Astronomy Astrophysics Linear polarization of rapidly rotating ultracool dwarfs &

Astronomy Astrophysics Linear polarization of rapidly rotating ultracool dwarfs &
Astronomy
&
Astrophysics
A&A 556, A125 (2013)
DOI: 10.1051/0004-6361/201321851
c ESO 2013
Linear polarization of rapidly rotating ultracool dwarfs
P. A. Miles-Páez1 ,2 , M. R. Zapatero Osorio3 , E. Pallé1,2 , and K. Peña Ramírez1,2
1
2
3
Instituto de Astrofísica de Canarias, 38205 La Laguna, Spain
e-mail: [pamp;epalle;karla]@iac.es
Departamento de Astrofísica, Universidad de La Laguna, Av. Astrofísico Francisco Sánchez, s/n, 38206 La Laguna, Spain
Centro de Astrobiología (CSIC-INTA), Carretera de Ajalvir km 4, 28850 Torrejón de Ardoz, Madrid, Spain
e-mail: [email protected]
Received 7 May 2013 / Accepted 26 June 2013
ABSTRACT
Aims. We aim to study the near-infrared linear polarization signal of rapidly rotating ultracool dwarfs with spectral types ranging
from M7 through T2 and projected rotational velocities of v sin i 30 km s−1 . These dwarfs are believed to have dusty atmospheres
and oblate shapes, which is an appropriate scenario to produce measurable linear polarization of the continuum light.
Methods. Linear polarimetric images were collected in the J-band for a sample of 18 fast-rotating ultracool dwarfs, of which five were
also observed in the Z-band using the Long-slit Intermediate Resolution Infrared Spectrograph (LIRIS) on the Cassegrain focus of
the 4.2-m William Herschel Telescope. The measured median uncertainty in the linear polarization degree is ±0.13% for our sample,
which allowed us to detect polarization signatures above ∼0.39% with a confidence interval of ≥3σ.
Results. About 40 ± 15% of the sample is linearly polarized in the Z- and J-bands. All positive detections have linear polarization
degrees ranging from 0.4% to 0.8% in both filters independent of spectral type and spectroscopic rotational velocity. However, simple
statistics point at the fastest rotators (v sin i 60 km s−1 ) having a larger fraction of positive detections and a larger averaged linear
polarization degree than the moderately rotating dwarfs (v sin i = 30–60 km s−1 ). Our data suggest little linear polarimetric variability
on short timescales (i.e., observations separated by a few ten rotation periods), and significant variability on long timescales (i.e.,
hundred to thousand rotation cycles), supporting the presence of long-term weather in ultracool dwarf atmospheres.
Key words. polarization – brown dwarfs – stars: atmospheres – stars: late-type – stars: low-mass – stars: general
1. Introduction
Dwarfs with spectral types that are cooler than M7 (T eff ≤
2700 K; typically referred to as ultracool dwarfs) are believed
to undergo the formation of a wide range of atmospheric condensate species (solid and liquid particles), such as corundum
(Al2 O3 ), iron (Fe), enstatite (MgSiO3 ), forsterite (Mg2 SiO4 ), titanium dioxide (TiO2 ), and gehlenite (Ca2 Al2 SiO7 ) among others (Jones & Tsuji 1997; Ackerman & Marley 2001; Helling
et al. 2008; Witte et al. 2011). According to models, these condensates may build up into structures (e.g., clouds), which are
located in the outer layers of the atmosphere when T eff >
∼ 1300 K
and in layers below the visible photosphere when T eff <
∼ 1300 K
(Allard et al. 2001). Condensates or dusty particles represent one
relevant, yet poorly understood source of opacity in ultracool
dwarfs. The presence of atmospheric dust may also polarize the
object’s output light at particular wavelengths through scattering
processes as suggested by the theoretical work of Sengupta &
Krishan (2001). Observationally, it is demonstrated by the positive detection of linear polarization at optical and near-infrared
frequencies (Ménard et al. 2002; Zapatero Osorio et al. 2005;
Goldman et al. 2009; Tata et al. 2009; Zapatero Osorio et al.
2011). Polarization may become a useful tool for comprehending the complexity of ultracool atmospheres.
Additionally, ultracool dwarfs have high values of projected
rotational velocities (v sin i), indicating that they are indeed rapid
rotators (Blake et al. 2010; Konopacky et al. 2012; Mohanty &
Basri 2003; Reiners & Basri 2008, 2010; Zapatero Osorio et al.
2006). This result combined with convection and the presence of
dust could give rise to intricated atmospheric dynamics, likely
generating periodic and non-periodic photometric variability as
seen in some late-M, L, and T dwarfs (Bailer-Jones & Mundt
2001; Martín et al. 2001; Koen 2004; Buenzli et al. 2012;
Khandrika et al. 2013). From a theoretical perspective, Sengupta
& Krishan (2001), Sengupta (2003), Sengupta & Kwok (2005),
Sengupta & Marley (2010, 2011), and de Kok et al. (2011) predicted that ultracool dwarfs with atmospheric condensates and
high v sin i’s show measurable linear polarization degrees that
are typically <
∼1% in the optical and near-infrared. Fast rotation induces photospheres into the form of an oblate ellipsoid,
and this lack of symmetry leads to the incomplete cancellation
of the polarization from different areas of the dwarfs surfaces.
Gravity is an additional ingredient to consider since rotationally induced non-sphericity is more favored at lower atmospheric
gravities. For a similar amount of dust particles in the ultracool
atmospheres, it is expected that the largest rotations and lowest
gravities produce the largest polarization degrees.
Here, we aim at studying the capabilities of linear polarization in the near-infrared to probe the presence of atmospheric
condensates in ultracool dwarfs and to shed new light on the
dependence on the linear polarization with rotation. We selected a sample of 18 rapidly rotating ultracool dwarfs (v sin i >
∼
30 km s−1 ) with spectral types in the interval of M7–T2. We report on linear polarimetric imaging observations carried out in
the Z- and J-bands. In Sect. 2, we provide a description of the
targets. Section 3 presents the observations and data reduction.
Polarimetric analysis and discussion are introduced in Sects. 4
and 5. Finally, our conclusions are given in Sect. 6.
Article published by EDP Sciences
A125, page 1 of 11
A&A 556, A125 (2013)
Table 1. List of targets.
Name
2MASS J00192626+4614078
BRI 0021−0214
LP 349−25AB
2MASS J00361617+1821104
2MASS J00452143+1634446
2MASS J02281101+2537380
LP 415−20AB
2MASS J07003664+3157266AB
2MASS J08283419−1309198
2MASS J11593850+0057268
2MASS J12545393−0122474
2MASS J14112131−2119503
2MASS J15010818+2250020
2MASS J15210103+5053230
2MASS J18071593+5015316
2MASS J18353790+3259545
2MASS J20360316+1051295
2MASS J20575409−0252302
SpT
M8
M9.5
M8+M9
L3.5
L2
L0
M7+M9.5
L3.5+L6
L2
L0
T2
M9
M9
M7.5
L1.5
M8.5
L3
L1.5
J
(mag)
12.603 ± 0.021
11.992 ± 0.035
10.614 ± 0.022
12.466 ± 0.027
13.059 ± 0.022
13.839 ± 0.027
12.711 ± 0.021
12.923 ± 0.023
12.800 ± 0.030
14.084 ± 0.028
14.890 ± 0.040
12.437 ± 0.022
11.866 ± 0.022
12.014 ± 0.024
12.934 ± 0.024
10.270 ± 0.022
13.950 ± 0.026
13.121 ± 0.024
W2
(mag)
11.001 ± 0.020
9.900 ± 0.019
9.054 ± 0.020
10.237 ± 0.020
10.393 ± 0.019
11.887 ± 0.023
11.188 ± 0.021
10.377 ± 0.021
10.667 ± 0.022
12.045 ± 0.024
12.396 ± 0.025
10.815 ± 0.022
10.053 ± 0.020
10.419 ± 0.020
10.965 ± 0.021
8.539 ± 0.019
11.586 ± 0.023
10.981 ± 0.020
v sin ia
(km s−1 )
68 ± 10
33.7 ± 2.5
55 ± 2(A), 83 ± 3(B)
35.9 ± 2.0
32.8 ± 0.2
31.2 ± 0.8
40 ± 5(A), 37 ± 4(B)
30.1 ± 2.0(A)
30.1 ± 2.0
71 ± 2
28.4 ± 2.8
44 ± 4
60 ± 2
40 ± 4
73.6 ± 2.2
41.2 ± 4.7
67.1 ± 1.5
60.6 ± 2.0
T rot
(h)
–
4.8
–
3.1
–
–
–
–
2.9
–
–
–
2.0
–
–
2.8
–
–
Ref.
2
2, 4, 8
5
1, 3, 9
1
1
5
1, 3
1, 3, 10
3
7
2
4, 11
2
1, 3
2, 6, 12
1
1, 3
Notes. (a) Weighted mean rotational velocity for those targets with more than one measurement. Error bars correspond to the average of individual
uncertainties quoted in the literature.
References. (1) Blake et al. (2010); (2) Reiners & Basri (2010); (3) Reiners & Basri (2008); (4) Mohanty & Basri (2003); (5) Konopacky et al.
