for all column densities, but their contribution increases slightly with the
H i column density.
Very low-mass haloes (109 < Mhalo < 1010 M⊙ ) are most abundant and
therefore contain the largest amount of H i below NH i = 1021 cm−2 , accounting for about 40 per cent of the total absorption (top right panel). For NH i >
1021 cm−2 , a single very low-mass halo is simply not large enough to provide
a significant cross section. The contribution from haloes with Mhalo > 1011 M⊙
is dominant and steeply increasing at NH i > 1021 cm−2 . The fact that low(high-) mass haloes dominate low (high) column density DLAs agrees qualitatively with Pontzen et al. (2008), although they found that haloes more mas134
Results
135
Figure 5.4: Mean fraction of the H i column density at z = 3 contributed by the gas which fulfils the selection criteria listed in Table 5.1 as a
function of the total H i column density. Almost all of the contributing gas has Tmax < 105.5 K although hot-mode gas becomes significant,
accounting for up to 30 per cent of the absorption, above 1021 cm−2 . More than 80 per cent of NH i > 1018 cm−2 gas is located inside
(main) haloes. About 55 per cent of the H i is inflowing, but the contributions from static and outflowing gas are about 30 and 15 per
cent, respectively, and therefore not negligible. The contribution from gas accreting onto galaxies, i.e. gas that will join the ISM in the near
future, is dominant for 1017 − 1021 cm−2 , accounting for up to 70 per cent. Strong DLAs (NH i > 1021 cm−2 ) are dominated by ISM gas
(contributing more than 60 per cent to the absorption) and the Lyman-α forest by gas that will remain intergalactic down to at least z = 2
(contributing more than 60 per cent to the absorption).
Cold flows as H i absorption systems
sive than 1010.5 M⊙ only dominate for NH i > 1021.5 cm−2 . Unresolved haloes
(Mhalo < 109 M⊙ ) cannot dominate the absorption for NH i > 1017 cm−2 , because
most of it is already accounted for by resolved haloes.
We also split the gas into several SFR bins, but do not show the result. We
found that for NH i < 1021 cm−2 , the largest contribution (about 30 per cent),
comes from haloes with 0.01 < SFR < 0.1 M⊙ /yr. For higher column densities
objects with SFR > 10 M⊙ /yr are most important, accounting for 30–65 per cent
of the H i absorption, depending on the H i column density.
At all column densities, most H i gas is inflowing, but there are important
and roughly equal contributions from static and outflowing gas (bottom left
panel). The contributions from inflowing, static, and outflowing gas are nearly
constant (about 55, 30, and 15 per cent, respectively) up to NH i = 1021 cm−2 , at
which point the contribution of static gas increases relative to those of both inand outflows. If we separate the gas into inflowing or outflowing without any
minimum radial velocity threshold (not shown), then the ratio of inflowing to
outflowing remains approximately the same, with 65 per cent (35 per cent) of
the H i absorption due to inflowing (outflowing) gas.
Above NH i = 1018 cm−2 , the contribution to H i absorption from gas that
is in haloes and inflowing, static, or outflowing (bottom middle panel) is almost
equally large as that from all gas that is inflowing, static, or outflowing (bottom
left panel). Below NH i = 1018 cm−2 , their contribution is lower, because many
absorbers reside outside of haloes.
The fraction of H i absorption due to gas inside galaxies, i.e. the ISM, is only
significant for DLAs and dominates at NH i & 1021 cm−2 (bottom right panel).
Two-thirds of the 1017.5 < NH i < 1021 cm−2 material is not participating in star
formation yet, but will do so within the next 1.2 Gyr. About half of this gas
will accrete onto a galaxy for the first time. Gas previously ejected from galaxies
contributes a comparable amount of absorption as gas accreting onto galaxies
for the first time.
5.5 Discussion and conclusions
After post-processing with radiative transfer, the OWLS reference simulation
matches the observed z = 3 H i column density distribution over ten orders of
magnitude in NH i (Altay et al., 2011). This success gives us confidence that we
can use this simulation to study the relation between cold accretion and high
column density H i absorbers.
Like other simulations, our simulation also shows cold streams and filaments
inside and outside of haloes (van de Voort et al., 2011a). Gas in many of these
streams does not go through an accretion shock near the virial radius and, because it is able to accrete onto a galaxy much more efficiently than the hot,
diffuse gas, it is vital for fuelling star formation (e.g. Kereš et al., 2005; Ocvirk
et al., 2008; Kereš et al., 2009a; van de Voort et al., 2011a,b; van de Voort & Schaye,
136
Discussion and conclusions
2012; Faucher-Giguère et al., 2011). Here, we demonstrated that our simulation
would not have matched the observed H i column density distribution without
cold accretion. This fact alone provides evidence that cold accretion has already
been observed.
Motivated by the theoretical framework of cold, filamentary accretion, we
have investigated the importance of gas that satisfies certain selection criteria for
column densities above NH i = 1016 cm−2 at z = 3. It is difficult to check the
morphology of all the H i in the simulation, but from images (see also Figure 5.2)
we do know that a lot of the accreting cold-mode gas is filamentary. However,
the highest column density gas tends to be clumpy. Even though much of this
gas is infalling and has never gone through a virial shock, it would not all be
classified as streams based on its morphology.
We will first discuss the results separately for three column density regimes:
i) the Lyman-α forest; ii) LLSs and low column density DLAs, and iii) high
column density DLAs. We will then discuss our results in the context of the
cold-mode accretion paradigm, compare them to recent theoretical results from
Fumagalli et al. (2011a), and conclude.
1. Nearly all H i absorbing gas in the denser part of the Lyman-α forest
(NH i = 1016−17 cm−2 ) has never gone through a virial shock (Tmax <
105.5 K) and most of it is outside of haloes (the same is true for the low
column density forest, but we did not show this here). Even though 60
per cent is flowing towards the nearest halo (nearest in units of Rvir ) with
velocities greater than a quarter of its circular velocity, only 15–40 per cent
will participate in star formation before z = 2, i.e. within 1.2 Gyr. Most of
the Lyman-α forest gas that will accrete onto a galaxy before z = 2 will do
so for the first time.
2. Nearly all H i absorbing gas in LLSs (1017 < NH i < 1020.3 cm−2 ) and in low
column density DLAs (1020.3 < NH i < 1021 cm−2 ) has never gone through
a virial shock. About 60–95 per cent of the H i in LLSs is inside haloes
with larger contributions from lower-mass haloes: 30–40 per cent from
109−10 M⊙ , 20 per cent from 1010−11 M⊙ , 10–25 per cent from 1011−12 M⊙ ,
and less than 15 per cent from 1012−13 M⊙ haloes. Even inside haloes,
almost half of the neutral gas is inflowing with velocities greater than 25
per cent of the circular velocity. For LLSs, more than 90 per cent of the
H i is currently outside of galaxies, but 40–70 per cent will accrete onto
a galaxy within 1.2 Gyr and just over 30 per cent will do so for the first
time. The gas reservoir that is feeding galaxies is thus, at least in part,
associated with LLSs. A significant fraction of the gas in LLSs and low
column density DLAs has previously already been inside a galaxy. This
agrees with the finding that the re-accretion of gas that has been ejected is
important for the build-up of galaxies (Oppenheimer et al., 2010).
3. About 10–30 per cent of H i absorbing gas in high column density DLAs
137
Cold flows as H i absorption systems
(NH i > 1021 cm−2 ) was heated above 105.5 K in the past. This gas has
either been accreted in the hot mode or it has been shock-heated by a
galactic wind. Depending on the column density, 55–95 per cent of the
high-NH i DLA gas is contained in the ISM of galaxies and 50–70 per cent
of the H i is inside haloes more massive than 1011 M⊙ . Outflowing gas
contributes about 15 per cent of the H i. Inflowing gas provides the largest
contribution to the H i of high column density DLAs, but the static gas
component approaches the importance of the inflowing gas at the highest
column densities.
The simplest way of defining cold-mode accretion is purely based on its maximum past temperature. Gas with temperatures below 105.5 K is able to cool
efficiently, because the cooling function peaks at T ≈ 105−5.5 K (e.g. Wiersma
et al., 2009a). Above this temperature, cooling times become longer. We define
cold-mode gas as having Tmax < 105.5 K. Using this definition, practically all H i
absorption is due to cold-mode gas. This is not so surprising for the Lyman-α
forest, which is comprised mostly of gas outside of haloes and would therefore
not be expected to have been shock-heated to high temperatures. LLSs are dominated by low-mass haloes with Mhalo < 1011 M⊙ and Tvir < 105.4 K. Even if this
gas were heated to the virial temperature, we would still classify it as cold-mode
accretion. However, most neutral gas in haloes more massive than 1011 M⊙ cannot have been heated to the virial temperature, or we would have found that the
fraction of the H i with Tmax > 105.5 K exceeds the fraction of the H i contributed
by haloes with mass > 1011 M⊙ , which increases from about 20 to more than
95 per cent from NH i = 1018 to 1022 cm−2 . However, we find that the actual
fraction of H i contributed by gas with Tmax > 105.5 K is only 5–30 per cent for
this column density range. Thus, it is clear that even for high column density
absorbers, the H i content is dominated by gas that has never gone through an
accretion shock near the virial radius.
We can also think of cold-mode accretion as gas that has already accreted
onto haloes, but not yet onto galaxies, without having reached temperatures
above 105.5 K, flowing in with relatively high velocities, and that will accrete onto
a galaxy in the near future. About 30 per cent of all 1018 < NH i < 1020.5 cm−2
systems satisfy all these criteria. Therefore, even this set of highly restrictive criteria leads to the conclusion that cold-mode accretion has already been observed
in the form of high column density H i absorption systems.
However, if we think of cold-mode accretion as accreting onto galaxies for
the first time, in addition to having low Tmax , being inside haloes, and rapidly
inflowing, the fraction of LLSs satisfying this requirement is about a factor of
two lower, but still around 15 per cent. Cold streams also contain galaxies, so
the gas that is being recycled could still be accreting along these streams. If
we include previously ejected gas in our definition of cold-mode accretion, the
metallicity of cold-mode gas would not necessarily be low.
Fumagalli et al. (2011a) already pointed out that cold streams have likely
138
Discussion and conclusions
been detected as LLSs. They used high-resolution simulations of seven galaxies
with 1010.7 < Mhalo < 1011.5 M⊙ at z ≈ 3 by resimulating a cosmological simulation. They included ionizing radiation from local stellar sources, which we
did not. Nagamine et al. (2010) have shown that local stellar sources change the
column density distribution function by less than 0.1 dex, although Fumagalli
et al. (2011a) find a somewhat larger effect (0–0.5 dex). Fumagalli et al. (2011a)
investigated H i absorption from “central galaxies”, which they defined as all
gas within 0.2Rvir , and from “streams”, defined as all gas at radii 0.2Rvir < R <
2Rvir , and found that “cold streams” mostly have 1017 < NH i < 1019 cm−2 .
However, their definition of “cold streams” was all gas at 0.2Rvir < R < 2Rvir ,
which excludes neither gas that has been shock-heated to the virial temperature,
i.e. hot accretion, nor gas that is outflowing.