(2012); (6) Deshpande et al. (2012); (7) Zapatero Osorio et al. (2006); (8) Martín et al. (2001); (9) Hallinan et al. (2008); (10) Koen (2004);
(11) Hallinan et al. (2007); (12) Hallinan et al. (2008).
2. Target selection
2
We selected 18 bright (typically J < 14.1 mag) ultracool dwarfs
with spectral types ranging from M7 through T2 and published
projected rotational velocities, v sin i ≥ 30 km s−1 (Mohanty
& Basri 2003; Zapatero Osorio et al. 2006; Reiners & Basri
2008; Blake et al. 2010; Reiners & Basri 2010; Konopacky
et al. 2012; Deshpande et al. 2012). All dwarfs are observable from northern astronomical observatories and sufficiently
bright at near-infrared wavelengths to achieve accurate polarimetric photometry (σP ≤ 0.2%) using short exposures and 4-m
class telescopes. They represent ∼37% of all dwarfs cooler than
M7 that have v sin i ≥ 30 km s−1 available in the literature.
In Table 1, we provide the targets’ complete names (abridged
names will be used in what follows), their spectral types, nearinfrared 2MASS J (Skrutskie et al. 2006) and mid-infrared WISE
W2 magnitudes, spectroscopic rotational velocities (v sin i), and
published rotation periods, when available. We found WISE
data for six of our targets (BRI 0021−0214, J0036+1821,
J0700+3157, J1254−0122, J1835+3259, and J2036+1051) in
Dupuy & Liu (2012); we extracted the W2 photometry of the
remaining sources from the WISE catalog (Wright et al. 2010).
For those sources with more than one v sin i measurement in the
literature, we provide their weighted mean rotational velocity.
Trigonometric and spectrophotometric distance estimates for all
objects in our sample are ≤30 pc (Reid et al. 2008; Reiners &
Basri 2009; Faherty et al. 2009).
All targets are field dwarfs (e.g., they likely have metal abundance close to solar), and none is reported to be exceptionally
young, except for J0045+1634, which has an optical spectrum
with evidence of low-gravity features, a likely age and mass
around 50–400 Myr and 0.025–0.055 M (Cruz et al. 2009;
Zapatero Osorio et al. 2013). The remaining M7–L3.5 and T2
dwarfs have masses estimated at 0.05–0.09 and 0.035–0.065 M ,
respectively, for an age interval of 0.5–5 Gyr typical of the field
(Baraffe et al. 2003). All dwarfs are either very low-mass stars
A125, page 2 of 11
v sin i (km s−1)
10
↓
1
10
↓
0
10
M0
M5
L0
L5
T0
T5
Y0
Spectral Type
Fig. 1. Spectroscopic rotational velocities of M, L, and T dwarfs as
a function of spectral type. Data taken from Blake et al. (2010);
Konopacky et al. (2012); Mohanty & Basri (2003); Reiners & Basri
(2008, 2010); Zapatero Osorio et al. (2006). Ultracool dwarfs rotate
faster with decreasing temperature (and very likely mass). The 18 targets (star symbols) have a v sini ≥ 30 km s−1 and spectral types ≥M7.
Typical uncertainties of projected rotational velocities (1–3 km s−1 ) and
upper limits on the rotational velocities of dwarfs warmer than M7 are
not plotted for the clarity of the figure. The majority of the M0–M4
dwarfs rotate at speeds below ∼3 km s−1 .
or brown dwarfs. The majority of the sample objects (M7–L3.5)
have masses around the substellar borderline and have similar
high surface gravities in the interval of log g = 5.1–5.3 (in units
of cm s−2 , given by the evolutionary models of Baraffe et al.
2003). Figure 1 illustrates the location of our targets in the projected rotational velocity versus spectral type diagram. As seen
P. A. Miles-Páez et al.: Linear polarization of rapidly rotating ultracool dwarfs
Table 2. Observing log.
Object
J0019+4614
BRI 0021−0214
LP349−25AB
J0036+1821
J0045+1634
J0228+2537
LP415−20AB
J0700+3157AB
J0828−1309
J1159+0057
J1254−0122
J1411−2119
J1501+2250
J1521+5053
J1807+5015
J1835+3259
J2036+1051
J2057−0252
SA29−130c
GJ 3805c
BD+284211c
Feige 110c
HD 283855d
HRW 24d
Aperturea
(FWHM)
3–4
2–3
3–4
3–4
3–4
3–4
3–4
3–4
3–4
3–4
3–4
2–3
3–4
2–3
1–2
2.5–3.5
3–4
3–4
3–4
3–4
2.5–3.5
2–3
2–3
2–3
3–4
3–4
2–3
3–4
3–4
2–3
2–3
3–5
3–4
2–3
2–3
Obs. date
(UT)
2012 Oct. 06
2012 Oct. 07
2012 Oct. 06
2012 Oct. 06
2012 Oct. 07
2012 Oct. 06
2012 Oct. 06
2012 Oct. 06
2012 Oct. 06
2012 Oct. 07
2012 Oct. 06
2011 Dec. 31
2013 Jan. 29
2012 Jun. 16
2013 Jan. 29
2013 Jan. 29
2012 Jun. 16
2013 Jan. 29
2013 Jan. 29
2012 Jun. 15
2012 Oct. 07
2012 Jun. 15
2012 Jun. 15
2012 Oct. 07
2012 Oct. 06
2013 Jan. 29
2012 Jun. 15
2012 Oct. 06
2012 Oct. 07
2011 Dec. 31
2012 Jun. 16
2012 Oct. 06
2012 Oct. 07
2011 Dec. 31
2013 Jan. 29
Filter
J
Z
J
J
Z
J
J
J
J
Z
J
J
J
J
J
J
J
J
J
J
Z
J
J
Z
J
J
J
J
Z
J
J
J
Z
J
J
Exposure Timeb
(s)
1 × 9 × 30, 1 × 9 × 50
1 × 9 × 120, 1 × 9 × 120
1 × 9 × 20, 1 × 9 × 20
2 × 9 × 6, 2 × 9 × 6
1 × 9 × 50, 1 × 9 × 50
2 × 9 × 35, 2 × 9 × 35
1 × 9 × 50, 1 × 9 × 50
1 × 9 × 70, 1 × 9 × 70
1 × 9 × 40, 1 × 9 × 60
1 × 9 × 120, 1 × 9 × 120
1 × 9 × 60, 1 × 9 × 60
1 × 9 × 120, 1 × 9 × 80
1 × 9 × 60, 1 × 9 × 60
1 × 9 × 120, 1 × 9 × 120
1 × 9 × 120, 1 × 9 × 120
2 × 9 × 120, 2 × 9 × 120
2 × 9 × 120, 2 × 9 × 120
1 × 9 × 60, 1 × 9 × 60
1 × 9 × 60, 1 × 9 × 60
1 × 9 × 120, 1 × 9 × 120
1 × 9 × 120, 1 × 9 × 180
1 × 9 × 5, 1 × 9 × 5
1 × 9 × 90, 1 × 9 × 90
1 × 9 × 180, 1 × 9 × 180
1 × 9 × 40, 1 × 9 × 30
1 × 9 × 100, 1 × 9 × 100
1 × 9 × 100, 1 × 5 × 100
1 × 9 × 7, 1 × 9 × 7
1 × 9 × 60, 1 × 9 × 60
1 × 9 × 90, 1 × 5 × 90
1 × 9 × 120, 1 × 5 × 120
2 × 9 × 3, 2 × 9 × 3
2 × 9 × 6, 2 × 9 × 6
1 × 9 × 20, 1 × 9 × 20
1 × 9 × 10, 1 × 9 × 10
FWHM
(")
0.9
1.0
0.9
0.7
0.8
0.7
1.0
0.9
0.8
0.8
0.8
0.9
0.8
1.5
1.1
0.9
2.5
0.9
0.8
1.0
0.8
0.8
1.0
1.1
0.7
0.8
1.0
0.7
0.9
1.4
1.7
0.7
0.7
0.9
0.7
S /N
Airmass
2500
1750
3540
10900
7740
6580
2570
1100
2800
2000
3070
4420
1820
380
425
470
460
2930
3950
2710
1500
6100
870
516
2617
1060
992
4900
8423
1100
1240
12600
7400
3414
1230
1.40–1.33
1.06–1.03
1.60–1.57
1.04–1.02
1.05–1.03
1.03–1.02
1.02–1.04
1.04–1.02
1.02–1.04
1.04–1.09
1.07–1.04
1.43–1.56
1.34–1.35
1.33–1.71
1.40–1.30
1.44–1.21
1.85–2.79
1.35–1.27
1.31–1.26
1.14–1.21
1.26–1.44
1.12–1.15
1.06–1.08
1.12–1.28
1.25–1.21
1.05–1.04
1.14–1.13
1.06–1.05
1.10–1.05
1.31–1.41
1.40–1.28
1.06–1.04
1.00–1.01
2.54–2.92
1.36–1.37
Notes. (a) Range of circular photometric apertures (in units of FWHM) used to determine the normalized Stokes parameters. (b) Number of times
the 9-dither pattern is repeated × 9 images × single exposure time, where one column for each telescope rotator angle and retarder plate. With
very few exceptions, the exposure times were identical for the two telescope rotator angles and retarder plates. (c) Zero-polarized standard star.
(d)
Polarized standard star (Whittet et al. 1992).
from the figure, our sample includes some of the fastest ultracool
rotators known to date.
In the target sample, there are three binary dwarfs, of which
two (LP 349−25AB and LP 415−20AB) are resolved, and v sin i
values are available for each component separately (Konopacky
et al. 2012). The components of the pairs have similar spectral types (Table 1) and magnitudes: ΔJ = 0.84 ± 0.15 mag
for LP 415–20 (Siegler et al. 2003), and ΔJ = 0.35 ± 0.03
mag for LP 349–25 (Dupuy et al. 2010). The third binary
(J0700+3157AB) in the target list has differing spectral types
and a v sin i measured from the combined light at optical and
near-infrared wavelengths (Reiners & Basri 2008; Blake et al.
2010). This v sin i value is dominated by the primary member
since the near-infrared contrast between both components is
ΔJ = 1.2 mag (Reid et al. 2006), and the contrast is even larger
in the visible.
3. Observations and data reduction
For the 18 targets, we conducted polarimetric imaging photometry using the Z- and J-band filters and the long-slit intermediate
resolution infrared spectrograph (LIRIS; Manchado et al. 2004)
that is attached to the Cassegrain focus of the 4.2-m William
Herschel Telescope (WHT) at the Roque de los Muchachos
Observatory (La Palma, Spain). LIRIS has a 1024 × 1024 pixel
Hawaii detector, covering the spectral range 0.8–2.5 μm. The
pixel projection on the sky is 0. 25 yielding a field of view of
4. 27 × 4. 27. In its polarimetric imaging mode, LIRIS uses a
wedged double Wollaston device (Oliva 1997), consisting of the
combination of two Wollaston prisms that deliver four simultaneous images of the polarized flux at vector angles 0◦ and
90◦ , 45◦ , and 135◦. An aperture mask that is 4 × 1 in size is
in the light path to prevent overlapping effects between the different polarization vector images. LIRIS does not have an adaptive optics system; binary objects are thus not resolved in our
linear polarimetric data. The central wavelengths and widths
of the LIRIS Z- and J-band filters are 1.035/0.073 μm and
1.25/0.16 μm, respectively.
Observations were carried out during four observing campaings in 2011 December, 2012 June, 2012 October, and 2013
January. The journal of the observations is provided in Table 2.
Weather conditions were mainly clear during all campaigns. The
A125, page 3 of 11
A&A 556, A125 (2013)
– The nine dither frames were combined from their medians
to create the sky frame, which was later subtracted from the
individual data.
– Skyflats were obtained through the polarimetric optics during the sunsets of all observing runs pointing to the east at
high airmasses (sec z ∼ 3.0) to avoid the strong polarization
of the sunlight close to the zenith during dusk. All images
were divided with the corresponding skyflats, which were
normalized to unity, to remove detector flat-field variations.
– Sky-subtracted and flat-fielded images were registered for
proper alignement.
– All aligned images were stacked together to produce deep
data.
The S/N of the final science images was computed as the ratio between the peak of the flux provided by a Moffat fit to the
sources’ radial profile and the standard deviation of the background in a ring with a inner radius that was four times (4 ×) the
FWHM and had a width of 1 × FWHM. The S/N measurements
1
IRAF is distributed by the National Optical Astronomy
Observatories, which are operated by the Association of Universities
for Research in Astronomy, Inc., under cooperative agreement with the
National Science Foundation.
A125, page 4 of 11
1.5
→
q (%)
0.5
←
−0.5
−1.5
0
1
2
3
4
5
6
R (× FWHM)
3.5
2.5
→
1.5
u (%)
raw seeing varied between 1 and 3 in 2011 December and
2012 June and was roughly constant at around 1 during the
nights of 2012 October and 2013 January.
For each target, we obtained linear polarimetric images following a nine-point dither pattern for a proper sky background
contribution removal. Typical dither offsets were ∼20 and
∼10 along the horizontal and vertical axis, respectively. We systematically located our targets on the same spot of the detector,
which is close to the center of the LIRIS field of view and optical axis. An example of a LIRIS polarimetric frame obtained
through the two Wollaston prisms is given in Fig. 1 of Alves
et al. (2011): Per frame, there are four images of the main source
corresponding to vector angles of 0◦TR , 90◦TR, 135◦TR, and 45◦TR
from top to bottom, where the subindex TR stands for the telescope rotator angle. The early observations of 2011 December,
2012 June, and 2012 October were acquired at two different positions of the WHT telescope rotator: TR = 0◦ and 90◦ . The benefits of this observing strategy are twofold: The flat-fielding effects of the detector are minimized, and the signal-to-noise ratio
(S/N) of the polarimetric measurements is improved (Alves et al.
2011). The overheads introduced by the rotation and de-rotation
of the telescope rotator were typically about 5 min per target. For
the most recent observation run in 2013 January, we used two retarder plates, which is an implementation added to one of the filter wheels of LIRIS during late 2012. These two retarder plates
minimize the overhead times (by not having to move the telescope rotator) and provide polarimetric images with exchanged
orthogonal vector angles, i.e., 0◦90 , 90◦90 , 135◦0 , 45◦0 , and 0◦0 , 90◦0 ,
135◦90 , 45◦90 after the aforementioned nomenclature. Typical exposure times per dither ranged from 6 s to 180 s depending on the
target brightness, seeing conditions and filter. Total on-source
integrations, the Universal Time (UT) observing dates, filters,
air masses, and raw seeing, as measured from the averaged fullwidth-at-half maximum (FWHM) over the reduced images, are
listed in Table 2.
Raw data frames were divided into four slices corresponding
to the polarimetric vectors, and each slice was reduced following
standard procedures for the near-infrared using packages within
the Image Reduction and Analysis Facility software (IRAF1 ).
The data reduction steps applied were as follows:
←
0.5
−0.5
−1.5
−2.5
0
1
2
3
4
5
6
R (× FWHM)
Fig. 2. Normalized Stokes parameters q (top) and u (bottom) as a function of the aperture radius (in FWHM unit) for the polarized standard
star HD 283855. For this plot, the sky annulus was fixed at 6 × FWHM
and 1.5 × FWHM in size. The vertical dashed lines indicate the selected
apertures (3–5 × FWHM) to compute the mean Stokes parameters.
listed in Table 2 represent the average values of all four vectors,
telescope rotator angles, and retarder plates. We note that S/N
is always larger for the J-band than for the Z-band, because our
targets are very red sources. Nevertheless, the S/N values are
generally high for the two filters (typically ≥500), thus securing
the quality of the subsequent photometry.
Together with the science targets, we also observed polarized
and zero-polarized standard stars from the catalogs of Schmidt
et al. (1992) and Whittet et al. (1992). We also observed nonmagnetic white dwarfs, which are supposed to be intrinsically
unpolarized. The journal of the observations from the standard
stars is provided in Table 2. These data were reduced in the same
manner as the science targets. We used them to control the linear
polarization introduced by the telescope and the LIRIS instrument and to check the efficiency of the LIRIS polarimetric optics
(see next section).
4. Polarimetric analysis
The normalized Stokes parameters, q and u, were computed using the flux-ratio method and the equations given in
Zapatero Osorio et al. (2011). Fluxes of all polarimetric vectors were measured using the IRAF PHOT package, defining
circular photometric apertures of different sizes (from 0.5 to
6 × FWHM with steps of 0.1 × FWHM), and 18 sky rings, which
were annuli with inner radii of 3.5 through 6 × FWHM (steps of
0.5 × FWHM) and widths of 1, 1.5, and 2 × FWHM. The sky annuli account for possible background residuals remaining from
the previous data reduction steps. In summary, a total of 990
fluxes were computed for each polarimetric vector. In Fig. 2,
we illustrate the resulting normalized Stokes parameters of a polarized standard star as a function of the circular photometric
aperture (we fixed the sky annulus for the clarity of the figure).
The final q and u values were obtained by selecting the range
of apertures providing a flat distribution of the Stokes parameters (as shown in Fig. 2) and by averaging all the bracketed q
and u measures (including all sky annuli). The selected range of
photometric apertures for each science target and standard star
P. A. Miles-Páez et al.: Linear polarization of rapidly rotating ultracool dwarfs
Table 3. Linear polarimetry photometry of science targets.