The halo sample of Fumagalli et al. (2011a) underproduces NH i < 1017 cm−2
systems, which they argue is because many of these absorbers live outside of
haloes. This is in agreement with our finding that the contribution of halo gas
is strongly declining with decreasing NH i , although we find that up to 30 per
cent still stems from low-mass haloes not covered by their simulations. We find
that for 1016 < NH i < 1020 cm−2 , haloes with 109 < Mhalo < 1010 M⊙ account
for about as much H i absorption as all higher-mass haloes combined. The fact
that 1018 < NH i < 1020 cm−2 systems are also underproduced in their sample
is therefore consistent with our finding that very low-mass haloes dominate the
H i column density distribution function. Fumagalli et al. (2011a) conclude that
haloes in the mass range 1010 < Mhalo < 1012 M⊙ already account for 20–30 per
cent of the LLSs and DLAs. We have found this fraction to be even larger: 30–40
per cent for LLSs and 40–70 per cent for DLAs. This difference could be due to
their inclusion of ionizing radiation from local sources.
Our results lead to the somewhat stronger conclusion that for 1018 < NH i <
cm−2 more than 80 per cent of the H i absorption is caused by cold-mode
halo gas. Only about 5 per cent is caused by hot-mode gas. The remainder may
arise from the high-density part of the IGM or from haloes with Mhalo < 109 M⊙ .
At lower column densities (NH i < 1018 cm−2 ), the contribution of halo gas
declines, though more than 95 per cent of the absorbing gas is still cold mode.
For higher column densities (NH i > 1021 cm−2 ), the absorption is dominated
by the ISM of galaxies in haloes with Mhalo > 1011 M⊙ and, depending on
the column density, the mean cold-mode contribution is between 70 and 90 per
cent. At all column densities, inflowing gas accounts for most of the H i column
density, but there are significant contributions from static and outflowing gas.
1021
We conclude that cold streams are real. They have already been observed
in the form of high column density absorbers, mainly in systems with 1017 <
NH i < 1021 cm−2 . Cold flows are critical for the success of our simulation in
reproducing the observed z = 3 column density distribution of damped Lymanα and particularly that of Lyman limit systems.
139
Cold flows as H i absorption systems
Acknowledgements
We would like to thank Olivera Rakic and all the members of the OWLS team for
valuable discussions and Claudio Dalla Vecchia and Alireza Rahmati for helpful
comments on an earlier version of the manuscript. The simulations presented
here were run on the Cosmology Machine at the Institute for Computational
Cosmology in Durham as part of the Virgo Consortium research programme.
The ICC Cosmology Machine is part of the DiRAC Facility jointly funded by
STFC, the Large Facilities Capital Fund of BIS, and Durham University. This
work was sponsored by the National Computing Facilities Foundation (NCF) for
the use of supercomputer facilities, with financial support from the Netherlands
Organization for Scientific Research (NWO), also through a VIDI grant, and from
the Marie Curie Initial Training Network CosmoComp (PITN-GA-2009-238356).
140
6
Soft X-ray and ultra-violet
metal-line emission from the gas
around galaxies
The gas around galaxies is diffuse and much fainter than the galaxies themselves.
A large fraction of the gas has temperatures between 104.5 and 107 K. If the gas
has metallicities above 0.1 Z⊙ , it will cool primarily through metal-line emission.
With current and upcoming instruments we may be able to detect the halo gas
in emission, either directly or statistically. We stack the galaxies in several large
cosmological, hydrodynamical simulations and calculate the expected metal-line
surface brightness as a function of radius from the centre. We then compare it to
the capabilities of current and future facilities. At low redshift, proposed X-ray
telescopes can detect O viii emission out to the virial radius of groups and clusters (assuming a detection limit of 10−1 photon s−1 cm−2 sr−1 ). C vi, N vii, O vii,
and Ne x can also be detected to smaller radii, 0.1 − 0.5Rvir . At high redshift it
will be possible to observe rest-frame UV lines, C iii, C iv, O vi, Si iii, and Si iv,
out to 10 − 20 per cent of the virial radius in haloes larger than 1011 M⊙ with upcoming instruments (assuming a detection limit of 10−20 erg s−1 cm−2 arcsec−2).
Most of these lines have surface brightnesses a factor of a few higher at low
redshift and could therefore easily be detected with the next generation UV
space telescope. The metal-line emission is, in general, biased towards regions
of high density and high metallicity and also towards the temperature where the
emissivity peaks. This bias varies with radius, halo mass, redshift and between
different emission lines. We can quantify the clumpiness of the emitting gas
with respect to the underlying density using the clumping factor. The clumping factor is highest in the most massive haloes, because for these haloes the
mass-weighted temperature is much higher than the peak emissivity temperature and the emission is thus dominated by cold, dense clumps. The X-rayflux-weighted properties are similar for all metal lines considered, whereas the
UV-flux-weighted properties vary strongly between metal lines.
Freeke van de Voort & Joop Schaye
Monthly Notices of the Royal Astronomical Society
To be submitted
Soft X-ray and UV emission from halo gas
6.1 Introduction
Haloes grow by accreting gas from their surroundings, the intergalactic medium
(IGM), which is the main reservoir of baryons. Galaxies grow by accreting gas
from their haloes, from which they can form stars. Some of the gas is returned
to the circumgalactic medium (CGM) in galactic winds driven by supernovae or
active galactic nuclei. Metals produced in stars are also blown out of the galaxy
and enrich the CGM. To understand the evolution of galaxies, one needs to study
the evolution of the halo gas.
UV and X-ray absorption line studies have revealed cold, neutral gas and
the warm-hot intergalactic medium around galaxies. Unfortunately, this type
of observation can only provide information along the line of sight, so there is
no information about the transverse extent of the absorbing gas cloud. Another
limitation is that we can only probe gas in case there is a bright background object. Therefore, absorption line studies are excellent for the regions of moderate
overdensity in the IGM, but because galaxies are rare, the statistics are poor for
relatively dense halo gas.
The gas emissivity scales with the square of the density. The signal is thus
dominated by high-density regions and more sensitive to the CGM than to the
general IGM. In this way, emission line studies complement absorption line studies. They have the added advantage of providing a two-dimensional image, in
addition to the third dimension provided by the redshift of the emission line,
allowing us to study the three-dimensional spatial distribution.
H i Lyman-α (Lyα) emission originates from regions with T ≈ 104 K. It therefore provides an excellent route to studying cold gas in the CGM. Diffuse Lyα
emission has been (statistically) detected around high-redshift galaxies at z ∼ 3
(e.g. Steidel et al., 2000; Matsuda et al., 2004; Bower et al., 2004; Steidel et al.,
2011). A large fraction of the halo gas is expected to heat to temperatures above
104.5 K, either through photo-ionization, accretion shocks, or through shocks
caused by galactic winds. UV metal-line emission enables us to probe gas with
T = 104.5−5.5 K, which is more diffuse than colder Lyα emitting gas and a better
probe of the average gas properties around galaxies. X-ray metal-line emission
traces even hotter gas T = 106−7 K, which is the relevant temperature of the
halo gas around high-mass galaxies and in galaxy groups. At T ∼ 104.5−7 K the
emission is dominated by metal lines for Z & 0.1 Z⊙ (e.g Wiersma et al., 2009a)
and not by hydrogen lines or continuum emission as is the case at lower and
higher temperatures.
Dilute halo gas that has been shock-heated to the virial temperature is routinely detected in X-ray observations of the centres of clusters and groups of
galaxies, and it may even have been seen around individual galaxies (e.g. Crain
et al., 2010a,b; Anderson & Bregman, 2011; Li & Wang, 2012). Most of the detections are made in X-ray continuum emission and Fe lines, see Böhringer &
Werner (2010) for a recent review. In the last year, a lot of progress has been
made on observing X-ray emission close to the virial radii of clusters (Simionescu
142
Method
et al., 2011; Akamatsu et al., 2011; Miller et al., 2011; Urban et al., 2011), but see
also Eckert et al. (2011). Additionally, there are claims of detections of metal
lines (e.g. Kaastra et al., 2003; Takei et al., 2007), whereas other observations set
upper limits at lower values than these claimed detections (e.g. Mitsuishi et al.,
2011, and references therein).
Observing metal-line emission from diffuse halo gas would yield a lot of information about the physical state of the gas, the distribution of metals, and thus
the cycle of gas between haloes and galaxies. In general, however, emission from
gas outside of galaxies is faint and thus difficult to detect. Many missions have
been proposed to study the diffuse halo gas in emission. With the next generation of spectrographs we should be able to detect certain metal lines. Motivated
by future instrumentation and recent proposals, recent studies have quantified
the expected emission using cosmological, hydrodynamical simulations (Furlanetto et al., 2004; Bertone et al., 2010a,b; Takei et al., 2011; Frank et al., 2011;
Bertone & Schaye, 2012). These studies are focussed mostly on quantifying the
emission expected from the warm-hot intergalactic medium in a large section of
the Universe or in mock datacubes.
It is possible to increase the signal-to-noise by stacking many observations,
centred on a galaxy. In this way we cannot study the halo gas around a single
object, but we can characterize the general properties of gas around a certain
type of galaxy. In this work we will quantify the expected surface brightness
(SB) for the brightest metal lines for a range of halo masses, both in UV at high
and low redshift and in soft X-ray at low redshift. Our study complements
previous work by predicting mean surface brightness profiles for different halo
masses.
In Section 6.2 we describe the simulations we used, how we identify haloes,
and how we calculate the emission signal. The results obtained for soft X-ray
lines at z = 0.125 and UV lines at z = 0.125 and z = 3 and their detectability
are described in Section 6.3. This Section also contains the prediction for H i
Balmer-α (Hα). Finally, we conclude in Section 6.4.
In all our calculations we assume the same cosmological parameters as during our simulation (see Section 6.2.1). Most notably Ωm = 1 − ΩΛ = 0.238 and
h = 0.73.
6.2 Method
6.2.1 Simulations
We use a modified version of gadget-3 (last described in Springel, 2005b), a
smoothed particle hydrodynamics (SPH) code that uses the entropy formulation
of SPH (Springel & Hernquist, 2002), which conserves both energy and entropy
where appropriate. This work is part of the OverWhelmingly Large Simulations
(OWLS) project (Schaye et al., 2010), which consists of a large number of cos143
Soft X-ray and UV emission from halo gas
mological simulations with varying (subgrid) physics. Here we make use of the
so-called ‘reference’ model. The model is fully described in Schaye et al. (2010)
and we will only summarize its main properties here.
The simulations assume a ΛCDM cosmology with parameters Ωm = 1 −
ΩΛ = 0.238, Ωb = 0.0418, h = 0.73, σ8 = 0.74, n = 0.951. These values are
consistent1 with the WMAP year 7 data (Komatsu et al., 2011). In the present
work, we use the simulation output at redshifts 3 and 0.125.
A cubic volume with periodic boundary conditions is defined, within which
the mass is distributed over 5123 dark matter and as many gas particles. The
box size (i.e. the length of a side of the simulation volume) of the simulations
used in this work are 25, 50, and 100 h−1 comoving Mpc. The (initial) par3 M
ticle masses for baryons and dark matter are 2.1 × 106 ( 25 hL−box
⊙ and
1 Mpc )
3 M , respectively. The gravitational softening length is
1.0 × 107 ( 25 hL−box
⊙
1 Mpc )
−1 comoving kpc, i.e. 1/25 of the mean dark matter particle
1.95 ( 25 hL−box
1 Mpc ) h
−1 proper kpc, which is reached
separation, with a maximum of 0.5 ( 25 hL−box
1 Mpc ) h
at z = 2.91.
Star formation is modelled according to the recipe of Schaye & Dalla Vecchia
(2008). A polytropic equation of state Ptot ∝ ρ4/3
gas is imposed for densities ex−
3
ceeding nH = 0.1 cm , where Ptot is the total pressure and ρgas the density of
the gas. Gas particles with proper densities nH ≥ 0.1 cm−3 and temperatures
T ≤ 105 K are moved onto this equation of state and can be converted into star
particles. The star formation rate (SFR) per unit mass depends on the gas pressure and reproduces the observed Kennicutt-Schmidt law (Kennicutt, 1998) by
construction.