Object
J0019+4614
BRI0021−0214
LP349−25AB
J0036+1821
J0045+1634
J0228+2537
LP415−20AB
J0700+3157AB
J0828−1309
J1159+0057
J1254−0122
J1411−2119
J1501+2250
J1521+5053
J1807+5015
J1835+3259
J2036+1051
J2057−0252
Filter
J
Z
J
J
Z
J
J
J
J
Z
J
J
J
J
J
J
J
J
J
J
Z
J
J
Z
J
Obs. time
(JD−2 450 000.5)
6206.8719
6207.9954
6206.8988
6206.9830
6208.4696
6207.0147
6207.0275
6207.0697
6207.2099
6208.2221
6207.2425
5927.1754
6321.0538
6094.9304
6321.1119
6321.1575
6094.9835
6321.1950
6321.2133
6094.1371
6207.8720
6094.1755
6094.1880
6207.9429
6206.8253
q
(%)
−0.40 ± 0.06
0.31 ± 0.07
−0.10 ± 0.03
0.14 ± 0.02
−0.22 ± 0.02
−0.11 ± 0.04
−0.01 ± 0.03
−0.15 ± 0.08
0.41 ± 0.06
0.39 ± 0.06
−0.50 ± 0.08
−0.15 ± 0.02
0.26 ± 0.10
0.23 ± 0.08
0.42 ± 0.07
−0.31 ± 0.25
0.30 ± 0.06
−0.10 ± 0.06
0.49 ± 0.07
−0.54 ± 0.03
0.07 ± 0.09
−0.02 ± 0.02
−0.10 ± 0.11
−0.78 ± 0.18
0.43 ± 0.08
u
(%)
0.11 ± 0.09
−0.49 ± 0.05
0.10 ± 0.03
0.15 ± 0.05
−0.02 ± 0.02
0.20 ± 0.03
−0.08 ± 0.03
−0.35 ± 0.06
−0.01 ± 0.05
0.01 ± 0.05
−0.03 ± 0.04
0.07 ± 0.02
0.09 ± 0.06
0.50 ± 0.08
0.05 ± 0.05
−0.01 ± 0.21
−0.41 ± 0.13
0.51 ± 0.04
0.36 ± 0.04
0.41 ± 0.04
0.20 ± 0.07
−0.12 ± 0.01
−0.22 ± 0.05
0.07 ± 0.20
−0.05 ± 0.08
P
(%)
0.41 ± 0.15
0.58 ± 0.13
0.14 ± 0.11
0.21 ± 0.11
0.22 ± 0.10
0.23 ± 0.11
0.08 ± 0.11
0.38 ± 0.14
0.41 ± 0.12
0.39 ± 0.12
0.50 ± 0.14
0.17 ± 0.10
0.27 ± 0.15
0.55 ± 0.15
0.42 ± 0.13
0.31 ± 0.34
0.51 ± 0.17
0.52 ± 0.12
0.61 ± 0.13
0.68 ± 0.11
0.21 ± 0.15
0.12 ± 0.10
0.24 ± 0.16
0.78 ± 0.28
0.43 ± 0.15
p∗
(%)
0.38 ± 0.15
0.57 ± 0.13
0.09 ± 0.11
0.18 ± 0.11
0.20 ± 0.10
0.20 ± 0.11
0.00 ± 0.11
0.35 ± 0.14
0.39 ± 0.12
0.38 ± 0.12
0.48 ± 0.14
0.14 ± 0.10
0.22 ± 0.15
0.53 ± 0.15
0.40 ± 0.13
0.00 ± 0.34
0.48 ± 0.17
0.51 ± 0.12
0.60 ± 0.13
0.67 ± 0.11
0.15 ± 0.15
0.07 ± 0.10
0.18 ± 0.16
0.73 ± 0.28
0.40 ± 0.15
Θ
(deg)
–
146.8 ± 6.7
–
–
–
–
–
–
174.9 ± 9.0
176.3 ± 9.4
87.3 ± 7.8
–
–
28.3 ± 8.0
179.0 ± 9.0
–
148.7 ± 10.0
46.2 ± 7.0
13.8 ± 6.2
67.0 ± 5.0
–
–
–
–
–
Table 4. Linear polarimetry photometry of standard stars.
Object
SA29−130
GJ 3805
BD+284211
Feige 110
HD 283855
HRW 24
Filter
J
J
J
Z
Jb
Jc
J
Z
Jb
Je
q
(%)
−0.03 ± 0.12
−0.04 ± 0.26
0.00 ± 0.05
0.06 ± 0.03
0.08 ± 0.13
0.03 ± 0.04
0.19 ± 0.02
0.56 ± 0.01
−2.19 ± 0.03
−2.34 ± 0.09
u
(%)
0.05 ± 0.11
−0.06 ± 0.06
0.11 ± 0.04
−0.09 ± 0.05
0.02 ± 0.08
−0.06 ± 0.05
2.07 ± 0.02
3.41 ± 0.03
−0.03 ± 0.02
−0.03 ± 0.08
P
(%)
0.05 ± 0.16
0.08 ± 0.26
0.11 ± 0.07
0.12 ± 0.06
0.09 ± 0.15
0.07 ± 0.07
2.08 ± 0.10
3.46 ± 0.10
2.19 ± 0.11
2.34 ± 0.16
p∗
(%)
–
–
–
–
–
–
2.07 ± 0.10
3.45 ± 0.10
2.18 ± 0.11
2.33 ± 0.16
Θ
(deg)
–
–
–
–
–
–
42.4 ± 1.5
40.4 ± 1.0
90.4 ± 1.5
90.4 ± 1.9
Plit , Θlit a
(%, deg)
–
–
–
–
–
–
2.58 ± 0.05, 46 ± 1
3.3 ± 0.1, 46 ± 1d
2.10 ± 0.03, 86 ± 1
Notes. (a) Literature data from Whittet et al. (1992). (b) 2011 December. (c) 2012 June. (d) Computed from the literature I and J data for a wavelength
of 1.03 μm (LIRIS Z-band). (e) 2013 January.
is listed in Table 2: typical photometric aperture sizes go from
2 to 4 × FWHM. The uncertainties associated with q and u were
determined as the standard deviation of all selected individual
measures. Tables 3 and 4 provide the final normalized Stokes
parameters and their error bars for both science targets and standard stars. The high S/N photometry leads to small uncertainties
in q and u, typically below ± 0.1%.
The degree of linear polarization, P, and the linear polarization vibration angle, Θ ∈ [0, π] rad, are calculated from the q
and u normalized Stokes parameters using the equations given
in Zapatero Osorio et al. (2011). Error bars associated with P
are computed as the quadratic sum of the q and u quoted uncertainties plus the uncertainty of 0.10% introduced by a possible instrumental linear polarization (see below). The error in
the polarization vibration angle is obtained from the following
expression:
2
σΘ = (28.65 σP/P)2 + σΘ0
(1)
where σΘ and σΘ0 are in deg, and the factor 28.65 σP/P comes
from Serkowski (1974) and Wardle & Kronberg (1974). All
measured P and Θ values and their associated uncertainties are
provided in Tables 3 and 4. We note that P and Θ error bars
are typically dominated by the instrumental polarization uncertainty. The median error in P is ±0.13% for both Z- and J-band
measurements.
Before proceeding to the discussion of the polarimetric
measurements, we dealt with the data systematics. Because the
polarimetric images were acquired with two slightly different
observing configurations (two angles of the telescope rotator
versus retarder plates), we first checked that both configurations
are compatible and yielded the same results. The non-polarized
standard star SA29−130 was observed using the retarder plates
in 2013 January (Table 4). The measured linear polarization in
the J-band is P = 0.05 ± 0.16% compatible with null polarization at 1.25 μm and suggests that the retarding plates configuration does not introduce significant instrumental polarization.
A125, page 5 of 11
A&A 556, A125 (2013)
Observations of other unpolarized standard stars from previous
campaigns and from the use of the “two angles of the telescope
rotator” configuration also yielded negligible instrumental linear
polarization within an uncertainty of ±0.1%. This agrees with
previous bibliography of Alves et al. (2011) and Zapatero Osorio
et al. (2011). In addition, the polarized standard star HRW 24
was observed with the two instrumental configurations in 2011
December and 2013 January (Table 4). This showed that its
J-band linear polarization degree and polarization vibration angle are consistent at the 1-σ level with each other and with the
published data. Therefore, we concluded that the two instrumental configurations do not introduce a relative bias in our measurements and that all observations can be considered homogeneously obtained in the following discussion.
We also checked that our previously described data reduction procedure did not introduce an extra polarization signal in
the measurements. The raw images of the standard stars were
re-reduced skipping the flat-fielding correction step and/or using skyflat images obtained without the polarimetric optics. We
observed that the new reduction for polarized stars delivered P
and Θ values far from what is tabulated in the literature (published measurements are given in Table 4, permitting a proper
comparison with our determination). In addition, zero-polarized
stars appeared linearly polarized with degrees of ∼0.3−0.4% in
the newly reduced J-band images. The situation dramatically
changed when we applied the standard data reduction procedure that includes flat-field correction using skyflat images obtained with the polarimetric optics. From Table 4 and the observations of unpolarized standard stars, we derived that LIRIS on
the Cassegrain focus of the WHT has small (if any) instrumental linear polarization, likely below 0.1–0.2% at both the Z- and
J-band filters.
The response or efficiency of LIRIS polarimetric optics was
controlled by the observations of the strongly polarized standard stars HD 283855 and HRW 24. As shown in Table 4, our
J-band linear polarization degrees are in good agreement (at the
1-σ level) with the data from the literature, indicating no correction factor for efficiency loss at the J-band. Unfortunately, there
are no published polarimetric indices in the Z-filter for the standard stars. However, our Z-band measurements for HD 283855,
PZ = 3.45 ± 0.1% and ΘZ = 40.4 ± 0.2 deg, lie intermediately between the linear polarization degrees in the I- and
J-filters found in the literature, i.e., PZ,lit = 3.3 ± 0.1% and
ΘZ,lit = 46 ± 1 deg Whittet et al. (1992), which is expected.
Therefore, we did not apply any correction factor due to efficiency loss to our Z-band measurements. There is, however,
a zero-point correction to be applied to the position angle of
the polarization vibration in the J-band, which is measured at
Θo = +4.4 ± 1.3 deg. This is indeed very similar to the quantity
Θo = +4.46 ± 1.5 deg given in Zapatero Osorio et al. (2011).
For this, we did not consider the observations of the standard
star HD 283855 since its q values are close to 0.0, thus introducing large uncertainty in the determination of Θo . There are
not sufficient data to determine the zero-point of the polarization
vibration angle for the Z-band. This correction is wavelength dependent; yet we applied the same Θo to Z- as to the J-band given
the proximity in wavelength of the filters Z and J.
We discarded any correlation between our P measurements
and the airmass at which the targets were observed. The P versus airmass plane was divided into four quadrants with an origin at the median values of airmass and P (1.17 and 0.38%,
respectively). In the case of any positive correlation, measurements would be located in preferred quadrants. We did not observe any grouping of our data in any of the quadrants. The
A125, page 6 of 11
Pearson’s r correlation coefficient is r = 0.13 ± 0.21 for the
P measurements, implying that only ∼1.7% of the data could
be explained by a model of linear correlation with airmass.
Therefore, we concluded that the polarization measurements are
not biased by the airmass of the observations.
Because the linear polarization degree P is always a positive quantity, small values of P and values of P affected by poor
S/N data are statistically biased toward an overestimation of the
true polarization (see Simmons & Stewart 1985). We applied the
equation given by Wardle & Kronberg (1974) to derive the debiased linear polarization degree, p∗ , by considering the measured
P and its associated uncertainty:
p∗ = P2 − σ2P .
(2)
The debiased linear polarization degrees p∗ and polarization vibration angles are provided in Tables 3 and 4 for the science
targets and standard stars, respectively. At high values of polarization, changes are negligible; that is this correction does not
affect the positive detection of linear polarization in eight ultracool dwarfs in the sample.
5. Discussion
We adopted the 3-σ criterion to identify positive detection of linear polarization, i.e., P/σP ≥ 3. This criterion
has been extensively used in previous works (Ménard et al.
2002; Zapatero Osorio et al. 2005; Goldman et al. 2009;
Zapatero Osorio et al. 2011). It sets the confidence of positive detections at the level of 99% under the assumption of a Gaussian
distribution of the measurements within their associated error
bars. Given the median uncertainty of our data (±0.13%, Sect. 4),
linear polarization degrees above ∼0.39% can be detected in
both Z- and J-bands.
Based on this criterion, seven out of 18 ultracool
dwarfs in our sample appear to be linearly polarized
in the J-band (J0700+3157AB, J1159+0057, J1411−2119,
J1501+2250, J1521+5053, J1807+5015, and LP 415−20AB),
and two out of five (J0019+4614 and LP 415−20AB) observed
in the Z-filter appear linearly polarized at 1.03 μm. This yields
a frequency of about 40 ± 15% of the sample being polarized at
1.03 and 1.25 μm. This incidence level is similar to that reported
by Ménard et al. (2002) and Zapatero Osorio et al. (2005) for
shorter wavelengths (I-band) and dwarfs of similar temperatures
and spectral types as our sample.
Possible scenarios to account for the observed linear polarization are the following:
– Interstellar grains in the line of sight toward the targets can
act as polarizers. Tamburini et al. (2002) determined that interstellar polarization contributes effectively after 70 pc. As
stated in Sect. 2, our sample is located at closer distances
(Reid et al. 2008; Reiners & Basri 2009; Faherty et al. 2009),
and there is no interstellar extinction reported for any of
them. Interstellar polarization is not expected to contribute
to our data, and consequently this scenario is rejected.
– Strong magnetic fields can also produce linear polarization
by Zeeman splitting of atomic and molecular lines or by
synchrotron emission. X-ray and radio observations show
that ultracool dwarfs can host magnetic fields in the range
of 0.1–3 kG (Neuhauser & Comeron 1998; Berger et al.
2005; Berger 2006; Berger et al. 2008, 2010), which agrees
with predictions from numerical simulations (Reiners &
Christensen 2010). Leroy (1995) measured typical blue optical (B-band) linear polarization degrees of <
∼0.1% in Aptype stars with magnetic fields of ∼1 kG, finding that the
P. A. Miles-Páez et al.: Linear polarization of rapidly rotating ultracool dwarfs
disks with particle sizes significantly larger than 1.2 μm are
not expected to produce linear polarization in our filters of
interest.
– Dust particles present in the upper photospheres or dusty
envelopes (e.g., debris disks containing tiny grains of typical size on the order of 1 μm), causing light scattering processes, are the most likely scenarios to explain the observed
linear polarimetric data of the ultracool dwarfs in our sample.
Atmospheres have to show inhomogeneities to produce measurable polarization signals as widely discussed by Sengupta
& Krishan (2001) and de Kok et al. (2011). Inhomogeneities
could be related to the presence of nonuniform dusty cloud
coverage and/or to rapid rotation enhancing/generating additional nonuniformity of the atmospheric clouds.
Sample
Field dwarfs
J − W2
4
3
2
1
5.1. Linear polarization versus rotation
M5
L0
L5
T0
Spectral Type
T5
Y0
Fig. 3. J−W2 color as a function of spectral type. Our targets are plotted
as black circles; the mean location of field dwarfs is represented by
gray circles, where the error bars account for the dispersion of the field
(Dupuy & Liu 2012). Spectral types for our targets are slightly shifted
for the clarity of the diagram.
linear polarization amplitude is a function of the intensity
of the magnetic field and the number of atomic lines in the
stellar spectra. Our targets have spectra fully dominated by
the absorption of molecular species, for which the global
Zeeman-splitting polarization is expected to be even smaller
than for the atomic lines. These low levels of linear polarization are indeed below our detection limit. Persistent radio emission at ∼8.5 GHz has been detected in a significant
number of cool and ultracool dwarfs (McLean et al. 2012).
In our sample, BRI 0021−0214, J0036+1821 (Berger 2002),
LP 349−25 (McLean et al. 2012), and J1501+2250 (Hallinan
et al. 2007) have been detected as radio sources. Assuming
gyro- and synchrotron processes associated with their magnetic fields, linear polarization is not expected to be significant at short wavelengths. Of the four radio sources in our
sample, only J1501+2250 is linearly polarized in the J-band.
We do not believe that magnetic fields explain our linear polarimetric findings.
– Another source of linear polarization is the presence of
dusty material surrounding our targets in the form of protoplanetary disks or debris disks. On the one hand, protoplanetary disks have lifetimes up to ∼10 Myr (Luhman &
Mamajek 2012) and imprint intrinsic linear polarization degrees of P ∼ 1−25% (Kandori et al. 2007; Kusakabe et al.
2008; Hashimoto et al. 2009). None of our targets have such
young ages (Sect. 2), and our polarization measurements are
typically below ∼0.8%. In Fig. 3, we show the color J − W2
as a function of spectral type for our targets, and we compare them to the average colors of field dwarfs (Dupuy & Liu
2012). As seen from the figure, our objects nicely follow the
trend delineated by field dwarfs, indicating no measurable
mid-infrared flux excesses. Therefore, there is no evidence of
the presence of warm disks around the targets that could account for the observed linear polarization degrees. The scenario of proto-planetary disks is thus rejected for our sample.
On the other hand, we cannot discard the presence of debris
disks in our sample, since these disks are cold and typically
detected at wavelengths longer than 4.5 μm. Those debris
We investigated whether there is a correlation between the observed degree of linear polarization and the projected rotational
velocity (v sin i). We plot the debiased J- and Z-band polarization degree as a function of v sin i for our sample in Fig. 4.
Two objects from the literature (J0136+0933 and J1022+5825,
Zapatero Osorio et al. 2011) were added to the J-band data,
because they were observed with the same instrumental configuration as our targets, the uncertainties associated with their
polarimetric measurements are ≤±0.30%, and they have published spectroscopic rotational velocities or photometric rotation periods (see Table 6 by Zapatero Osorio et al. 2011). We
obtained their debiased linear polarization degree by applying
Eq. (2) to the P values given by the authors. Both sources have
v sin i ≤ 50 km s−1 and are unpolarized in the J-band.