Feedback from star formation is implemented using the prescription of Dalla
Vecchia & Schaye (2008). About 40 per cent of the energy released by type
II supernovae is injected locally in kinetic form, while the rest of the energy
is assumed to be lost radiatively. The initial wind velocity is 600 km s−1 and
the initial mass loading is two, meaning that, on average, a newly formed star
particle kicks twice its own mass in neighbouring gas particles.
The abundances of eleven elements released by massive stars and intermediate mass stars are followed as described in Wiersma et al. (2009b). We assume
the stellar initial mass function (IMF) of Chabrier (2003), ranging from 0.1 to
100 M⊙ . As described in Wiersma et al. (2009a), radiative cooling and heating are computed element by element in the presence of the cosmic microwave
background radiation and the Haardt & Madau (2001) model for the UV/X-ray
background from galaxies and quasars assuming the gas to be optically thin and
in (photo-)ionization equilibrium.
Using the suite of simulations from OWLS, Wiersma et al. (2011) have shown
that galactic winds driven by supernovae are essential for the enrichment of the
1
The only significant discrepancy is in σ8 , which is 8 per cent, or 2.3σ, lower than the value
favoured by the WMAP 7-year data.
144
Method
IGM. Close to the centre of a halo, most gas has been enriched to Z > 0.1 Z⊙ ,
but at the virial radius the scatter is very large (van de Voort & Schaye, 2012).
6.2.2 Identifying haloes
The first step towards finding gravitationally bound structures is to identify dark
matter haloes. These can be found using a Friends-of-Friends (FoF) algorithm.
If the separation between two dark matter particles is less than 20 per cent of
the average separation (the linking length b = 0.2), they are placed in the same
group. Baryonic particles are linked to a FoF halo if their nearest dark matter
neighbour is in that halo. We then use subfind (Dolag et al., 2009) to find the
most bound particle of a FoF halo, which serves as the halo centre and also
corresponds to the location of the central galaxy. We compute the virial radius,
Rvir , within which the average density agrees with that predicted by the top-hat
spherical collapse model in a ΛCDM cosmology (Bryan & Norman, 1998). The
halo mass is the mass contained inside Rvir .
Table 6.1 lists which simulation and halo mass bins are used for various lines
and redshifts. It also lists the median halo mass, median stellar mass, median
star formation rate, and the number of haloes in the different mass bins.
6.2.3 Emission
We calculate the emissivities of the gas following Bertone et al. (2010a). We only
summarize the method here and refer the reader to Bertone et al. (2010a) for
details on the procedure. The names and wavelengths of the lines considered in
this work are given in Table 6.2 for soft X-rays, which also includes the energy
of the lines, and in Table 6.4 for UV and Hα.
We created emissivity tables as a function of temperature, density, and redshift with the photo-ionization package cloudy, which was last described in
Ferland et al. (1998). The gas is assumed to be optically thin and in ionization
equilibrium in the presence of the cosmic microwave background and the Haardt
& Madau (2001) UV background. These assumptions were also made when
calculating cooling rates during the simulation (Wiersma et al., 2009a) and are
thus fully consistent with the simulation. We further assumed solar abundances
when creating the tables, but the results are scaled to the abundances derived
from the simulation. The tables are created for temperatures 102 K< T < 108.5 K
with ∆Log10 T = 0.05 bins and densities 10−8 cm−3 < nH < 10 cm−3 with
∆Log10 nH = 0.2 bins.
We calculate the emission only for gas with nH < 0.1 cm−3 , which is therefore
not star forming. Our simulations do not resolve the multiphase interstellar
medium at nH ≥ 0.1 cm−3 . As we are interested in determining the emission
from diffuse gas in haloes, this is consistent with our aims.
The emissivity, ǫ, for an emission line is derived from the tables as a function
of Log10 T and Log10 nH through interpolation. A gas particle’s luminosity is
145
redshift
0.125
band
X-ray
simulation
100 h−1 Mpc
0.125
UV & Hα
50 h−1 Mpc
3.0
UV
25 h−1 Mpc
Log10 Mhalo range
12-13 [M⊙ ]
13-14 [M⊙ ]
14-15 [M⊙ ]
11-12 [M⊙ ]
12-13 [M⊙ ]
13-14 [M⊙ ]
10-11 [M⊙ ]
11-12 [M⊙ ]
12-13 [M⊙ ]
Log10 Mhalo
12.3 [M⊙ ]
13.2 [M⊙ ]
14.2 [M⊙ ]
11.3 [M⊙ ]
12.3 [M⊙ ]
13.2 [M⊙ ]
10.3 [M⊙ ]
11.3 [M⊙ ]
12.2 [M⊙ ]
Log10 Mstar
10.8 [M⊙ ]
11.8 [M⊙ ]
12.6 [M⊙ ]
9.3 [M⊙ ]
10.9 [M⊙ ]
11.7 [M⊙ ]
8.2 [M⊙ ]
9.5 [M⊙ ]
11.0 [M⊙ ]
SFR
8.9 M⊙ yr−1
46
M⊙ yr−1
144
M⊙ yr−1
0.05 M⊙ yr−1
9.3 M⊙ yr−1
39
M⊙ yr−1
0.11 M⊙ yr−1
4.2 M⊙ yr−1
111
M⊙ yr−1
# haloes
2771
301
18
2723
374
46
1857
117
5
146
Soft X-ray and UV emission from halo gas
Table 6.1: List of the simulation box sizes and halo mass ranges used for different emission lines at different redshifts. Included are also
the median halo mass, median stellar mass, median star formation rate, and the number of haloes in each halo mass bin.
Method
then
L = ǫ(z, T, nH )
mgas Xy
ρ Xy⊙
(6.1)
in erg s−1 , where mgas is its mass, ρ is its density, Xy is the ‘SPH-smoothed’ mass
fraction of the element corresponding to the emission line, and Xy⊙ is the solar
mass fraction of the same element. We use smoothed abundances as described
by Wiersma et al. (2009b). This is consistent with the simulation, because these
smoothed abundances were also used in the simulation to compute the cooling
rates. The flux is
L
(6.2)
F=
4πd2L
in erg s−1 cm−2 , or
F=
λ
L
(1 + z )
4πd2L hp c
(6.3)
in photon s−1 cm−2 , with dL the luminosity distance, hp the Planck constant, c
the speed of light, and λ the rest-frame wavelength of the emission line.
To calculate the emission profiles, we project the flux using a flux-conserving
SPH interpolation scheme onto a two-dimensional grid, centred on the halo centre. The surface brightness is calculated by dividing the flux by the solid angle
subtended by a pixel either in arcsec2 or in sr,
SB = F/Ω.
(6.4)
In this paper, we investigate the detectability of the emission lines listed in
Tables 6.2 and 6.4, originating from circumgalactic gas. We quantify the expected surface brightness as a function of radius for a range of halo masses.
Our predictions made should be considered with care. We did not take into
account the velocities of the gas and thus the width of the lines, nor the effect
of the atmosphere. A robust study of detectability should produce datacubes,
including noise, and analyze them using the same pipeline as the observations.
This is beyond the scope of the present work in which we show and discuss the
theoretically expected surface brightnesses.
O vii is a line triplet at 0.574, 0.568, and 0.561 keV. The first line is a resonance
line, the second one an intercombination line and the last one a forbidden line.
Resonance photons have large cross-sections and will be scattered in random
directions, giving rise to lower observed fluxes or even absorption. The intercombination line is significantly weaker (0.5 − 0.6 dex) than the other two. The
resonance line is only slightly stronger than the forbidden line (by about 0.1 dex)
without taking into account attenuation. The actual 0.574 keV surface brightness
may be much lower due to resonant scattering. We therefore only show the surface brightness of the forbidden line at 0.561 keV, but note that if the emission at
all three wavelengths is added together, the signal could be more than twice as
strong.
147
Soft X-ray and UV emission from halo gas
Table 6.2: List of ion, rest-frame wavelength, and energy for the X-ray emission lines
used in this work.
ion
C vi
N vii
O vii
O viii
Ne x
λ (Å)
33.74
24.78
22.10
18.97
12.14
E (keV)
0.367
0.500
0.561
0.654
1.021
The UV doublets, C iv, O vi, and Si iv, have flux ratios of 2:1. We consider
only the strongest line in this paper, but the results for the weaker lines thus
follow directly.
6.3 Results
6.3.1 Soft X-ray
Current X-ray telescopes, i.e. Chandra and XMM-Newton, have not detected metalline emission from diffuse, intergalactic gas, which is consistent with the predictions (Yoshikawa et al., 2003, 2004; Fang et al., 2005). To map the halo gas with
future instruments, a combination of high angular and spectral resolution and a
large field of view are preferred (Bertone et al., 2010a). As the emission is dominated by bright, compact regions, high angular resolution is necessary prevent
smearing out the emission, in which case it would be harder to detect as well
as impossible to correctly identify its origin. ASTRO-H2 will be launched in a
few years, but its field of view is rather small and its spatial resolution is coarse
(e.g. Soong et al., 2011). Therefore, it is not an ideal instrument for studying
halo X-ray profiles. A number of X-ray missions have been proposed in the past
years, such as IXO/ATHENA3 and ORIGIN (den Herder et al., 2011). Their proposed specifications are listed in Table 6.3, as are those for existing and future
UV instruments, which are discussed in Sections 6.3.2 and 6.3.3.
The instrumental background is 2 × 10−2 photon s−1 cm−2 keV−1 , which corresponds to 1.3 × 103 photon s−1 sr−1 keV−1 for CRIS on ORIGIN (with a pixel
size of 300 µm and 24 arcsec). In the narrow field mode, the energy resolution is
2.5 eV, so this corresponds to 3 photon s−1 sr−1 . For an effective area of 103 cm2 ,
the surface brightness of the instrumental background equals 3 × 10−3 photon
s−1 cm−2 sr−1 . (It would be twice as much in the wide field mode.)
For XMS on IXO/ATHENA the instrumental background is also 2 × 10−2 photon s−1 cm−2 keV−1 , which corresponds to 8.5 × 104 photon s−1 sr−1 keV−1 (with
2 http://astro-h.isas.jaxa.jp/
3 http://ixo.gsfc.nasa.gov/,
148
http://sci.esa.int/ixo
Table 6.3: Summary of technical specifications for instruments discussed in the main text.
Telescope (instrument)
ORIGIN (CRIS)
IXO/ATHENA (XMS)
ASTRO-H (SXS)
FIREBALL
Hale (CWI)
Keck (KCWI)
VLT (MUSE)
Field of view
(arcmin2 )
10×10 (30 × 30)
2×2 (5 × 5)
3×3
2.67 × 2.67
1 × 0.67
0.33 × (0.14 − 0.57)
1×1
Angular resolution
(arcsec)
30
5
78
10
2.5 × 1
0.35 − 1.4
0.2
Spectral resolution
2.5 (5) eV
2.5 (10) eV
5 eV
0.4 Å
0.12 Å
0.03-0.6 Å
0.4 Å
Soft X-ray results
149
Soft X-ray and UV emission from halo gas
a pixel size of 300 µm and 3 arcsec). For an energy resolution of 2.5 eV, which
is appropriate for the narrow field mode, this corresponds to 2 × 102 photon
s−1 sr−1 . For an effective area of 3 × 104 cm2 , the surface brightness of the instrumental background equals 7 × 10−3 photon s−1 cm−2 sr−1 . (It would be four
times as much in the wide field mode.)