As shown in Fig. 1 and Table 1, some of our ultracool dwarfs
define the upper envelope of the v sin i versus spetral type diagram. These have v sin i ≥ 60 km s−1 and rotational velocities
approaching the ∼10−20% of their break-up speed (computed
with the assumption that all ultracool dwarfs have the same size
as Jupiter for ages older than ∼500 Myr and masses as those
given in Sect. 2). Konopacky et al. (2012) reported that some
ultracool dwarfs are rotating even at ∼30% of their break-up velocity. The group of seven targets with v sin i ≥ 60 km s−1 likely
have a rotation axis almost perpendicular to the line of sight, i.e.,
sin i ∼ 1; the measured spectroscopic rotational velocities reflect
their true fast rotation. However, sources with v sin i < 60 km s−1
in our sample may present a variety of rotation axis angles, and
the uncertainty introduced by the sin i prevents us from segregating the very fast rotators (v ≥ 60 km s−1 ) from those rotating
moderately (v = 30–60 km s−1 ).
From the diagram illustrated in Fig. 4, it is seen that the
J-band linearly polarized sources have p∗ = 0.4–0.8% for all rotational velocities. Simple statistics can be performed by including the two objects taken from Zapatero Osorio et al. (2011) and
by excluding the three binary dwarfs (two of them are polarized)
since it is unknown how each component contributes to the measured polarimetric signal. We derived that 50±29% (3 out of 6 ultracool dwarfs) in the group of the very fast rotators (v sin i ≥
60 km s−1 ) are linearly polarized in the J-band. This contrasts
with the frequency of 18 ± 13% (2 out of 11) polarized sources
among the targets with v sin i < 60 km s−1 . The average value
of the debiased linear polarization is p∗ = 0.43 ± 0.16% for
the very fast rotators, while it is smaller, p∗ = 0.18 ± 0.24%,
for the dwarfs with moderate spectroscopic rotational velocities. Including the three binaries (each component with its own
spectroscopic rotational velocity and the polarimetric measurement of the combined light) does not change the incidence of
A125, page 7 of 11
A&A 556, A125 (2013)
Fig. 4. Debiased J- (le f t) and Z-band (right) linear polarization degree as a function of projected rotational velocity. Our data are plotted as black
dots and data from the literature (see text) as open diamonds (the arrow stands for an upper limit on v sin i). Positive detection of linear polarization
(P/σ ≥ 3) is indicated by open circles surrounding the black dots. Some objects are labeled. For LP 415−20AB we plotted the average v sin i since
both components share similar values; for the LP 349−25 binary system both components are plotted separately given their differing spectroscopic
rotational velocities. Velocity measurements and their associated error bars are taken from the literature as explained in the text and Table 1.
5.2. Linear polarization versus spectral type
The debiased linear polarization is shown as a function of spectral type in Fig. 6 using our measurements in the J-band. If we
assume that the age of the sample is that of the field (typically
A125, page 8 of 11
0.7
0.6
J1501+2250
0.5
J−band p* (%)
J-band linear polarization significantly: 43 ± 25% (3 out of 7)
and 29 ± 14% (4 out of 14) for the very fast and moderately rotating dwarfs, respectively. We caution that the measured linear
polarization degrees of the binaries likely represent a lower limit
on the true polarization signal since polarization is diluted by
combining light coming from different sources and conditions.
Our data suggest that ultracool dwarfs with v sin i ≥
60 km s−1 have a higher J-band linear polarimetry detection fraction by about a factor of 1.5–2 compared to objects
with v sin i = 30–60 km s−1 . The number of observations in the
Z-band is very reduced, and we did not attempt any statistics.
However, the Z-band linear polarimetric data currently available
do not appear to contradict the results obtained for the J-filter.
Nevertheless, the numbers are still small even for the J-band
observations, and additional data are required for more robust
statistics.
Diagrams illustrating p∗ as a function of true rotational velocity or rotation period are ideal to study the linear polarization
dependence on rotation. For five sources in our sample there are
rotation periods published in the literature (see Table 1), and the
T2.5 source studied by Zapatero Osorio et al. (2011) also has
a rotation period determination. These were obtained from the
analysis of photometric light curves at wavelengths similar to
those of our study. Figure 5 shows the measured J-band linear
polarization degree versus rotation period for a total of six ultracool dwarfs with spectral types ranging from M8.5 to T2.5. Note
that either true rotational velocity or period can be used without distinction because all ultracool dwarfs in our sample are
supposed to have a similar radius. Of the six sources, only one
is linearly polarized and it happens to have the shortest period
or fastest rotation, suggesting that very fast rotation may play a
role in the detectability of linear polarization (as suggested by
theory). Additional data are demanded to fill in the diagram of
Fig. 5 before any solid conclusion can be obtained.
0.4
0.3
0.2
J0828−1309
J0036+1821
J0136+0933
BRI 0021−0214
0.1
J1835+3259
0
1
2
3
4
Rotational period (h)
5
6
Fig. 5. Debiased J-band linear polarization degree as a fuction of rotation period. Positive polarimetric detections are indicated with open
circles surrounding the black dots. Black dots stand for our measurements, the diamond represents data from the literature (see text). Error
bars of rotation periods were computed from the FWHM of the peaks
in the periodograms reported in the literature (see Table 1).
≥0.5 Gyr, except for J0045+1634, which is discussed below), we
may easily relate mass to spectral type in our study: the warmer
the spectral classification, the more massive the target object. As
indicated in Sect. 2, the M7–L3.5 sources have likely masses
ranging from 0.09 through 0.05 M and similar surface gravity
of log g = 5.3–5.1 (cm s−2 ). Despite claiming the need for additional data, Ménard et al. (2002) and Zapatero Osorio et al.
(2005) argued that there is a slight trend for a larger I-band linear polarization degree with decreasing surface temperature for
field dwarfs. The spectral type coverage of these previous works
expands from the late-Ms to the late-Ls. In our study, no trend is
observed for the narrower spectral type interval M7–L3.5; actually, the linear polarimetry scatter appears nearly constant over
this spectral range.
P. A. Miles-Páez et al.: Linear polarization of rapidly rotating ultracool dwarfs
0.8
0.7
J1159+0057
J−band p* (%)
0.6
0.5
0.4
J0828−1309
0.3
0.2
0.1
0
M5
L0
L5
Spectral Type
T0
T5
Fig. 6. Debiased J-band linear polarization degree as a function of spectral type. Objects with v sin i ≥ 60 km s−1 are plotted as black dots,
and sources with slower spectroscopic rotational velocities are indicated
with gray dots. Binary objects are indicated with triangles. Encircled
symbols stand for linearly polarized sources. The two extra objects
taken from Zapatero Osorio et al. (2011) (v sin i < 50 km s−1 ) are shown
with diamonds.
In addition, J1254−0122 (T2) is the coolest target in our
sample. Sengupta & Marley (2009) theoretically studied the possible detection of linear polarization in the oblate atmospheres of
cloudless T-type sources, which are even cooler than the L-types.
Their calculations showed that polarization may arise only for
λ ≤ 0.6 μm (a range where T-dwarfs are extremely faint), and
the net disk integrated polarization may be neglible. We found
p∗ = 0.00 ± 0.34% for J1254−0122; this measurement and the
one obtained for J0136+0933 (T2.5; p∗ = 0.14 ± 0.33%) by
Zapatero Osorio et al. (2011) are the only two near-infrared linear polarimetric data available for T-dwarfs. They agree with the
theory.
The youngest, lowest gravity (log g = 4.2–5.0 cm s−2 according to the evolutionary models by Baraffe et al. 2003), and possibly one of the least massive objects in our sample, J0045+1634,
is found to be unpolarized (p∗ = 0.00 ± 0.11% in the J-band) in
contrast with the theoretical predictions of Sengupta & Marley
(2010). This may be explained by a true moderate rotation velocity (v sin i = 32.8 km s−1 ) or a low inclination angle of the
spin axis (i.e., the object is seen near pole-on). To test the linear polarimetric predictions of low gravity (young), cool lowmass dwarfs made by Sengupta & Marley (2010) and Marley &
Sengupta (2011), a larger number of observations is demanded.
5.3. Linear polarization versus time
We investigated the variability of the linear polarization degree
for objects with measurements available on different occasions.
For future references, the Julian date of the observations are provided in Table 3. In the following discussion we separate observations taken at short and intermediate-to-long timescales.
There are three objects (J0019+4614, LP 349–25AB, and
LP 415–20AB) whose Z- and J-band polarimetric data were
taken with a separation of approximately one day. The M8+M9
binary LP 349–25AB has pair members with different rotational
velocities, and the contribution of each component to the polarization measurements is not well constrained. The polarimetric
observations taken ∼1-day apart, or after ∼16 rotation cycles, do
not reveal significant linear polarization at either 1.03 or 1.25 μm
(to compute the number of rotation cycles, we adopted the size
of Jupiter, sin i = 1, and the measured v sin i of the primary given
in Table 1. Note that the number of rotation periods estimated
in this way always represents a lower limit on the true number
of rotation cycles if sin i 1). The M8 dwarf J0019+4614 is
linearly polarized in the Z-band but does not show polarization
at the longest wavelength of our study. This source will be discussed further in the following subsection. The M7+M9.5 pair
LP 415–20AB has components with similar spectroscopic rotational velocities, and despite that each member contribution to
the polarization is unconstrained, this source shows a significant
linear polarization degree at both wavelengths. Furthermore,
both the intensity of the linear polarization and the vibration angle are nearly constant at the two observing epochs, suggesting
that the geometry of the structures responsible for the polarization has likely remained unmodified during at least ∼8 rotation
cycles.