Hickox & Markevitch (2006) determined that the unresolved cosmic X-ray
background is about 14 ± 1 photon s−1 cm−2 sr−1 keV−1 in the energy range we
are interested in (0.5 − 1 keV). This unresolved signal is dominated by diffuse
Galactic emission and local thermal-like emission. Part of this unresolved background could be resolved in deeper observations (Hickox & Markevitch, 2007).
We will use the limit of 14 ± 1 photon s−1 cm−2 sr−1 keV−1 as it is an upper limit
on the unresolved background for future observations. For the energy resolution
of CRIS on ORIGIN and XMS on IXO/ATHENA (i.e. 2.5 eV) this corresponds to
about 3 × 10−2 photon s−1 cm−2 sr−1 . The instrumental background is therefore
lower than the unresolved X-ray background. Observations should be able to
probe down to 10−1 photon s−1 cm−2 sr−1 without being strongly affected by the
background. For this surface brightness a 1 Msec exposure would result in about
2 detected photons per resolution element for a 1 arcmin2 feature with ORIGIN
at 30 arcsec resolution and IXO/ATHENA at 5 arcsec resolution.
Figure 6.1 shows images of the mean surface brightness in the O viii (0.654
keV) line at z = 0.125, which is the brightest soft X-ray line we consider. We
use three halo mass bins, corresponding to (the haloes of) galaxies, groups, and
clusters, with masses of Mhalo = 1012−13 M⊙ , 1013−14 M⊙ , and 1014−15 M⊙ with
Rvir ≈ 0.25, 0.51, and 1.1 h−1 comoving Mpc, respectively. The images are 3 h−1
comoving Mpc on a side, which corresponds to 28 arcmin at z = 0.125, and the
white circles indicate the median virial radii of the haloes. Haloes with Mhalo >
1013 M⊙ have O viii emission that is stronger than 10−1 photon s−1 cm−2 sr−1 out
to 0.7Rvir , whereas for Mhalo = 1012−13 M⊙ this is only the case at R . 0.4Rvir .
To make emission profiles for all the metal lines listed in Table 6.2, we calculate the average of the surface brightness azimuthally. In Figure 6.2 we show
the mean (median) X-ray line surface brightness profiles for haloes at z = 0.125
as solid (dotted) curves. We show the same three halo mass bins as in Figure 6.1
out to twice the median virial radius.
The strongest observable soft X-ray line is O viii (0.654 keV). It is followed by
C vi (0.367 keV) and Ovii (0.561 keV) for galaxies. In groups, Ne x (1.021 keV)
is the second strongest line in the centre of the halo, but it is much weaker than
C vi and O vii in the halo outskirts. As mentioned in Section 6.2.3, O vii is a
triplet and the emission will be stronger when adding the contributions of the
three lines. For both galaxies and groups, the Ne x profile is steeper than that of
all the other lines shown. In clusters C vi and Ne x are of comperable brightness
at all radii and about 0.6 dex below O viii. N vii (0.500 keV) is similar to O vii at
all radii for cluster haloes and about an order of magnitude fainter than O viii.
Ne x has the lowest surface brightness for Mhalo = 1012−13 M⊙ , but it is as strong
as C vi for clusters. We also computed the emissivities of C v (0.308 keV), N vi
150
151
Soft X-ray results
Figure 6.1: Mean O viii emission maps for haloes with Mhalo = 1012−13 M⊙ , 1013−14 M⊙ , and 1014−15 M⊙ , from left to right, at z = 0.125.
The images are 3 h−1 comoving Mpc on a side, span 28 arcmin on the sky, and have a pixel size of 5 arcsec. The white circles indicate the
median virial radius.
152
Soft X-ray and UV emission from halo gas
Figure 6.2: Mean surface brightness (solid curves) as a function of radius at z = 0.125 for the same haloes as in Figure 6.1 for the X-ray
lines indicated in the legend. Dotted curves the median profile. The radius is normalized by dividing by the median virial radius in each
mass bin. The surface brightness in photon s−1 cm−2 sr−1 indicated by the left y-axis is exact. For the right y-axis it has been converted
to erg s−1 cm−2 arcsec−2 using hλi = 22.2 Åfor the right axis. The pixel size was 5 arcsec before binning it and the thickness of the region
is 5 h−1 comoving Mpc. O viii is the brightest line at all halo masses, followed by C vi. The relative strengths of the lines vary with halo
mass. For galaxy-sized haloes, the profiles flatten at R . 10 h−1 kpc, because this region is dominated by the ISM, which we excluded from
our analysis.
Soft X-ray results
(0.420 keV), Ne ix (0.922 keV), Mg xii (1.472 keV), Si xiii (1.865 keV), Si xv (2.460
keV), Fe xvii (0.727 keV), which were generally all weaker than the lines shown
(see also Bertone et al., 2010a). The emissivities of Ne ix and Fe xvii are as high
as those of N x in galaxies and Fe xvii is as high as O vii for R < 0.2Rvir in
groups. Both lines are fainter in cluster centres, but possibly still detectable.
At a limiting surface brightness of 10−1 photon s−1 cm−2 sr−1 , we would be
able to detect O viii emission out to the 80 per cent of the virial radius of cluster
with Mhalo = 1014−15 M⊙ , C vi out to 40 per cent, and O vii and N vii out to
20 per cent. For lower-mass haloes, Mhalo = 1013−14 M⊙ , O vii can be observed
out to the same physical scale, 200 h−1 comoving kpc, which corresponds to a
larger fraction of the virial radius, 0.4Rvir . In this case, O viii is observable out
to 0.7Rvir and C vi out to 0.5Rvir . For Mhalo = 1012−13 M⊙ , O viii, O vii, and
C vi can be observed out to the same radius of 0.3Rvir.
The instrumental background for SXS on ASTRO-H is even lower, but its
angular resolution is much worse and the effective area is very small. It should
be able to detect O viii emission in the centres of groups, but it will not be able
to see detailed structure, because the emission would be contained in a single
pixel.
Figure 6.3 shows the X-ray flux-weighted median overdensity, clumping factor, temperature, and metallicity. The solid lines and crosses show the result for the gas at 0.1Rvir − 0.5Rvir , while the dashed lines and triangles show
0.5Rvir −Rvir . The flux-weighted overdensities of the gas responsible for the different lines are very similar and close to the 84th percentile of the mass-weighted
overdensity and this is ∼ 0.2 − 0.7 dex above the median density. The reason for
this is that the emissivity scales as ρ2 , which biases the emission towards high
densities. The flux-weighted densities increase by ∼ 0.7 − 0.9 dex over two
orders of magnitude in halo mass, but the mass-weighted median density increases by only 0.4 dex over the same range of halo masses, indicating that the
clumpiness of the gas probed by the lines increases with halo mass.
Because the line flux scales with ρ2 and the mass with ρ, we can quantify the
clumpiness of the emitting gas with respect to the underlying density using the
clumping factor. In this case the clumping factor is calculated as
2
C = hρiFlux /hρiMass
(6.5)
where hρiFlux is the flux-weighted density and hρiMass the mass-weighted density. If the clumping factor is known, it is possible to derive the underlying
density profile from metal-line observations. The assumption C = 1 is clearly
not applicable.
For galaxies and groups, C . 3 and it is lower in the halo outskirts than in
the halo core. For clusters, the story is very different. The clumping factor is
around 10, with a spread of 0.4 dex for the different lines, so in this case the
emission gives a more biased view. The clumping factor is higher in the cluster
outskirts than in the centre, possibly indicating that a larger part of the emission
originates from satellites.
153
154
Soft X-ray and UV emission from halo gas
Figure 6.3: Mass-weighted (black curves) and X-ray flux-weighted (colours for different lines as in Figure 6.2) median overdensity,
clumping factor, temperature, and metallicity at z = 0.125 averaged over haloes with Mhalo = 1012−13 M⊙ , Mhalo = 1013−14 M⊙ , and
Mhalo = 1014−15 M⊙ , from left to right. The solid curves and crosses show the result for the gas at 0.1Rvir − 0.5Rvir , while the dashed
curves and triangles show 0.5Rvir −Rvir . The dotted, black curves show the mass-weighted 16th and 84th percentiles for the inner halo. The
flux-weighted properties are biased towards high density and metallicity. The flux-weighted temperature is biased towards the temperature
at which the line reaches its peak emissivity. The clumping factor is large in clusters.
Low-z UV results
Table 6.4: List of ion and rest-frame wavelengths for the Hα and UV metal-line emission
lines used in this work.
ion
H i (Hα)
C iii
C iv
O vi
Si iii
Si iv
λ (Å)
6563
977
1548
1032
1207
1394
λ2 (Å)
1551
1038
1403
The temperature at which the emissivity peaks is highest for Ne x, at ∼
K, and O viii, around 106.5 K, and it decreases slowly towards higher temperatures (Bertone et al., 2010a). This is the reason why, for galaxies and groups,
these lines have the highest flux-weighted temperatures. For clusters, the Ne xweighted temperature is lower than that of O viii. The flux-weighted median
temperatures increase less steeply with halo mass than the mass-weighted median temperature, although the former still increase by ∼ 0.7 dex for an increase
of 2 dex in halo mass. For the lowest (highest) mass bin the flux-weighted temperatures are higher (lower) than the mass-weighted temperature. The O vii
flux-weighted temperature stays roughly constant with halo mass. This is due
to the fact that the emissivity curve of O vii is more strongly peaked in temperature than the emissivity of the other lines (see Figure 1 of Bertone et al., 2010a).
It peaks at 106.3 K and drops quickly for higher and lower temperatures.
In the halo outskirts, the temperatures probed are somewhat lower, by 0.2 −
0.3 dex, than in the inner parts. The densities are lower by 0.5 − 0.7 dex. This
is true for flux-weighted as well as mass-weighted median temperatures and
densities, so they follow the same trend.
The median mass-weighted metallicity is 0.04-0.1Z⊙, but the flux-weighted
metallicities are 0.5-1.0 dex higher. The median flux-weighted metallicities are
similar to the 84th percentile of the mass-weighted metallicity, for galaxies and
groups. The flux-weighted metallicities for clusters are significantly above the
84th percentile, especially for O vii, which also has the highest overdensity and
lowest temperature. Thus, perhaps not surprisingly, X-ray metal-line emission
is biased towards high-metallicity gas. As metal lines dominate the emission in
the soft X-ray band (0.5-1.0 keV), the same will be true for broad band emission
(e.g. Crain et al., 2010a).
106.8
6.3.2 Low-redshift UV
For detecting UV metal-line emission as a tracer of halo gas, instruments should
ideally have a large field of view and a high spatial and angular resolution, as is
also the case for X-ray emission. The emission will be dominated by relatively
155
Soft X-ray and UV emission from halo gas
high-density material. With high spatial resolution, it will be possible to verify
its clumpiness.
A surface brightness limit of order 10−18 erg s−1 cm−2 arcsec−2 , as is the case
for the FIREBALL4 balloon experiment (Tuttle et al., 2008, 2010), will only be
sufficient to detect metal-line emission in the centres of massive haloes. The
wavelength range of FIREBALL (2000–2200 Å) is such that it will only probe
the UV metal lines at a somehat higher redshift than shown here (z ≈ 0.35 for
C iv) where the surface brightness is a bit lower. A detection limit of order
10−21 erg s−1 cm−2 arcsec−2 is envisioned for the next generation UV mission
ATLAST (Postman, 2009).
Figure 6.4 shows images of C iii (977 Å) line emission at z = 0.125. We use
three halo mass bins of Mhalo = 1011−12 M⊙ , 1012−13 M⊙ , and 1013−14 M⊙ with
Rvir ≈ 0.11, 0.25, and 0.50 h−1 Mpc, respectively. The images are 1 h−1 comoving
Mpc on a side, which corresponds to 9 arcmin at z = 0.125. The surface brightness in the haloes with mass below 1013 M⊙ looks relatively smooth, because it
has been averaged over many haloes (see Table 6.1 . There are only 46 haloes in
the last bin and the image looks very patchy. We will discuss the clumpiness of
the gas responsible for the emission below.
As in the previous section, we calculate the average of the surface brightness
azimuthally for the UV metal lines listed in Table 6.4. We include also Hα from
the same haloes and discuss it in Section 6.3.4. Figure 6.5 shows the mean
(median) surface brightness profiles for different UV lines for stacked haloes at
z = 0.125 as the solid (dotted) curves. We use the same three halo mass bins as
in Figure 6.4.
C iii (977 Å) is the brightest line, followed by Si iii (1207 Å). The emission
profile for all lines peaks in the halo core, where it may, however, be outshone by
the galaxy. O vi (1032 Å) gives the most extended profile, in the sense that the
ratio between emission in the halo core and outskirts is largest. This is caused by
the fact that O vi traces warmer and more diffuse gas than the other lines. C iv
(1548 Å) and Si iv (1294 Å) are weaker than C iii and Si iii, but because they have
frequencies redward of Lyα, they are less easily absorbed. We also computed the
emissivities of He ii (1640 Å) and N v (1239 Å), which were weaker and therefore
not shown.
A surface brightness limit of 10−18 erg s−1 cm−2 arcsec−2 should enable us to
observe metal-line emission from the centres of fairly massive galaxies (Mhalo >
1012 M⊙ . However, it is possible that the galaxy will outshine the halo in these
regions.
By stacking haloes, FIREBALL could in principle probe down to a surface
brightness limit of 10−19 erg s−1 cm−2 arcsec−2 . Its wavelenth rage is such that
it can only detect C iii and Si iii at z ≈ 1. As the surface brightness is lower at
z = 1 as compared to z = 0.125 by ∼ 0.5 (not shown), it may see emission out to
∼ 0.1Rvir for Mhalo > 1012 M⊙ . A complicating factor is that C iii and Si iii have
4 http://www.srl.caltech.edu/sal/fireball.html
156
157
Low-z UV results
Figure 6.4: Mean C iii emission maps for haloes with Mhalo = 1011−12 M⊙ , Mhalo = 1012−13 M⊙ , and Mhalo = 1013−14 M⊙ , from left to
right, at z = 0.125. The images are 1 h−1 comoving Mpc on a side, span 9.4 arcmin on the sky, and have a pixel size of 2 arcsec. The white
circles indicate the median virial radius.
158
Soft X-ray and UV emission from halo gas
Figure 6.5: Mean UV (solid curves) and Hα (dashed curve) surface brightness as a function of radius at z = 0.125 for the same haloes as in
Figure 6.4. The emission lines are indicated in the legend. Dotted curves show the median profile. The radius is normalized by dividing by
the median virial radius in each mass bin. The surface brightness in erg s−1 cm−2 arcsec−2 on the left y-axis is exact. It has been converted
to photon s−1 cm−2 sr−1 using hλi = 1232 Å. The pixel size was 2 arcsec before it was binned and the thickness of the region is 2.2 h−1
comoving Mpc. C iii is the brightest line, followed by Si iii.
Low-z UV results
frequencies blueward of Lyα and could therefore be absorbed by intervening
hydrogen, an effect that is much worse for C iii than Si iii.
With a detection limit of order 10−21 erg s−1 cm−2 arcsec−2 we would be able
to detect C iii out to the virial radius and several other metal lines out to 50
per cent of Rvir . Such a low surface brightness limit may be attainable for the
next generation UV mission ATLAST (Postman, 2009). As Lyα emission is even
brighter (e.g. Furlanetto et al., 2003), one can even probe the gas in emission
outside galactic haloes, in the filaments of the cosmic web.
In Figure 6.6 the UV flux-weighted overdensity, clumping factor, temperature, and metallicity are shown for several metal lines at z = 0.125 for the same
three halo mass bins as in Figure 6.4. The solid lines and crosses show the result for the gas at 0.1Rvir − 0.5Rvir , while the dashed lines and triangles show
0.5Rvir −Rvir . The different metal lines probe very different densities, all higher
than the mass-weighted overdensity. O vi results in the lowest flux-weighted
overdensity. The flux-weighted density increases via C iv to C iii to Si iv and
is the highest for Si iii. For all halo masses, the silicon lines have higher fluxweighted densities than the 84th percentile of the mass-weighted density. In
group-sized haloes all lines are dominated by gas denser than the mass-weighted
84th percentile. The difference between the O vi and Si iii flux-weighted overdensities is ∼ 1 dex. The flux-weighted overdensities increase somewhat more
steeply with halo mass than the mass-weighted overdensity, by about 1.5 dex for
an increase of 2 dex in halo mass.
Because the median flux-weighted densities vary a lot between different UV
metal-lines, the clumping factor, defined in Equation 6.5, does so as well. The
clumpiness is lowest for O vi emission and highest for Si iii, with a difference in
clumping factor of around 1.5 dex for a fixed halo mass. The clumping difference
between centre and outskirts is relatively minor, ∆Log10 C . 0.2 dex. For O vi in
galaxy haloes (Mhalo < 1013 M⊙ ), the clumping factor is close to one and hence a
good tracer of the density (although it is still biased towards high metallicities).
For the metal lines and halo mass range probed, the clumping factor varies
between ∼ 1 − 103. This means that the UV metal-line emission is quite clumpy.
This is in agreement with Bertone et al. (2010b) and Frank et al. (2011) who find
that most of the UV flux comes from discrete, compact sources.
The flux-weighted temperature depends on the specific metal line, decreasing
as the corresponding overdensity increases. They are insensitive to the massweighted temperature of the halo, because the emissivities are strongly peaked
at specific temperatures (Bertone et al., 2010b). The difference between Si iii
and O vi is just over an order of magnitude. All UV metal-lines probe gas with
temperatures 104.5−5 K with the exception of O vi, which is dominated by 105.5 K
gas.
The mass-weighted temperature is up to 0.2 dex lower in the outskirts of
the halo than in to the core, but the flux-weighted temperatures differ by at
most 0.1 dex. The overdensity is consistently lower by 0.3 − 0.6 dex in the halo
outskirts for both flux-weighted and mass-weighted densities.
159
160
Soft X-ray and UV emission from halo gas
Figure 6.6: Mass-weighted (black curves) and UV flux-weighted (colours for different lines as in Figure 6.5 and indicated in the legend)
median overdensity, clumping factor, temperature, and metallicity at z = 0.125 averaged over haloes with Mhalo = 1011−12 M⊙ , 1012−13 M⊙ ,
and 1013−14 M⊙ , from left to right. The solid curves and crosses show the result for the gas at 0.1Rvir − 0.5Rvir , while the dashed curves
and triangles show 0.5Rvir −Rvir . The dotted, black curves show the mass-weighted 16th and 84th percentiles for the inner halo.
High-z UV results
The flux-weighted median metallicity is about an order of magnitude higher
than the mass-weighted median metallicity and it is also higher than the massweighted 84th percentile. For high-mass haloes with Mhalo > 1012 M⊙ , O vi
probes gas with ∼ 0.3 dex lower metallicities than the other lines. In the centres
of groups the emission is dominated by gas with supersolar metallicities, even
though on average the gas is enriched to Z ≈ 0.1 Z⊙ . All computed metallicities increase with halo mass. Low-mass haloes with Mhalo = 1011−12 M⊙ have
0.6 dex lower mass-weighted metallicities in their outskirts as compared to their
cores. This difference is somewhat smaller for flux-weighted metallicities and
for higher mass haloes.
6.3.3 High-redshift UV
It is possible to detect rest-frame UV emitted at high redshift from the ground,
in the optical. In the near future, several integral field unit spectrographs will
become operational, such as the Multi-Unit Spectroscopic Explorer5 (MUSE) on
the Very Large Telescope (Bacon et al., 2010) and the Keck Cosmic Web Imager6
(KCWI) on Keck (Martin et al., 2010). The Cosmic Web Imager7 (CWI) is already
installed on the 200-inch Hale telescope (Rahman et al., 2006; Matuszewski et al.,
2010).
With narrow band observations it has already been demonstrated that diffuse
Lyα emission can be detected down to ∼ 10−18 erg s−1 cm−2 arcsec−2 in individual objects (e.g. Steidel et al., 2000; Matsuda et al., 2004) and down to ∼ 10−19 erg
s−1 cm−2 arcsec−2 in stacks (Steidel et al., 2011). New instrumentation, such as
MUSE and KCWI8 , will allow us to go one order of magnitude deeper. This is
essential for the detection of metal lines (Bertone & Schaye, 2012).
Figure 6.7 shows images of C iii line emission at z = 3. We use halo mass bins
of Mhalo = 1010−11 M⊙ , 1011−12 M⊙ , and 1012−13 M⊙ with Rvir ≈ 0.06, 0.14, and
0.29 h−1 comoving Mpc, respectively. The images are 0.5 h−1 comoving Mpc on a
side, which corresponds to 22 arcsec on the sky at z = 3. The surface brightness
is smoother than at z = 0.125 even though there are less haloes per bin, so the
flux is coming from less clumpy material.
As before, we calculate the average of the surface brightness azimuthally
for the metal-lines listed in Table 6.4. Figure 6.8 shows the mean (median) UV
line surface brightness profiles at z = 3 as the solid (dotted) curves for the
same three halo mass bins as in Figure 6.8. The surface brightness is about one
order of magnitude lower at z = 3 than at z = 0.125 at a fixed fraction of Rvir .
Additionally, the profile shows a strong flattening inside 10 per cent of the virial
radius. This is because we are probing down to smaller physical scales, where
the emission is dominated by star-forming gas, which we have excluded from
5 http://muse.univ-lyon1.fr/
6 http://www.srl.caltech.edu/sal/keck-cosmic-web-imager.html
7 http://http://www.srl.caltech.edu/sal/cosmic-web-imager.html
8 http://www.srl.caltech.edu/sal/keck-cosmic-web-imager.html
161
162
Soft X-ray and UV emission from halo gas
Figure 6.7: Mean Ciii emission maps for haloes with Mhalo = 1010−11 M⊙ , 1011−12 M⊙ , and 1012−13 M⊙ , from left to right, at z = 3. The
images are 0.6 h−1 comoving Mpc on a side, span 26 arcsec on the sky, and have a pixel size of 0.2 arcsec. The white circles indicate the
median virial radius.
163
High-z UV results
Figure 6.8: Mean UV surface brightness (solid curves) as a function of radius at z = 3 for the same haloes as in Figure 6.7. Dotted curves
the median profile. The emission lines are indicated in the legend. The radius is normalized by dividing by the median virial radius in
each mass bin. The surface brightness in erg s−1 cm−2 arcsec−2 on the left y-axis is exact. For the right y-axis, it has been converted to
photon s−1 cm−2 sr−1 using hλi = 1232 Å. The pixel size was 0.2 arcsec before it was binned and the thickness of the region is 1.2 h−1
comoving Mpc. C iii is the brightest line. C iv, Si iii, and Si iv are of similar strength. The surface brightnesses are lower than at z = 0.125
and the flattening at small radii is more pronounced.
Soft X-ray and UV emission from halo gas
our calculations.