The ultracool dwarfs J0828−1309, J1159+0057,
J1807+5015, and J2036+1051 were observed on timescales
of months (time intervals of 13.1, 7.5, 3.7, and 3.7 months,
respectively). The two later sources were studied at different
wavelengths on the two occasions after completing at least
1400 rotation cycles. Because some variability may be expected
at long timescales (Martín et al. 2001), the two observations
cannot be compared. On the contrary, J0828−1309 (L2) and
J1159+0057 (L0) were imaged in the J-filter after passing a
minimum of ∼2300 and ∼3000 rotation cycles. The former
dwarf does not show measurable linear polarization beyond the
3-σ detection. The L0 source appears linearly polarized at both
observing epochs; however, although the polarimetric degree
seems unchanged within the quoted uncertainties, the polarization vibration angles look different. This can be interpreted as
follows: The amounts of photospheric dust/condensates responsible for the light scattering processes may be similar at the two
epochs, but the location or distribution of the heterogeneous
cloud coverage may have evolved across the observable disk.
Based on LP 415–20AB and J1159+0057, our data hint
at small linear polarimetric variability amplitudes on short
timescales of about days or a few ten rotation cycles, and larger
polarimetric variability on longer timescales of over hundred to
thousand rotation periods. Theory predicts that low-mass objects
with M ≤ 0.35 M become fully convective (Chabrier & Baraffe
2000). The very fast rotation has an impact in the dwarfs convection processes (Showman & Kaspi 2012); the models produced
by these authors suggest that patchy clouds will form leading to
variability that is not canceled out in a disk integrated light when
cloud condensation levels lie in the atmosphere (e.g., late-M and
L dwarfs). According to Showman & Kaspi (2012), changes in
the detailed structure of the atmospheric turbulence occur on
timescales of about ∼10–100 rotation cycles for a typical brown
dwarf with a rotation period of ∼104 s. This qualitatively agrees
with our (yet scarce) polarimetric observations and with the photometric light curves of some late-M and L dwarfs available in
the literature. For example, Martín et al. (2001), Artigau et al.
(2009) and Radigan et al. (2012) reported on ultracool dwarfs
photometric variations not only on rotational timescales (a few
hours) but also over many rotation cycles. The polarimetric monitoring along with simultaneous photometric light curves may
provide new insights into the weather of ultracool dwarfs.
Six of our targets have published linear polarimetric data at
optical wavelengths (R- and I-bands). In Table 5, we compiled
all available measurements by providing the central wavelengths
A125, page 9 of 11
A&A 556, A125 (2013)
2.4
Table 5. Other polarimetric measurements.
This work
ZO05
T09
2.2
BRI0021−0214
J0036+1821
J0045+1634
J1807+5015
J1835+3259
J2057−0252
λc , δλa
(μm)
0.85, 0.15
0.64, 0.16
0.77, 0.14
0.77, 0.14
0.85, 0.15
0.85, 0.15
0.85, 0.15
0.81, 0.14
0.64, 0.14
0.85, 0.15
0.77, 0.14
0.85, 0.15
p∗
(%)
0.06 ± 0.17
0.52 ± 0.33
0.20 ± 0.03
0.03 ± 0.05
0.00 ± 0.06
0.00 ± 0.12
0.00 ± 0.06
0.70 ± 0.14
1.55 ± 0.61
0.04 ± 0.03
0.04 ± 0.02
0.00 ± 0.38
Θ
(deg)
–
–
17.6 ± 4.0
–
–
–
–
46.7 ± 1.2
101 ± 1.2
–
–
–
Ref.
2
2
1
3
2
2
2
4
4
2
1
2
Notes. (a) Passband central wavelength and width as reported by the
authors.
References. (1) Ménard et al. (2002); (2) Zapatero Osorio et al. (2005);
(3) Goldman et al. (2009); (4) Tata et al. (2009).
and widths of the passbands of the observations, the debiased
linear polarization degrees, the polarization vibration angles (in
the case of positive polarimetric detections), and the bibliographic references. These data were acquired years before our
observations and were taken using different filters, instruments,
and telescopes. BRI 0021−0214, J0045+1634, J1835+3259, and
J2057−0252 do not show linear polarization at either optical
or near-infrared wavelengths on different epochs of observations. The L3.5 dwarf J0036+1831 was reported to be linearly
polarized in the Bessel I-band by Ménard et al. (2002), while
Goldman et al. (2009) did not detect polarization above the 3σ level in observations taken with the same instrumental configuration as the first data four years later. Images collected at
longer wavelengths in the present work and in Zapatero Osorio
et al. (2005) did not reveal any significant linear polarization.
The L1.5 dwarf J1807+5015 is reported to be polarized and unpolarized at different wavelengths and epochs, suggesting strong
polarimetric variability. This object is further discussed in the
next subsection.
5.4. Linear polarization versus wavelength
The degree of linear polarization produced by light scattering
increases significantly when the size of the grain particles is
comparable to the wavelength of the observations (Sengupta &
Krishan 2001). Therefore, a multiwavelength study of ultracool
dwarfs linear polarization may provide relevant information on
the typical sizes of the atmospheric grains/condensates, which
is a key ingredient for the theory of model atmospheres (e.g.,
Allard et al. 2001). We caution that the linear polarization degree is also a function of the wavelength-dependent gas opacity: In atmospheric dusty regions with strong gas opacity, there
will be less scattering processes and less polarization (see discussion in Marley & Sengupta 2011). Consequently, linear polarization measurements reflect a combination of various factors:
Gas opacity function, presence of dust, and grain physical sizes.
In addition, if polarimetric observations are not simultaneous,
variability of dusty patterns may become an issue. Our sample
objects are brighter in the J-band than at shorter wavelengths;
that is gas opacity is reduced at around 1.2 μm. Unfortunately,
none of our Z- and J-band observations are simultaneous.
A125, page 10 of 11
2.0
1.8
2006 Jun 18
1.6
1.4
p* (%)
Object
1.2
1.0
0.8
2006 Jun 18
2012 Jun 15
0.6
0.4
0.2
2004 Aug 15
2012 Oct 07
0.0
0.4
0.6
0.8
1.0
Wavelength ( μm )
1.2
1.4
Fig. 7. Debiased linear polarization degree measured for J1807+5015
as a function of wavelength. Data were compiled from Zapatero Osorio
et al. (2005), Tata et al. (2009), and this work. Vertical error bars correspond to the quoted uncertainties in polarization, and the horizontal
error bars account for the width of the filters.
By combining our observations and the data from the literature we may draw some preliminary results. The L1.5 source
J1807+5015 has the largest number of polarimetric measurements among all studied ultracool dwarfs. Figure 7 illustrates
the debiased linear polarization degree as a function of wavelength from the R- through the J-bands (Tables 3 and 5). Despite
that gas opacity is stronger at the R-band wavelengths, linear
polarization intensity is found to be the largest at the shortest
wavelength, likely implying submicron atmospheric particles,
as shown in Fig. 7 of Sengupta & Kwok (2005). The two measurements taken in the I-band (although slightly different filters,
Table 5) differ by δp∗ ∼ 0.7% and were obtained on two occasions separated by nearly 2 yr. We ascribe this polarimetric difference to a likely atmospheric variability. The high value of p∗
obtained for the J-band as compared to the Z-filter in our work
cannot be attributed only to differing gas opacities, since more
than ∼1400 rotation periods were completed between these two
observations and changes are expected to occur in atmospheric
dusty structures (Freytag et al. 2010).
The predominant submicron-to-micron size of the dusty particles is also supported by the observations of J0019+4614
(M8) and J2036+1051 (L3), whose linear polarization indices
at 1.03 μm are larger than those at 1.25 μm, and the observations
of LP 415−20AB, which show similar polarization degrees at
both wavelengths. Simultaneous multiwavelength polarimetric
observations may help constrain model atmospheres, since the
models available in the literature tend to agree on the global atmospheric structure but differ in details like grain size and other
opacity-related parameters (e.g., see Helling et al. 2008).
6. Conclusions
Using the LIRIS instrument on the William Herschel telescope,
we obtained Z- (1.03 μm) and J-band (1.25 μm) linear polarimetric images of a sample of 18 bright, rapidly rotating ultracool dwarfs with v sin i 30 km s−1 and spectral types ranging
from M7 through T2. All these sources are believed to form condensates of liquid and solid particles in their atmospheres and to
have oblate shapes, given their large rotational velocities (some
P. A. Miles-Páez et al.: Linear polarization of rapidly rotating ultracool dwarfs
are rotating at nearly one third of their break-up velocity). This
provides an appropriate scenario for the detection of linear polarization in the continuum light produced by scattering processes.
Three of the targets are known binaries. The median uncertainty
associated with our Z- and J-band measurements was ±0.13%
in the linear polarization degree, indicating that our data are sensitive to strong polarization indices p∗ ≥ 0.39% at the ≥3-σ
confidence level.