Comparing our metal-line results to the Lyα profile observed by Steidel et al.
(2011) for Mhalo ∼ 1012 and hzi = 2.65, we predict that the C iii surface brightness is about 1–2 dex lower than the Lyα brightness. The other metal lines that
are shown are about 0.5–1 dex fainter than C iii. Because C iii has a much shorter
wavelength than Lyα, it is strongly absorbed by the intervening medium. It is
therefore possible that the other metal lines are in fact stronger than C iii. We
calculated, but do not show, the Lyα surface brightness profile from our simulations in the optically thin limit and without a contribution from star formation.
The observed profile is ∼ 0.7 dex higher than the predicted profile, which is not
surprising considering that the Lyα emission is thought to be originating from
H ii regions in the ISM.
With a detection limit of 10−20 erg s−1 cm−2 arcsec−2, C iii can be seen out
to 0.3Rvir for Mhalo = 1011−12 M⊙ and out to 0.2Rvir for 1012−13 M⊙ at z = 3.
Other metal lines are weaker, but can still be probed to 10 per cent of Rvir for
Mhalo > 1011 M⊙ . Nothe, however, that the emission may in reality be brighter at
these small radii, because we excluded emission from gas with NH > 0.1 cm−3 .
We predict that the surface brightness for lower-mass haloes is below this limit.
In Figure 6.9 the UV flux-weighted overdensity, clumping factor, temperature, and metallicity are shown at z = 3 for the same metal lines as in Figure 6.6. The solid lines and crosses show the result for the gas at 0.1Rvir − 0.5Rvir ,
while the dashed lines and triangles show 0.5Rvir −Rvir . The general picture is
unchanged at high redshift, although the density differences between different
lines is somewhat reduced. The flux-weighted overdensities are lower, but the
physical densities are higher at high redshift.
At z = 3 and for Mhalo < 1012 M⊙ , O vi and C iv have clumping factors
(see Equation 6.5) below unity, which means that the emission is biased towards
lower-density regions. For the same haloes, C ≈ 1 for C iii emission and the
clumping factor is 1–3 for the silicon lines. At higher halo masses, the clumping
facor is 1 − 1.5 dex higher and for most lines C ≈ 10 − 100. Because the average
temperature of the gas in these haloes is much higher than the temperature at
which the emissivity of the UV metal lines peaks, the emission is originating
from cold, dense clumps in the much hotter halo. For O vi the temperature
difference and hence the clumping factor is smallest.
At z = 3 the scatter in density is larger than at z = 0.125: the difference
between the 16th and 84th percentile is more than an order of magnitude as opposed to 0.4 dex. As a result, none of the lines are dominated by overdensities
above the 84th percentile at this redshift. O vi and C iv are tracing densities below the median mass-weighted density for low-mass haloes (Mhalo < 1012 M⊙ ).
The flux-weighted densities increase with halo mass, even if the mass-weighted
density does not. The median density in the outskirts is lower than in the centre,
for both flux- and mass-weighted quantities, by up to ∼ 0.6 dex.
The flux-weighted temperatures are insensitive to halo mass. They trace temperatures near or above the median mass-weighted temperature for low-mass
164
High-z UV results
165
Figure 6.9: Mass-weighted (black curves) and UV flux-weighted (colours for different lines as in Figure 6.8 and indicated in the legend)
median overdensity, clumping factor, temperature, and metallicity at z = 3 averaged over haloes with Mhalo = 1010−11 M⊙ , Mhalo =
1011−12 M⊙ , and Mhalo = 1012−13 M⊙ , from left to right. The solid curves and crosses show the result for the gas at 0.1Rvir − 0.5Rvir , while
the dashed lines and triangles show 0.5Rvir −Rvir . The dotted, black curves show the mass-weighted 16th and 84th percentiles for the inner
halo.
Soft X-ray and UV emission from halo gas
haloes (Mhalo < 1012 M⊙ ), but the opposite is true for higher-mass haloes. The
scatter in temperature increases with halo mass and becomes very large, with
the mass-weighted 84th percentile 2.2 dex above the 16th percentile. This reflects
the bimodal nature of halo gas in massive high-redshift galaxies, where the gas
either has a temperature close to the virial temperature and or has T < 105 K
(e.g. van de Voort & Schaye, 2012). O vi traces gas about an order of magnitude
warmer than the other metal lines shown, because its emissivity peaks around
105.5 K.
As we found before, the flux-weighted properties are biased towards high
metallicities. All lines trace metallicities of about 0.1–0.4 Z⊙ in the inner halo
and 0.1 − 0.4 dex lower in the outer halo. Because the spread in metallicity is
much larger at z = 3 than at z = 0.125, the flux-weighted metallicities trace the
mass-weighted 84th percentile at z = 3 as opposed to being significantly higher
at z = 0.125.
6.3.4 Low-redshift Hα
Hα (6563 Å) emission at low redshift is observable with the same instruments as
high redshift rest-frame UV emission. The predicted emission from gas around
galaxies is shown in Figure 6.5 as a dashed, black curve. Interestingly, the Hα
emission is comparable to C iii emission at R > 50 kpc for all haloes with
Mhalo = 1011−14 M⊙ . However, for R < 50 kpc, Hα is much brighter than
C iii for the lowest halo mass bin (Mhalo = 1011−12 M⊙ ) and up to an order of
magnitude fainter for the highest halo mass bin (Mhalo = 1013−14 M⊙ ). We stress
again that we ignored emission from gas with nH > 0.1 cm−3 .
Assuming a limiting surface brightness of 10−20 erg s−1 cm−2 arcsec−2, Hα
emission from halo gas can be detected out to 0.5Rvir for haloes with Mhalo =
1011−12 M⊙ , 0.25Rvir for haloes with Mhalo = 1012−13 M⊙ , and out to 0.4Rvir
for group-sized haloes. This is feasible when stacking deep observations with
MUSE or KCWI centred on galaxies.
6.4 Discussion and conclusions
A large fraction of the gas in galaxy haloes, groups, and clusters has temperatures T = 104.5−7 K (van de Voort & Schaye, 2012). At these temperatures, the
cooling is dominated by metal-line emission for metallicities Z & 0.1 Z⊙ (e.g.
Wiersma et al., 2009a). Observing these lines therefore constitutes an excellent
route to studying the diffuse, warm-hot gas around galaxies, both at low and at
high redshift. Additionally, metal-line emission may also provide us with clues
as to how the circumgalactic gas was enriched and thus about the feedback process responsible for this enrichment.
We used cosmological, hydrodynamical simulations to quantify the surface
brightness profiles of diffuse, circumgalactic gas, for both soft X-ray and rest166
Discussion and conclusions
frame UV metal lines. The lines we considered are C vi (0.367 keV), N vii (0.500
keV), Ovii (0.561 keV), O viii (0.654 keV), and Ne x (1.021 keV) in the X-ray band
and C iii (977 Å), C iv (1548 Å), Si iii (1207 Å), Si iv (1294 Å), and O vi (1032
Å) in the rest-frame UV band. We discussed their detectability with current and
future instruments and computed the flux-weighted physical properties of the
gas in the halo core and outskirts.
The strongest soft X-ray line at redshift z = 0.125 is O viii. It traces gas that
is denser than the mass-weighted density, but the clumping factor is only a few
for haloes with Mhalo < 1014 M)⊙ and of order 10 for clusters. The temperature
probed is within a factor of three from 106.5 K, the temperature at which the
emissivity peaks. It increases with halo mass, but less steeply than the massweighted temperature. The emission originates from regions with metallicities
of about 0.3 Z⊙ , whereas the mass-weighted metallitcity is a factor of three lower.
The difference between the inner and outer halo is largest for the flux-weighted
density, about a factor of three. The other X-ray lines are biased towards the
same densities, temperatures, and metallicity, but are at least a factor of three
weaker.
The strongest UV metal-line, both at z = 0.125 and z = 3, is C iii. The
temperature of the gas the emission originates from is very close to 104.7 K,
the temperature at which the emissivity peaks, and does not vary with halo
mass. At low redshift, the line is severely biased towards high metallicities. The
flux-weighted metallicity is about an order of magnitude higher than the massweighted metallicity. At high redshift, the bias is smaller and the difference
is a factor of a few. The clumping factor varies with halo mass from 10 to
100 at z = 0.125 and from 1 to 10 at z = 3. The flux-weighted overdensity
increases from O vi to C iv to C iii to Si iv to Si iii by a facor of ∼ 3 − 10. The
Si iii clumping factor reaches 103 in massive haloes. The temperature of the gas
probed is about the same for all lines, except for O vi, whose emissivity peaks
around 105.5 K.
Proposed X-ray missions with detection limits of 10−1 photon s−1 cm−2 sr−1
will be able to easily detect metal-line emission in galaxy haloes, groups, and
clusters at z = 0.125. O viii emission can be detected out to 80 per cent of the
virial radius of groups and clusters and out to 0.4Rvir for Mhalo = 1012−13 M⊙ .
C vi, N vii, O vii, and Ne x can also be detected out to smaller radii, 0.1 − 0.5Rvir.
Assuming a detection threshold of 10−20 erg s−1 cm−2 arcsec−2 , future optical
instruments should be able to detect several rest-frame UV metal lines, C iv, O vi,
Si iii, and Si iv, out to 0.1Rvir at z = 3 for haloes more massive than 1011 M⊙ .
C iii can be observed out to twice that distance. The same instruments can also
observe Hα at low redshift, which provides a good probe of the cold (104 K) halo
gas. Assuming the same detection threshold, Hα can be detected out to 0.2, 0.3,
and 0.5 Rvir for Mhalo = 1011−12, 1012−13, and 1013−14 M⊙ , respectively. Because
C iii has a frequency blueward of Lyα, it may be strongly absorbed, especially
when it is emitted at high redshift. The other UV metal lines may therefore be
stronger.
167
Soft X-ray and UV emission from halo gas
If we assume the same detection limit of 10−20 erg s−1 cm−2 arcsec−2 for UV
metal lines at z = 0.125, C iii can be detected out to 0.3Rvir for 1011−13 M⊙
haloes and out to 0.5Rvir for 1013−14 M⊙ haloes. C iv, O vi, Si iii, and Si iv can be
detected out to 0.1 − 0.2 Rvir for all haloes, and Si iii can even be seen out to the
same radius as C iii for 1013−14 M⊙ haloes.
Galaxies form inside (intersections of) filaments and we therefore expect that
neighbouring galaxies are connected by these filaments. Stacking haloes randomly will not show filamentary emission, because the filaments will be oriented randomly. However, before stacking the galaxies, we can first rotate them
towards their nearest neighbour of similar mass. This should enhance the emission of the gas in one direction. The signal at large radii is hard to detect, so
the brightest emission lines should be chosen for this. We tested this using our
simulations, but found that the enhancement is only about 0.2 dex (not shown).
Apart from stacking all images, one can stack only pixels with a detection in
the brightest emission line and then look for emission from other lines. Because
the emission is highest in the densest regions, the emission from different lines
will be correlated. This also leads to an enhancement of the signal. Using pixels
with a detection in Lyα would be well suited for detecting C iii, C iv, Si iii, and
Si iv as these probe cold (104.5 K) gas.
In the near future, before we submit this paper to a journal, we will recompute the surface brightness profiles for simulations that include AGN feedback,
because this feedback has been shown to be important (e.g. McCarthy et al.,
2010; Bertone et al., 2010a). Additionally, we will test the dependence of our results on the resolution, pixel size, bin size of the surface brightness profile, and
on the thickness of the region for which the emission is added.
Acknowledgements
We would like to thank Serena Bertone for allowing us to use the emissivity tables and all the members of the OWLS team for valuable discussions. The simulations presented here were run on Stella, the LOFAR BlueGene/L system in
Groningen, on the Cosmology Machine at the Institute for Computational Cosmology in Durham as part of the Virgo Consortium research programme, and
on Darwin in Cambridge. This work was sponsored by the National Computing
Facilities Foundation (NCF) for the use of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research (NWO),
also through a VIDI grant, and from the Marie Curie Initial Training Network
CosmoComp (PITN-GA-2009-238356).
168
Nederlandse samenvatting
De groei van sterrenstelsels en hun gasrijke halo’s
Wanneer je omhoog kijkt op een donkere plek op Aarde op een maanloze nacht,
kun je een lichte band van sterren zien. Dit komt doordat het merendeel van de
sterren in ons eigen sterrenstelsel verdeeld zit in een schijf, die we de Melkweg
noemen. De Melkweg bevat ongeveer 100 miljard sterren en er wordt elk jaar
ongeveer één nieuwe geboren. Deze sterren worden gemaakt in grote, koude
gaswolken. Daarbinnen trekken verdichtingen zich steeds verder samen onder
invloed van de zwaartekracht, totdat de dichtheid groot genoeg wordt om kernfusie te laten plaatsvinden, waarbij zodoende een ster ontstaat.
Sterren in sterrenstelsels vormen maar een klein deel van de totale materie
in het heelal. Omdat ze zo helder zijn, zijn ze relatief eenvoudig waar te nemen. Om te bestuderen hoe sterrenstelsels groeien wordt daarom vaak gekeken
naar hoe snel ze sterren vormen. Wat moeilijker te bepalen is via waarnemingen is waar het materiaal waaruit sterren vormen vandaan komt, omdat dit
gas erg weinig licht uitstraalt. Daarom gebruiken we bovendien kosmologische
simulaties om de vorming van sterrenstelsels te bestuderen. Hierbij wordt de
ontwikkeling van een representatief deel van het heelal gesimuleerd, van vlak
na de oerknal tot nu, waarbij alle relevante natuurwetten worden meegenomen.
Met kosmologische simulaties is het juist makkelijk om uit te zoeken waar de
materie zich bevindt. Bovendien zien we in observaties altijd een stilstaand
beeld, terwijl we met simulaties de ontwikkeling in de tijd kunnen volgen. Een
ander voordeel van simulaties is dat we precies weten welke ingredienten we
in ons ‘heelal’ stoppen. Willen we vervolgens weten wat het effect van een
enkel proces is, dan kunnen we een tweede simulatie doen waarbij we dit proces uitschakelen en deze beide simulaties vergelijken.
In het jonge heelal was alle materie vrijwel homogeen verspreid. Kleine verschillen in dichtheid trokken vervolgens samen onder de invloed van zwaartekracht. Hierbij ontstond een ‘kosmisch web’ van filamenten. Tussen deze filamenten bevinden zich grote leegtes, maar in deze filamenten vormen zich
gebonden objecten, die we halo’s noemen. Deze halo’s bestaan voor het grootste gedeelte uit donkere materie, maar ook uit baryonische materie9 . Donkere
materie kan zijn kinetische energie heel moeilijk verliezen, maar gas kan licht
uitstralen en zodoende energie kwijtraken. Hierdoor kan het gas nog verder samentrekken dan de donkere materie en op deze manier ontstaan sterrenstelsels
in de centra van halo’s.
9
Dit is de materie die we het beste kennen, waar alles op aarde uit gemaakt is en waar ook sterren
uit bestaan.
169
Nederlandse samenvatting
De inhoud van dit proefschrift
Hieronder volgt een vereenvoudigde samenvatting van dit proefschrift. Voor
meer informatie verwijs ik graag naar het desbetreffende hoofdstuk.
Hoofdstuk 2: Het invallen van gas op sterrenstelsels en halo’s
Het invallen van gas op halo’s gebeurt ongeveer even efficiënt als het invallen
van donkere materie. Dit komt doordat in dit geval de zwaartekracht allesbepalend is. Hoe snel dit gas vervolgens deel wordt van het sterrenstelsel, hangt af
van hoe snel het kan koelen. Dit hangt op zijn beurt weer af van de temperatuur
van het gas, dat weer afhangt van de massa van de halo. Bovendien koelt het
gas efficiënter als het veel zware metalen heeft, omdat deze ook licht uitstralen.
Wanneer er in de simulaties niets gedaan wordt om het instromen van gas
tegen te gaan, vindt er te veel stervorming plaats en komen de simulaties niet
overeen met de werkelijkheid. Daarom bevatten veel simulaties modellen om de
feedback van sterren en zwarte gaten te beschrijven. Een deel van de energie
die vrijkomt bij het ontploffen van sterren, zogenaamde supernova explosies, en
bij het groeien van zwarte gaten koppelt terug naar het gas eromheen. Op deze
manier een gedeelte van het gas uit het sterrenstelsel geblazen. Hierbij botst het
ook tegen invallend gas aan, waardoor het invallen vertraagd wordt.
In dit hoofdstuk laten we zien dat feedback vooral een groot effect heeft,
tot wel een orde van grootte, op de inval van gas op sterrenstelsels en in mindere mate op de inval op halo’s. De halomassa waarbij sterrenstelsels het snelst
groeien verschuift met een factor honderd omhoog door de toevoeging van feedback processen.
Het gas stroomt halo’s binnen met een hoge snelheid en dus met een hoge
kinetische energie. Om deel te worden van de halo moet het deze kinetische
energie kwijtraken. Als het gas supersonisch beweegt, kan het bij inval een
schok ondergaan en daarbij zijn kinetische energie omzetten in thermische energie. Het bereikt daarbij de karakteristieke temperatuur van de halo. Als het
gas heter wordt dan ongeveer 300.000 graden Celsius, wordt afkoelen door het
uitstralen van licht steeds inefficiënter. Het kan ook zijn dat er geen schok
plaatsvindt wanneer het gas de halo binnenkomt. Daardoor zal het gas met
dezelfde snelheid blijven bewegen, richting het centrale sterrenstelsel, en pas
later afremmen bij veel hogere dichtheid. Omdat de emissie sterk toeneemt met
de dichtheid kan het gas snel zijn energie wegstralen en zal het altijd een relatief
lage temperatuur behouden.
Welke van deze twee routes het gas volgt, hangt af van de massa van de halo
en van de dichtheid van het gas bij invallen. Als de halomassa laag is valt al het
gas ‘koud’ in. Als de halomassa hoog is en de dichtheid laag, vindt er een schok
plaats en valt het gas ‘heet’ in. Stel nu echter dat de halomassa hoog is, maar dat
de dichtheid van het invallende gas tegelijkertijd ook hoog is, dan vindt er ook
geen schok plaats en blijft het gas dus ‘koud’. De grens tussen de ‘hete’ en de
‘koude’ modus definiëren we als een maximum temperatuur die bereikt is van
170
De groei van sterrenstelsels en hun halo’s
ongeveer 300.000 graden.
In dit hoofdstuk beschrijven we bovendien dat de ‘hete’ modus belangrijker
is naarmate de halomassa toeneemt en naarmate het heelal ouder wordt. De
‘koude’ modus is het belangrijkst voor de voeding van sterrenstelsels in het centrum van halo’s, zelfs als die halo voornamelijk gevoed wordt door ‘hete’ inval.
Feedback en veranderingen in de koeling (door wel of geen zware elementen
mee te nemen in de berekening) hebben weinig effect op de verhouding van
‘heet’ en ‘koud’ invallend gas voor halo’s, maar wel of geen feedback geeft wel
enig verschil voor sterrenstelsels.
Hoofdstuk 3: De val van de kosmische stervormingssnelheid
Vanuit waarnemingen weten we dat, als we alle stervorming in het heelal
bij elkaar optellen op verschillende tijdstippen, de stervormingssnelheid per
volume-eenheid eerst toeneemt, tot het universum ongeveer 3 miljard jaar oud
was, en daarna sterk afneemt tot nu toe10 . Omdat de structuur van het heelal
blijft groeien onder invloed van de zwaartekracht, is dit niet een logisch gevolg
van structuurvorming. In dit hoofdstuk beschrijven we een aantal belangrijke
ingrediënten voor het begrijpen van de evolutie van de kosmische stervormingssnelheid.
Allereerst volgt de globale stervormingssnelheid de globale inval van ‘koud’
gas, maar niet de globale inval van ‘heet’ gas of van de totale inval. Hierdoor kunnen we direct concluderen dat de totale hoeveelheid stervorming in
het heelal wordt bepaald door de hoeveelheid ‘koude’ inval van gas. Feedback
van zwarte gaten speelt hierbij een cruciale rol doordat het voorkomt dat ‘heet’
gas in massieve halo’s de centrale sterrenstelsels bereikt. Zonder deze zwarte
gaten zou de ‘hete’ modus in het huidige heelal de overhand hebben bij het
veroorzaken van stervorming. In dat geval zou de kosmische stervormingssnelheid veel hoger zijn dan nu wordt waargenomen en de val van de kosmische
stervormingssnelheid veel minder groot.
Hoofdstuk 4: De eigenschappen van gas in en rond galactische halo’s
Zoals al eerder gezegd is de dichtheid van belang bij het bepalen van de maximale temperatuur van gas in halo’s. In dit hoofdstuk beschrijven we nog veel
meer eigenschappen van het gas als functie van straal en halomassa. In de buitendelen van halo’s zijn de eigenschappen van de ‘hete’ en ‘koude’ modus goed
te onderscheiden. Het gas dat altijd ‘koud’ is gebleven, bevind zich voornamelijk
in de filamenten van het kosmische web. Zodoende heeft de structuur van het
heelal een belangrijke invloed op de modus van gasinval en op de voeding van
sterrenstelsels. Naast het feit dat gas in deze modus kouder en dichter is, heeft
het gemiddeld genomen ook minder zware elementen en valt het sneller naar
het centrum van de halo. De spreiding rond het gemiddelde is echter groot.
Sterkere feedback zorgt voor hogere snelheden van het gas dat de halo uitstroomt. ‘Heet’ gas wordt naar grotere afstanden geduwd. Het verschil tussen
10 Het
universum is ongeveer 13,7 miljard jaar oud.
171
Nederlandse samenvatting
‘heet’ en ‘koud’ gas lijkt op het verschil tussen instromend en uitstromend gas,
alleen zijn de verschillen bij die laatste kleiner.
Hoofdstuk 5: Kanalen van koud gas in absorptie
Koud gas in de halo’s van sterrenstelsels absorbeert licht van heldere achtergrondbronnen. Deze bronnen zijn heel heldere, ver weg gelegen sterrenstelsels,
die licht uitzenden over een groot golflengtegebied. Het neutrale waterstof in
het gas binnen en buiten sterrenstelsels absorbeert licht met een golflengte van
precies 121,6 nm (oftewel licht van één bepaalde kleur). Dit is te zien als absorptielijn in het spectrum van de achtergrondbron. Met heel veel waarnemingen
van achtergrondbronnen kan er berekend worden hoeveel absorptiesystemen
er per volume-eenheid te vinden zijn in het heelal. We weten dan alleen nog
niet wat dit voor objecten zijn, behalve dan dat het gaswolken zijn met een redelijke hoeveelheid koud (10.000 graden) gas. Daarvoor kunnen we kosmologische
simulaties gebruiken. Als we daarmee de waarnemingen kunnen reproduceren,
kunnen we de simulaties vertrouwen en kijken wat de eigenschappen van deze
absorptiesystemen zijn.
In dit hoofdstuk kijken we naar in hoeverre de absorptiesystemen overeenkomen met de ‘koude’ modus, waarbij we specifiek kijken naar de maximum
temperatuur van het gas, diens lidmaatschap van halo’s, diens snelheid in de
richting van het centrale sterrenstelsel en diens connectie met stervorming. We
hebben ontdekt dat bijna alle 121,6 nm absorptie plaatsvindt in gas dat in de hele
geschiedenis van het heelal (de tijd vlak na de oerknal niet meegerekend) kouder
dan 300.000 graden is gebleven. Daarnaast valt het meeste gas met hoge snelheid
richting het dichtstbijzijnde sterrenstelsel. Sterke absoptiesystemen bevinden
zich bijna allemaal binnen de halo’s van sterrenstelsels, maar alleen de allersterkste zitten binnen de sterrenstelsels zelf. De absorptie wordt gedomineerd
door de kleinste halo’s, omdat er daar veel meer van zijn. De meeste sterke
121,6 nm absorptiesystemen bestaan uit gas dat in de nabije toekomst stervormend wordt.
Het bestaan van inval van ‘koude’ modus gas in de simulaties, beschreven in
de vorige hoofdstukken van dit proefschrift, is essentieel voor het reproduceren
van de waarnemingen. We concluderen daarom dat deze vorm van inval bestaat
en zelfs al gezien is als sterke 121,6 nm absorptiesystemen.
Hoofdstuk 6: Emissie van gas rond sterrenstelsels
Gas in het heelal straalt licht uit, waarbij het energie verliest. Dit gebeurt
wanneer een elektron een ion tegenkomt, dus dit proces schaalt met het kwadraat
van de dichtheid. Het atoom kan vervolgens recombineren, wat betekent dat het
vrije electron in een gebonden toestand rond de atoomkern terechtkomt. Hierbij wordt licht uitgezonden van een specifieke golflengte (oftwel een specifieke
kleur). Met simulaties kunnen we berekenen hoeveel licht van een bepaalde
golflengte we verwachten rondom een sterrenstelsel. In dit hoofdstuk wordt
beschreven hoeveel licht op een aantal golflengtes (zowel röntgen als ultravio172
De groei van sterrenstelsels en hun halo’s
let) corresponderend met diverse zware elementen, wordt uitgezonden door gas
in halo’s rond verschillende sterrenstelsels. Het licht uitgezonden door gas om
sterrenstelsels heen is veel zwakker dan het licht van de sterrenselsels zelf. Met
de emissielijnen die in dit hoofdstuk besproken worden, kunnen we het gas bestuderen dat niet heel koud en niet heel heet is, maar temperaturen heeft tussen
de 30.000 en 10 miljoen graden. De sterkte van de emissielijnen wordt berekend, zowel in dichtbijgelegen als ver weg gelegen halo’s. Vervolgens worden
voorspellingen gemaakt voor wat in de toekomst waarneembaar is met nieuwe
instrumenten en telescopen. De röntgenstraling zal zichtbaar zijn tot de rand
van halo’s en de ultraviolette straling tot 20 procent van deze straal. Dit is
dus een uitstekende manier om halogas te bestuderen. Deze emissielijnen zijn
afkomstig van gas met relatief hoge dichtheid en veel zware elementen. De
emissie is klonteriger dan de onderliggende gasdistributie. De temperatuur van
het gas dat op deze manier onderzocht kan worden, hangt sterk af van welke
emissielijn waargenomen wordt. Röntgenstraling ontstaat in heter gas dan ultraviolette straling. Hoe sterk de lijnen zijn hangt af van de massa van de halo
en van de leeftijd van het heelal.
De toekomst
Het proefschrift eindigt hier, maar het onderzoek gaat altijd door. Nieuwe vragen ontstaan als oude beantwoord zijn en er is dus nog genoeg te doen. Bovendien gaan de ontwikkelingen in dit vakgebied snel en in de nabije toekomst
zullen we betere simulaties en betere observaties hebben. De voorspellingen
die we in dit proefschrift maken, zullen zo ook getest kunnen worden in de
toekomst. Hoewel de simulaties die we hier gebruikt hebben, op verscheidene
fronten lijken op het waarneembare heelal, verschillen ze weer op andere punten. Als we begrijpen waarom dat zo is, kunnen we betere modellen maken voor
de relevante processen, zodat we steeds een stapje dichter bij de werkelijkheid
komen en steeds meer leren over hoe sterrenstelsels vormen.
173
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181
Publications
1. Properties of gas in and around galaxy haloes
Freeke van de Voort & Joop Schaye
2012, MNRAS, submitted, arXiv:1111.5039
2. Cold accretion flows and the nature of high column density HI absorption at redshift 3
Freeke van de Voort, Joop Schaye, Gabriel Altay, Tom Theuns
2012, MNRAS, in press, arXiv:1109.5700
3. ORIGIN: Metal Creation and Evolution from the Cosmic Dawn
Jan-Willem den Herder et al.
2011, Experimental Astronomy, 30
4. The drop in the cosmic star formation rate below redshift 2 is caused by a change
in the mode of gas accretion and by active galactic nucleus feedback
Freeke van de Voort, Joop Schaye, C. M. Booth, Claudio Dalla Vecchia
2011, MNRAS, 415, 2782
5. The rates and modes of gas accretion on to galaxies and their gaseous haloes
Freeke van de Voort, Joop Schaye, C. M. Booth, Marcel R. Haas, Claudio
Dalla Vecchia
2011, MNRAS, 414, 2458
6. The physics driving the cosmic star formation history
Joop Schaye, Claudio Dalla Vecchia, C.M. Booth, Robert P.C. Wiersma, Tom
Theuns, Marcel R. Haas, Serena Bertone, Alan R. Duffy, I.G. McCarthy,
Freeke van de Voort
2010, MNRAS, 402, 1536
183
Curriculum Vitae
I was born on 16 September 1983 in Eindhoven. I grew up in Hulsel and Bladel,
both in the South-East of the Dutch province North-Brabant. After my primary
school years at ‘De Sleutelaar’ I went to the ‘gymnasium’, i.e. taking ancient
languages as well as other courses, at ‘Pius-X college’. I was always interested
in far too many subjects and, besides Dutch, English, mathematics, physics,
chemistry, and biology, I also took French, Latin, music, and history. I graduated
in 2001 cum laude.
The reason I became interested in astronomy is that I joined my friend in
taking a master class in astronomy aimed at high-school students. I actually
wanted to go to chemistry, but she thought astronomy would be more fun. This
eventually led to my decision to study astronomy in Leiden. I assumed that
finding a job in a different part of society would be easy enough and that the
most important thing was to study something I enjoyed. I certainly did not
expect to stay at Leiden University for this long.
Because I was also intrigued by the physics I was taught, I started a bachelor
in physics as well and received two bachelor degrees after four years. Realizing
that I was fascinated most by astronomy, I continued with the master’s degree
in astronomy. I went to the Space Telescope Science Institute in Baltimore for half a
year to do one of my research projects. Back in The Netherlands, I did my final
project with Joop Schaye and graduated cum laude in 2008. I liked my research
project so much that I decided to stay for my PhD.
During my PhD, I enjoyed working with Joop Schaye and his research group.
I spent three months working in Saint-Genis-Laval, France, at the Centre de
Recherche Astrophysique de Lyon, Observatoire de Lyon and six months in Garchingbei-München, Germany, at the Max-Planck Institut für Astrophysik.
Over the years I gave approximately forty presentations about my research,
some of those were addressed at the general audience or high-school students,
but most of them were aimed at colleagues. I participated in international conferences in The Netherlands, Germany, France, Great-Britain, and Switzerland
and also in a summer school in the United States. During my PhD I was a
teaching assistant for the course ‘radiative processes’ twice and for ‘introductory
astrophysics’ once. Furthermore, I was a member of the board of the amateur
astronomy association Leidse Weer- en Sterrekundige Kring and spent many years
answering astronomy-related questions as a member of the outreach committee.
In April I will move to Córdoba in Argentina for half a year with an Early
Stage Researcher fellowship granted by the CosmoComp programme of the European Union. In October I will start as a post-doctoral researcher at the University
of California in Berkeley, United States, in collaboration with the Academia Sinica
Institute of Astronomy and Astrophysics in Taipei, Taiwan.
185
Acknowledgements
Four years is a long time, but now, quite suddenly, the end is near. I would like
to thank everyone at the Sterrewacht, including the people who have already
moved on and left me behind, for their excellent company and for making this
such a wonderful place to work. A special mention has to be made of the support
staff, who keep the institute together.
Being a (long-term) member of my research group has been awesome. Claudio, Andreas, Rob, you made sure the atmosphere in the group was excellent
when I arrived and it has never been the same since the three of you left. Luckily, we ran into each other on various occasions. I hope we will continue to do
so. Marcel, thanks for all your help at the start, your friendship, your directness,
and for always being your down to earth self. Olivera, thank you for educating
me about the dangers I am facing, from eating grapefruits to bungee jumping,
and for your never waning faith in me. I have the same faith in you. Ali, thanks
to you I was, finally, no longer the new one in the group. Thanks so much for
your interest in my work, for proof reading my papers, and for making our
meetings more lively. Ben, you are incredible. Please continue to amaze me and
others. Milan, Monica, Marco, Alex, Rob, I am very happy that all of you joined
our group. You are the future. Please keep the group as fun as it is now, because
I intend to come back to visit you. Marcel, it was great having you around in
Munich to keep the Leiden spirit (and gossip) going. You are a worthy office
mate replacement and a great help with the thesis formatting. Without you,
there would not be any unicorns. Craigy, thanks for your interesting contributions to our group meetings, for giving me all the advice and help I needed all
these years, and for being my bestest friend. No-one calls me Freaky like you
do. Making fun of you and being made fun of by you, mostly by recycling our
ten favourite jokes, were highlights of my day.
Lensing, i.e. Edo, Malin, Stefania, and Elisabetta, Sterrewacht life certainly
improved after we merged our tea breaks. Isa, I am so happy we suddenly
became good friends after many years. I value your good advice, your honest
opinions about everything, and I like that you are as loud as I am. Ann-Marie,
all the places where we end up together (Leiden, Dwingeloo, Princeton, and
Chicago, thus far) are always better with you there. I am excited about us both
going to Berkeley. Thank you for recruiting me. I will enjoy sharing a cubicle
with you. Edith, all of your cakes are as wonderful as you are. Shannon, you
are the best. Thank you for motivating me, as well as for distracting me, and for
keeping me alive during the thesis writing months.
Inge, Hilde, and Karolina, we changed and our lives changed since high
school, but we will be friends forever. I enjoy every minute we spend together,
especially when there are not enough of those minutes. Carola, having you
around all the time made Herengracht 14 in The Hague the best place to live. I
do not want it to end. Papa, mama, Tom, and Anne, I cannot think of a better
family to have. We are different and we are the same, which I find very inspiring.
187
Thank you for always supporting me in my decisions. Evelyn and Eveline, we
arrived in Leiden together more than a decade ago and, although you were no
longer at the Sterrewacht with me during my PhD, you suffered through all
my stories without any complaints. You were there at the beginning and I am
extremely happy and grateful that both of you will be by my side at the end.
My time in France and Germany would not have been as fantastic without
the amazing people I met there, both at work and outside of work. I would also
like to warmly thank the Leiden student scuba diver club LSD and The Hague
student orchestra Valerius for making the past four years about more than just
astronomy. Finally, to all my friends who are not mentioned here, thank you for
being who you are.
188
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