Eight ultracool dwarfs out of 18 targets appear to be linearly polarized in the J- and/or Z-bands, suggesting that about
40 ± 15% of the sample shows significant linear polarization in
the near-infrared. Measured positive detections have linear polarization degrees in the range of P = 0.4–0.8% independent of
spectral type and v sin i. Our derived polarimetric degrees agree
with theoretical predictions (Sengupta & Marley 2010; de Kok
et al. 2011). Additionally, our data hint at ultracool dwarfs with
the highest rotation (v sin i ≥ 60 km s−1 ) having a factor of about
1.5–2 larger J-band linear polarimetry detection fraction than ultracool dwarfs with v sin i = 30–60 km s−1 . The average value of
the debiased linear polarization (including detections and nondetections) is p∗ = 0.43 ± 0.16% for the very fast rotators,
while it is smaller, p∗ = 0.18 ± 0.24%, for the dwarfs with
moderate spectroscopic rotational velocities. There are six objects with true rotation period in the literature; the one with the
shortest period (2 h) and the largest v sin i (60 km s−1 ) show linear polarization in the J-band. More data are required for a more
robust statistics.
We also investigated the J-band linear polarimetry dependence on time and wavelength for the ultracool dwarfs in our
sample. For those objects with polarimetric observations obtained ∼1-day apart (or after completion of about a few ten
rotation periods), our data suggest little polarimetric variability (both in the linear polarization degree and vibration angle).
Observations taken months apart (over hundreds to thousand rotation cycles) display significant polarimetric variability, suggesting changes in the atmospheric structures responsible for
the observed linear polarization. For those sources with polarimetric detections in Z- and J-bands on short timescales, we observed that the linear polarization degree tends to be larger at
the shortest wavelength, implying submicron (or around the micron) grain sizes. Simultaneous observations of photometric and
polarimetric light curves of variable sources will shed new light
in our comprehension of the weather affecting ultracool dwarfs
and the sizes of the atmospheric dusty particles.
Acknowledgements. We are thankful to the referee, Prof. Mark Marley, for
his valuable report. The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del
Roque de los Muchachos of the Instituto de Astrofísica de Canarias. This research has made use of NASA’s Astrophysics Data System and the SIMBAD
database, the last one is operated at CDS, Strasbourg, France. Also, this publication makes use of data products from the Wide-field Infrared Survey Explorer,
which is a joint project of the University of California, Los Angeles, and the
Jet Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration. This work is partly financed
by the Spanish Ministry of Economics and Competitiveness through projects
AYA2010-21308-C03-02 and AYA2011-30147-C03-03.
References
Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872
Allard, F., Hauschildt, P. H., Alexander, D. R., Tamanai, A., & Schweitzer, A.
2001, ApJ, 556, 357
Alves, F. O., Acosta-Pulido, J. A., Girart, J. M., Franco, G. A. P., & López, R.
2011, AJ, 142, 33
Artigau, É., Bouchard, S., Doyon, R., & Lafrenière, D. 2009, ApJ, 701, 1534
Bailer-Jones, C. A. L., & Mundt, R. 2001, A&A, 367, 218
Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hauschildt, P. H. 2003,
A&A, 402, 701
Berger, E. 2002, ApJ, 572, 503
Berger, E. 2006, ApJ, 648, 629
Berger, E., Rutledge, R. E., Reid, I. N., et al. 2005, ApJ, 627, 960
Berger, E., Gizis, J. E., Giampapa, M. S., et al. 2008, ApJ, 673, 1080
Berger, E., Basri, G., Fleming, T. A., et al. 2010, ApJ, 709, 332
Blake, C. H., Charbonneau, D., & White, R. J. 2010, ApJ, 723, 684
Buenzli, E., Apai, D., Morley, C. V., et al. 2012, ApJ, 760, L31
Chabrier, G., & Baraffe, I. 2000, ARA&A, 38, 337
Cruz, K. L., Kirkpatrick, J. D., & Burgasser, A. J. 2009, AJ, 137, 3345
de Kok, R. J., Stam, D. M., & Karalidi, T. 2011, ApJ, 741, 59
Deshpande, R., Martín, E. L., Montgomery, M. M., et al. 2012, AJ, 144, 99
Dupuy, T. J., & Liu, M. C. 2012, ApJS, 201, 19
Dupuy, T. J., Liu, M. C., Bowler, B. P., et al. 2010, ApJ, 721, 1725
Faherty, J. K., Burgasser, A. J., Cruz, K. L., et al. 2009, AJ, 137, 1
Freytag, B., Allard, F., Ludwig, H.-G., Homeier, D., & Steffen, M. 2010, A&A,
513, A19
Goldman, B., Pitann, J., Zapatero Osorio, M. R., et al. 2009, A&A, 502, 929
Hallinan, G., Bourke, S., Lane, C., et al. 2007, ApJ, 663, L25
Hallinan, G., Antonova, A., Doyle, J. G., et al. 2008, ApJ, 684, 644
Hashimoto, J., Tamura, M., Kandori, R., et al. 2009, in AIP Conf. Ser. 1158, eds.
T. Usuda, M. Tamura, & M. Ishii, 111
Helling, C., Ackerman, A., Allard, F., et al. 2008, MNRAS, 391, 1854
Jones, H. R. A., & Tsuji, T. 1997, ApJ, 480, L39
Kandori, R., Tamura, M., Kusakabe, N., et al. 2007, PASJ, 59, 487
Khandrika, H., Burgasser, A. J., Melis, C., et al. 2013, AJ, 145, 71
Koen, C. 2004, MNRAS, 354, 378
Konopacky, Q. M., Ghez, A. M., Fabrycky, D. C., et al. 2012, ApJ, 750, 79
Kusakabe, N., Tamura, M., Kandori, R., et al. 2008, AJ, 136, 621
Leroy, J. L. 1995, A&AS, 114, 79
Luhman, K. L., & Mamajek, E. E. 2012, ApJ, 758, 31
Manchado, A., Barreto, M., Acosta-Pulido, J., et al. 2004, in SPIE Conf. Ser.
5492, eds. A. F. M. Moorwood, & M. Iye, 1094
Marley, M. S., & Sengupta, S. 2011, MNRAS, 417, 2874
Martín, E. L., Zapatero Osorio, M. R., & Lehto, H. J. 2001, ApJ, 557, 822
McLean, M., Berger, E., & Reiners, A. 2012, ApJ, 746, 23
Ménard, F., Delfosse, X., & Monin, J.-L. 2002, A&A, 396, L35
Mohanty, S., & Basri, G. 2003, ApJ, 583, 451
Neuhauser, R., & Comeron, F. 1998, Science, 282, 83
Oliva, E. 1997, A&AS, 123, 589
Radigan, J., Jayawardhana, R., Lafrenière, D., et al. 2012, ApJ, 750, 105
Reid, I. N., Lewitus, E., Allen, P. R., Cruz, K. L., & Burgasser, A. J. 2006, AJ,
132, 891
Reid, I. N., Cruz, K. L., Kirkpatrick, J. D., et al. 2008, AJ, 136, 1290
Reiners, A., & Basri, G. 2008, ApJ, 684, 1390
Reiners, A., & Basri, G. 2009, ApJ, 705, 1416
Reiners, A., & Basri, G. 2010, ApJ, 710, 924
Reiners, A., & Christensen, U. R. 2010, A&A, 522, A13
Schmidt, G. D., Elston, R., & Lupie, O. L. 1992, AJ, 104, 1563
Sengupta, S. 2003, ApJ, 585, L155
Sengupta, S., & Krishan, V. 2001, ApJ, 561, L123
Sengupta, S., & Kwok, S. 2005, ApJ, 625, 996
Sengupta, S., & Marley, M. S. 2009, ApJ, 707, 716
Sengupta, S., & Marley, M. S. 2010, ApJ, 722, L142
Sengupta, S., & Marley, M. S. 2011, Pramana, 77, 157
Serkowski, K. 1974, Polarization techniques., ed. N. P. Carleton, 361
Showman, A. P., & Kaspi, Y. 2012, ApJ, in press [arXiv:1210.7573]
Siegler, N., Close, L. M., Mamajek, E. E., & Freed, M. 2003, ApJ, 598, 1265
Simmons, J. F. L., & Stewart, B. G. 1985, A&A, 142, 100
Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
Tamburini, F., Ortolani, S., & Bianchini, A. 2002, A&A, 394, 675
Tata, R., Martín, E. L., Sengupta, S., et al. 2009, A&A, 508, 1423
Wardle, J. F. C., & Kronberg, P. P. 1974, ApJ, 194, 249
Whittet, D. C. B., Martin, P. G., Hough, J. H., et al. 1992, ApJ, 386, 562
Witte, S., Helling, C., Barman, T., Heidrich, N., & Hauschildt, P. H. 2011, A&A,
529, A44
Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
Zapatero Osorio, M. R., Caballero, J. A., & Béjar, V. J. S. 2005, ApJ, 621, 445
Zapatero Osorio, M. R., Martín, E. L., Bouy, H., et al. 2006, ApJ, 647, 1405
Zapatero Osorio, M. R., Béjar, V. J. S., Goldman, B., et al. 2011, ApJ, 740, 4
Zapatero Osorio, M. R., Béjar, V. J. S., Miles-Páez, P. A., et al. 2013, A&A,
submitted
A125, page 11 of 11
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement