ON THE ROAD TO IMAGING EXTRASOLAR PLANETS: NULL RESULTS,

ON THE ROAD TO IMAGING EXTRASOLAR PLANETS: NULL RESULTS,
ON THE ROAD TO IMAGING EXTRASOLAR PLANETS: NULL RESULTS,
OTHER DISCOVERIES ALONG THE WAY, AND SIGNPOSTS FOR THE
FUTURE
by
Eric Ludwig Nielsen
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF ASTRONOMY
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2011
2
T HE U NIVERSITY OF A RIZONA
G RADUATE C OLLEGE
As members of the Dissertation Committee, we certify that we have read the
dissertation prepared by Eric Ludwig Nielsen entitled “On the Road to Imaging
Extrasolar Planets: Null Results, Other Discoveries Along the Way, and Signposts
for the Future” and recommend that it be accepted as fulfilling the dissertation
requirement for the Degree of Doctor of Philosophy.
Date: 22 March 2011
Laird Close
Date: 22 March 2011
Don McCarthy
Date: 22 March 2011
Philip Hinz
Date: 22 March 2011
Glenn Schneider
Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction
and recommend that it be accepted as fulfilling the dissertation requirement.
Date: 22 March 2011
Dissertation Director: Laird Close
3
S TATEMENT B Y A UTHOR
This dissertation has been submitted in partial fulfillment of requirements for
an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for
permission for extended quotation from or reproduction of this manuscript in
whole or in part may be granted by the head of the major department or the
Dean of the Graduate College when in his or her judgment the proposed use of
the material is in the interests of scholarship. In all other instances, however,
permission must be obtained from the author.
S IGNED: Eric Ludwig Nielsen
4
A CKNOWLEDGMENTS
I want to thank everyone who’s helped me develop in my career as a scientist,
allowing me to finish this work.
Thanks to those of you at Berkeley, who helped me gain a solid foothold in
astronomy as an undergraduate: Debra Fischer, Geoff Marcy, Jason Wright, John
Johnson, Bernie Walp, James Graham, Eugene Chiang, Alex Filippenko, Nate
McCrady, Shane Bussmann, Brandon Swift, Lee Huss, Lindsey Pollack, and Amy
Jordan.
Thanks to the great mentors I’ve had at the University of Arizona, including my great advisor, Laird Close, who gave me so many opportunities over the
years. And thank you to Phil Hinz, Don McCarthy, Glenn Schneider, Erick Young,
and Matt Kenworthy.
Thanks to my fellow graduate students over the years, Shane Bussmann and
Brandon Swift again, as well as Jane Rigby, Andrea Leistra, Karen Knierman, Eric
Mamajek, Jackie Monkiewicz, Patrick Young, Jeremy Bailin, Kris Eriksen, Wilson Liu, Suresh Sivanandam, Julia Greissl, Jenn Donley, Iva Momcheva, Krystal
Tyler, Wayne Schlingman, Jonathan Trump, Vanessa Bailey, Dsika Narayanan,
Amy Stutz, Brandon Kelly, and Beth Biller. And a special thank you to Kristian
Finlator and Moire Prescott, who helped me get through both the best and most
difficult times.
Thanks to those of you who keep Steward running, Michelle Cournoyer, Erin
Carlson, Joy Facio, Catalina Diaz-Silva, Jeff Fookson, Cathi Duncan, Kim Chapman, Doris Tucker, Grisela Koeppen, and Paula Nielsen.
Another thank you to those beyond Steward who helped me move forward in
my research: Michael Liu, Niranjan Thatte, Zahed Wahhaj, Fraser Clarke, Mathias Tecza, Wolfgang Brandner, Markus Janson, Markus Hartung, Jose Guirado,
Trent Dupuy, Adam Kraus, and Justin Crepp.
Thank you to my family, to dad, Sven, Kristin, Ayumi, Gerri, and Joannie, for
always being there to support me.
Thank you to those groups that have funded my research, directly or indirectly over the years, including NASA, the NSF, the LAPLACE Institute, and the
Michelson Graduate Fellowship.
And finally, most of all, thank you to Sasha Kuchuk for being at my side.
Without you, I’d never have been able to get to this point.
5
D EDICATION
This thesis is dedicated to my friends and family: to dad, Sven, and Kristin for
always being there for me. To Kristian and Moire for getting me through the
worst and the best of it. And to Sasha for being by my side whenever I needed
her.
6
TABLE
OF
C ONTENTS
L IST
OF
F IGURES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
L IST
OF
TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
A BSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
C HAPTER 1 INTRODUCTION TO DIRECT IMAGING SURVEYS FOR
EXTRASOLAR PLANETS . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Extrasolar Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 How Direct Imaging Fits into Exoplanet Science . . . . . . . . . . .
1.3 Spectroscopy of Giant Planets . . . . . . . . . . . . . . . . . . . . . .
1.4 Testing Models of Planetary Atmospheres and Formation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Direct Imaging Surveys as a Way to Set Constraints on Extrasolar
Planet Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C HAPTER 2 AB DORADUS C: AGE, SPECTRAL TYPE, ORBIT, AND
COMPARISON TO EVOLUTIONARY MODELS . . . . . . . . . . . .
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 An Improved Spectral Reduction . . . . . . . . . . . . . . . . . . . .
2.3 Improved Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Spectral Type . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 The Age of AB Dor . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 HR Diagram and Evolutionary Models . . . . . . . . . . . .
2.5 New Spectra of AB Dor C from VLT SINFONI . . . . . . . . . . . .
2.5.1 Further Astrometric Confirmation . . . . . . . . . . . . . . .
2.5.2 Spectral Fit and a New Spectral Type . . . . . . . . . . . . .
2.5.3 Validation of the DUSTY models . . . . . . . . . . . . . . . .
2.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
14
15
18
20
21
24
24
26
32
35
35
38
41
43
45
48
52
55
C HAPTER 3 DESIGNING DIRECT IMAGING SURVEYS THROUGH SIMULATIONS OF EXTRASOLAR PLANET POPULATIONS . . . . . . 56
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Target Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7
TABLE
OF
C ONTENTS — Continued
C HAPTER 4 CONSTRAINTS ON EXTRASOLAR PLANET POPULATIONS
FROM VLT NACO/SDI AND MMT SDI AND DIRECT ADAPTIVE
OPTICS IMAGING SURVEYS: GIANT PLANETS ARE RARE AT LARGE
SEPARATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2.1 Target Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Completeness Plots . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.2 Detection Probabilities Given an Assumed Distribution of
Mass and Semi-major Axis of Extrasolar Planets . . . . . . . 90
4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4.1 Planet Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4.2 Host Star Spectral Type Effects . . . . . . . . . . . . . . . . . 99
4.4.3 Constraining the Semi-Major Axis Distribution . . . . . . . . 101
4.4.4 Testing Core Accretion Models . . . . . . . . . . . . . . . . . 107
4.5 Discussion: Systematic Effects of Models on Results and Other Work112
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
C HAPTER 5 A UNIFORM ANALYSIS OF 118 STARS WITH HIGH-CONTRAST
IMAGING: LONG PERIOD EXTRASOLAR GIANT PLANETS ARE
RARE AROUND SUN-LIKE STARS . . . . . . . . . . . . . . . . . . . . 120
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2.1 VLT NACO H and Ks Imaging . . . . . . . . . . . . . . . . . 123
5.2.2 VLT NACO and MMT SDI . . . . . . . . . . . . . . . . . . . 123
5.2.3 Gemini Deep Planet Survey . . . . . . . . . . . . . . . . . . . 124
5.2.4 Target Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.1 Theoretical Models of Giant Planet Fluxes . . . . . . . . . . . 135
5.3.2 Narrowband to Broadband Colors . . . . . . . . . . . . . . . 139
5.3.3 Completeness Plots . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3.4 Testing Power Law Distributions for Extrasolar Planet Mass
and Semi-Major Axis . . . . . . . . . . . . . . . . . . . . . . . 147
5.3.5 The Dependence on Stellar Mass of the Frequency of Extrasolar Giant Planets . . . . . . . . . . . . . . . . . . . . . . . . 151
5.3.6 Ida & Lin (2004) Core Accretion Formation Models . . . . . 164
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8
TABLE OF C ONTENTS — Continued
5.6 Online Figure Sets: Completeness Plots for Each Target Star . . . . 170
5.7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
C HAPTER 6 CHOOSING THE TARGET LIST AND OBSERVING STRATEGY FOR THE GEMINI NICI PLANET-FINDING CAMPAIGN . . . 176
6.1 The Near Infrared Coronagraphic Imager (NICI) . . . . . . . . . . . 176
6.1.1 The Gemini NICI Planet-Finding Campaign . . . . . . . . . 177
6.2 Defining the Input Target List . . . . . . . . . . . . . . . . . . . . . . 179
6.2.1 VLT Adaptive Optics H and Ks Band Imaging, SDI, GDPS
Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.2.2 A Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.2.3 Hipparcos R’HK Stars . . . . . . . . . . . . . . . . . . . . . . 180
6.2.4 Additional Moving Group Stars . . . . . . . . . . . . . . . . 181
6.2.5 Young Nearby M Stars . . . . . . . . . . . . . . . . . . . . . . 181
6.2.6 Debris Disk Host Stars . . . . . . . . . . . . . . . . . . . . . . 181
6.2.7 Additional Sources . . . . . . . . . . . . . . . . . . . . . . . . 182
6.3 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.4 Constructing a Survey . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.4.1 Scaling the Upper Cut-Off with Spectral Type . . . . . . . . 188
6.4.2 Parameters of the Target Stars . . . . . . . . . . . . . . . . . . 193
6.4.3 The Curve of Growth . . . . . . . . . . . . . . . . . . . . . . . 193
6.4.4 Implications for Spectral Type Composition of the Campaign Target List . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.4.5 Properties of the Detected Planets . . . . . . . . . . . . . . . 202
6.5 Final Survey Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.6 Current NICI Planet-Finding Campaign Status . . . . . . . . . . . . 215
C HAPTER 7 CONCLUSIONS AND FUTURE DIRECTIONS . . . . . .
7.1 A Unified Distribution of Extrasolar Planet Populations . . . . . .
7.2 Other Model Possibilities . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Correlated Distributions . . . . . . . . . . . . . . . . . . . .
7.2.2 Alternatives to Single Power Law Fits . . . . . . . . . . . .
7.3 Upcoming Surveys with Dedicated High-Contrast Planet Finders
7.4 Direct Detection of Extrasolar Planets from Space . . . . . . . . .
7.5 Final Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 216
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. 227
R EFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9
L IST
OF
F IGURES
1.1
1.2
The limits on planet populations set by direct imaging . . . . . . . .
The HR 8799 planetary system . . . . . . . . . . . . . . . . . . . . .
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19
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
Reflection and subtraction of AB Dor C spectra . . . . . . . . . . . .
Comparison of AB Dor C to USco 100 . . . . . . . . . . . . . . . . .
Comparison of AB Dor C to GSC 8047-0232 . . . . . . . . . . . . . .
The orbit of AB Dor C . . . . . . . . . . . . . . . . . . . . . . . . . .
Improved orbital fit . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AB Dor C compared to young, low-surface gravity objects . . . . .
AB Dor C compared to high SNR template spectra of field objects .
The age of the AB Dor moving group . . . . . . . . . . . . . . . . . .
AB Dor C on the color-magnitude diagram . . . . . . . . . . . . . .
AB Dor C with other young, low-mass calibrators . . . . . . . . . .
Orbit of AB Dor C including SINFONI data . . . . . . . . . . . . . .
Parameterized orbit of AB Dor C including SINFONI data . . . . .
SINFONI spectra of AB Dor C compared to young templates . . . .
SINFONI spectra of AB Dor C compared to field templates, K band
SINFONI spectra of AB Dor C compared to field templates, H band
Comparison of our new AB Dor C parameters to DUSTY models .
Placing AB Dor C in context with other young, low-mass objects
with dynamical masses . . . . . . . . . . . . . . . . . . . . . . . . . .
28
30
31
33
34
37
39
40
42
44
46
47
49
50
51
53
3.1
3.2
3.3
3.4
3.5
Contrast curves for different planet-finding instruments .
Mass and semi-major axis distributions . . . . . . . . . .
Simulations outputs for a single target star . . . . . . . .
Basic results from the simulation . . . . . . . . . . . . . .
Expected number of planets as a function of survey size .
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
Target stars in the sample . . . . . . . . . . . . . . . . . . . . .
Assumed eccentricity distribution . . . . . . . . . . . . . . . .
Simulation example at one grid point . . . . . . . . . . . . . .
Completeness plot for GJ 182 . . . . . . . . . . . . . . . . . . .
Assumed planet mass distribution . . . . . . . . . . . . . . . .
Assumed semi-major axis distribution . . . . . . . . . . . . . .
Detected and non-detected simulated planets around GJ 182 .
Upper limit on planet fraction for all stars, Burrows model . .
Upper limit on planet fraction for all stars, Baraffe model . . .
Upper limit on planet fraction for AFGK stars, Burrows model
Upper limit on planet fraction for AFGK stars, Baraffe model .
Upper limit on planet fraction for M stars, Burrows model . .
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10
L IST OF F IGURES — Continued
4.13 Upper limit on planet fraction for M stars, Baraffe model . . . . . . 105
4.14 Constraints on models of semi-major axis distribution, Burrows
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.15 Constraints on models of semi-major axis distribution, Baraffe model110
4.16 Our ability to rule out different semi-major axis distributions . . . . 111
4.17 Constraints on Ida & Lin (2004) core accretion models . . . . . . . . 113
5.1
5.2
5.3
5.4
5.5
5.16
5.17
5.18
5.19
Target stars considered in this chapter . . . . . . . . . . . . . . . . . 134
Comparing the Baraffe and Burrows models of planet luminosities 136
Comparing the Baraffe and Fortney models of planet luminosities . 138
Upper limit on planet fraction from all stars, using the Baraffe models143
Upper limit on planet fraction from all stars, using the Burrows
models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Upper limit on planet fraction from all stars, using the Fortney
models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Constraints on the semi-major axis distribution of exoplanets . . . . 150
Limits on the power law index and upper cut-off of the semi-major
axis distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Upper limit on planet fraction from M stars . . . . . . . . . . . . . . 154
Upper limit on planet fraction from FGK stars . . . . . . . . . . . . 155
The Johnson mass correction . . . . . . . . . . . . . . . . . . . . . . . 156
Upper limit on planet fraction from all stars, mass-corrected to 1
Solar mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Upper limit on planet fraction from all stars, mass-corrected to 0.5
Solar masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Limits on the semi-major axis distribution, with the mass correction applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Limits on power law cut-off and index with the mass correction
applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Upper limit on the Ida and Lin (2004) core accretion models . . . . 165
Completeness to planets using Baraffe et al. (2003) models . . . . . 173
Completeness to planets using Burrows et al. (2003) models . . . . 174
Completeness to planets using Fortney et al. (2008) models . . . . . 175
6.1
6.2
6.3
6.4
6.5
6.6
6.7
SDI imaging with NICI . . . . . . . . . . . . . . . . . . . . .
The assumed NICI contrast curve . . . . . . . . . . . . . . .
Number of observable stars as a function of exposure time
60 AU fixed survey make-up . . . . . . . . . . . . . . . . .
60 AU scaled survey make-up . . . . . . . . . . . . . . . . .
30 AU scaled survey make-up . . . . . . . . . . . . . . . . .
30 AU fixed survey make-up . . . . . . . . . . . . . . . . .
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
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11
6.22
6.23
F IGURES — Continued
60 AU scaled stellar parameters, Burrows Models . . . . . . . . . .
60 AU scaled stellar parameters, Fortney models . . . . . . . . . . .
30 AU fixed stellar parameters, Burrows models . . . . . . . . . . .
30 AU fixed stellar parameters, Burrows models . . . . . . . . . . .
60 AU scaled curve of growth . . . . . . . . . . . . . . . . . . . . . .
30 AU fixed curve of growth . . . . . . . . . . . . . . . . . . . . . . .
Spectral type versus probability, 60 AU scaled . . . . . . . . . . . .
Spectral type versus probability, 30 AU fixed . . . . . . . . . . . . .
Distance versus probability, 30 AU fixed . . . . . . . . . . . . . . . .
Age versus probability, 30 AU fixed . . . . . . . . . . . . . . . . . .
Histograms of detectable planets from the simulations, Burrows 60
AU scaled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Histograms of detectable planets from the simulations, Fortney 60
AU scaled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Histograms of detectable planets from the simulations, Burrows 30
AU fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Histograms of detectable planets from the simulations, Fortney 30
AU fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Detectable planets, Burrows 30 AU fixed . . . . . . . . . . . . . . . .
Detectable planets, Fortney 30 AU fixed . . . . . . . . . . . . . . . .
7.1
7.2
7.3
The GPI Contrast Curve . . . . . . . . . . . . . . . . . . . . . . . . . 222
Simulated GMT sensitivity to planets for a young A star . . . . . . 225
Simulated GMT sensitivity to planets for an intermediate age G star 226
L IST
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
6.21
OF
194
195
196
197
199
200
201
203
204
205
207
208
209
210
212
213
12
L IST
OF
TABLES
2.1
2.2
2.3
Astrometry of AB Dor C . . . . . . . . . . . . . . . . . . . . . . . . .
Our Improved Parameters for the Reflex Motion of AB Dor A. . . .
Improved Astrometry of AB Dor C . . . . . . . . . . . . . . . . . . .
4.1
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Target Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Age Determination for Target Stars . . . . . . . . . . . . . . . . . . . 82
Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
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5.3
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Target Stars . . . . . . . . . . . . . .
Age Determination for Target Stars
Summary of Results. . . . . . . . .
Binaries . . . . . . . . . . . . . . . .
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13
A BSTRACT
I present my experiences designing, conducting, and analyzing the results
from direct imaging surveys for extrasolar giant planets. Using the young, lowmass star AB Dor C, I show that models for low-mass stars and brown dwarfs
at young ages are good representations of reality. I discuss the design of the
Simultaneous Differential Imaging survey, and how Monte Carlo simulations
of giant planet populations allow for the design of imaging surveys, including
the choice of target list, that maximizes the expected yield of extrasolar planets. With the conclusion of the SDI survey, I examine how its null result for
planets sets constraints on the allowable populations of long-period exoplanets,
finding that fewer than 8% of sun-like stars can have planets more massive than
4MJup between 20 and 100 AU, at 68% confidence. When I include null results
from other direct imaging surveys, these constraints are further strengthened: at
68% confidence, fewer than 20% of sun-like stars can have planets more massive than 4MJup , at orbital semi-major axes between 8.1 and 911 AU. Even when
applying the mass scaling of Johnson et al. (2007), and the “cold start” planet
luminosity models of Fortney et al. (2008), the results remain consistent: giant
planets are rare at large separations around sun-like stars. I explain how these
constraints and planet simulations were used to design the Gemini South NICI
Planet-Finding Campaign survey and target list, in order to maximize the chance
of NICI detecting a planet, and so giving the campaign the greatest ability to
strongly constrain populations of extrasolar giant planets, even in the case of a
null result. Finally, I discuss future directions for direct imaging planet searches,
and the steps needed to move from existing surveys to a truly unified distribution
of extrasolar planet populations.
14
C HAPTER 1
INTRODUCTION TO DIRECT IMAGING SURVEYS FOR EXTRASOLAR
PLANETS
Directly imaging giant extrasolar planets allows us to study a regime of planet
populations that can’t be accessed by any other method, and provides the opportunity for using spectroscopy to understand the composition and structure of
these planets. With advances in adaptive optics at large telescopes, and improved
observing and data reduction techniques, surveys to directly image giant planets
have become increasingly sensitive. Despite this gain in sensitivity, discoveries of
imaged giant planets have been quite sparse, especially given the large amount of
telescope time dedicated to surveys. Nevertheless, the discoveries made to date
have challenged existing theories of planet formation and structure, and further
study of these and future planets will provide insight into the mechanisms by
which planetary systems form and evolve.
1.1 Extrasolar Planets
The study of planets and planetary systems around other stars is of great interest
not only to astronomers, but the public at large. By discovering and studying
planets that orbit nearby stars, we can understand how our own solar system,
and the Earth, fit into the context of planetary systems throughout the galaxy.
The ultimate goal we are pushing toward is to find habitable planets, planets
that can support life, and perhaps even detecting signs of life on those planets.
Whether or not we are alone in the universe is a fundamental question, one that
astronomers may finally be able to answer definitively in the coming decades.
While the technology required to determine if the atmospheres of extraso-
15
lar earth-like planets contain markers of life is still decades away, likely requiring a large-scale space telescope designed for the specific purpose of detecting
and characterizing Earth-like planets, astronomers today have vastly superior
knowledge of other planetary systems, compared to what was known just a few
decades ago. In fact, the first extrasolar around a sun-like star was not discovered
until 1995, and since then the field of studying extrasolar planets has rapidly expanded. We are now able to not only catalog extrasolar planets around nearby
stars, but also to probe the mechanisms by which planetary systems form and
evolve. We have a preliminary picture of how giant planets form and migrate
over time, and we are moving toward understanding the conditions required for
Earth-like planets to form and survive around other stars.
By studying and characterizing extrasolar planetary systems, we will be able
to better understand how planets form, how the systems evolve over time, and
what is the typical architecture of planetary systems around other stars. By understanding the mechanisms of planet formation and how systems evolve over
time, we can better explain how these processes took place in our own Solar system, and so understand how our own planet fits into context with planets around
other stars.
1.2 How Direct Imaging Fits into Exoplanet Science
The radial velocity (RV) technique has been key in driving exoplanet science over
the last sixteen years. Since the discovery of a planet orbiting 51 Peg (Mayor &
Queloz, 1995) in 1995, it has been RV detections of planets that have led the way
in the number of known extrasolar planets. In the last few years, the discovery of
planets by transit has become more efficient, and the Kepler spacecraft is finding
dozens of potential planets, which are currently awaiting confirmation (Borucki
16
Figure 1.1 The distribution of radial velocity planets (purple histogram), compared to limits on planet populations from direct imaging of sun-like stars, assuming a power-law fit to the semi-major axis distribution of giant planets (see
Chapter 5). The gap in between 2.5 and 23 AU remains to be probed, and direct
imaging is well-suited to fill that gap.
17
et al., 2011). There has also been an increase in the detections coming from microlensing, with 10 planets confirmed to date (Gaudi, 2010). In terms of number
of planets, direct imaging has historically lagged behind: as of the beginning of
2008, there was only one confirmed planetary-mass companion discovered by direct imaging, 2MASS 1207b (Chauvin et al., 2004). Since then, there has been a
flurry of exciting discoveries of directly imaged planets around A stars, including
four planets around HR 8799 (Marois et al., 2010), and single planets around Fomalhaut and Beta Pic (Kalas et al., 2008; Lagrange et al., 2009), and a very young
planet around the solar-type star 1RXS J160929.1 - 210524 (Lafrenière et al., 2010).
Direct imaging represents a complementary detection mechanism to radial
velocity, transits, and microlensing, probing a regime of planet properties that
cannot be reached by other methods. While RV and transit methods become less
sensitive to planets as orbital radius increases, and microlensing is most sensitive to planets in intermediate separations (a few AU), direct imaging can detect
planets at very large separations. And while there has been increased success at
obtaining transmission (very low resolution) spectra of transiting planets, direct
imaging allows for the study of planets “in isolation,” where their structure has
been allowed to evolve on its own, without being roasted in close proximity to
the parent star. In Chapter 5, I will show how null results from current direct
imaging surveys, when combined with a power-law fit to known distributions of
radial velocity planets, suggest that planets should not be found beyond 23 AU
(as imaged planets are found beyond this limit, clearly such a simple fit is not
adequate to describe planets at all separations and around all masses of stellar
hosts). Radial velocity surveys, meanwhile, are generally thought to be complete
out to a few AU (the volume-limited sample of Fischer & Valenti (2005) was complete to 2.5 AU), so that the two techniques, pushing from opposite directions,
18
are coming close to together providing a unified picture of planet populations at
all separations (see Fig. 1.1). Since moving outward with radial velocity requires
a time baseline of at least one orbital period, it will be decades before RV alone
can close this gap. Direct imaging, then, is the ideal solution to move these limits
closer, until there is overlap and we truly have a complete picture of giant planet
populations across all orbital periods.
1.3 Spectroscopy of Giant Planets
One of the great benefits of directly imaging extrasolar planets is the ability to
obtain spectra of these objects and study their atmospheres. Fig. 1.2 shows an
image of the four planets circling the A star HR 8799; just by making an image
like this we can study the colors of these objects, and careful observations can
provide spectra. The first spectra of these objects suggest much redder, dustier
atmospheres than predicted by models of planetary mass objects of these ages
(Marois et al., 2010; Patience et al., 2010).
Currie et al. (2011) have examined photometry of the HR 8799 planets from 1
to 5 µm and have found that in order to fit the observed properties of these planets, atmospheric models must include thicker cloud decks than have been used
to fit brown dwarf spectra. Patience et al. (2010), studying high resolution IFU
spectra of 2MASS 1207b, have similarly concluded that existing models cannot
fully reproduce the observed features of this planet. Additionally, Skemer et al.
(2011) have determined that dust external to 2MASS 1207b cannot be the culprit
in explaining this mismatch, and instead this must be an intrinsic property of the
planet itself.
19
Figure 1.2 The HR 8799 planetary system, showing the orbits of the four planets
detected to date. By being able to spatially separate the light of the host star from
the light of the planet, it is possible to study in detail the atmospheres of these
objects. Figure from Marois et al. (2010).
20
1.4 Testing Models of Planetary Atmospheres and Formation Mechanisms
Both the preparation and analysis of direct imaging surveys require the heavy use
of theoretical models in order to convert between observed magnitudes and spectral features of planets and masses. As we have seen in the case of the HR 8799
planets, however, these models need substantial adjustment when compared to
data from an actual imaged planet. This is the power of directly imaging planets:
that these models of planet structure and atmospheres can be tested against actual planets. These newly refined models can then be used to inform future direct
imaging surveys, and so theory and observation can move forward together. In
Chapter 2, I describe my experience using the low-mass star AB Dor C to calibrate
theoretical atmospheric models at young ages and low masses.
Since 2003, there have been two sets of atmospheric models of planets used
in the direct imaging community, the models of Burrows et al. (2003) and Baraffe
et al. (2003). These two models provide similar predictions for near IR magnitude
of planets as a function of mass and age (e.g., Fig. 5.2). In 2008, a new set of models was produced by Fortney et al. (2008), which were directly tied to the core accretion scenario of planet formation. These new models predicted systematically
fainter planets, especially at the youngest ages, as shown in Fig. 5.3. The main
difference in the physics that goes into each model is the origin of the planets:
the Burrows et al. (2003) and Baraffe et al. (2003) models represent the “hot start”
assumption, where planets begin hot and bright at very young ages (∼1 Myr).
Fortney et al. (2008) represent the “cold start” scenario, with the post-accretion
planets being relatively cool and faint, and then passively evolving forward from
there.
In a way, determining which, if either, of these two model sets is correct will
answer a key question about planet formation, solving the question of what is
21
the initial condition for young, giant planets. Another possibility is that that
there are two mechanisms for forming giant planets, core accretion (Ida & Lin,
2004) and gravitational instability (Boss, 2007), and that each is responsible for
some fraction of the extrasolar planets that are observed. If this is the case, it
would certainly be possible that the two formation scenarios would lead to separate relations between age, planet mass, and near infrared (NIR) flux. Analyses
by Marois et al. (2010), Close (2010), and Currie et al. (2011) of the HR 8799 system
show that neither camp of existing formation models adequately explains the observed properties of these planets. It will be through future discoveries that we
will be able to learn if this is the norm for young, giant extrasolar planets, or if
multiple sets of theoretical models, corresponding to different histories of formation and evolution, are required to fully reproduce the properties of different
planets.
1.5 Direct Imaging Surveys as a Way to Set Constraints on Extrasolar Planet
Populations
By conducting surveys to directly image extrasolar giant planets, we are probing areas of exoplanet parameter space that have been untouched by other techniques. Giant planets at large separations are best reached with direct imaging,
and so the most sensitive direct imaging surveys will be able to set constraints on
the behavior of planet populations at longer periods. Cumming et al. (2008) have
fit power laws to the distributions of planet mass and orbital period based on RV
detections for periods less than a few years. But direct imaging can determine if
those distributions hold at larger separations, and if there is an upper cut-off to
the semi-major axis distribution (see Chapters 5 and 4 for further details).
The semi-major axis distribution of giant planets will greatly inform models
22
of planet formation and evolution. The discovery of Hot Jupiters (planets the
mass of Jupiter or larger, but in orbits with periods of a few weeks or less) by
RV techniques was not predicted by any existing models; now modelers must account for the inward migration of planets in order to accurately describe observed
planet populations. Similarly, if it is true that there are multiple mechanisms for
planet formation (as we hypothesize in Section 1.4) that operate at different orbital radii, this should be detectable by examining the frequency of planets as a
function of separations. In short, while there are known questions that can be answered with a complete distribution of exoplanets across all orbital separations,
past experience has taught us to be on the lookout for new discoveries with new
data, and the outer parts of extrasolar planetary systems are the next frontier to
explore. One example of this is the discovery of a planet orbiting the star β Pic
(Lagrange et al., 2009), a star that is well-known for hosting a large debris disk.
The presence of a debris disk is associated with the process of planet formation,
and so possibly a clue that a system contains giant planets. Indeed, the other
two A stars with imaged planets, Fomalhaut and HR 8799, were also known to
host debris disks before the discovery of their planets (Kalas et al., 2008; Marois
et al., 2008). Whether the presence of a debris disk is a solid marker of giant planets will be borne out by further study, but it is an intriguing suggestion given
current knowledge of wide-separation giant planets.
In Chapters 3 and 6, I discuss the construction of surveys to directly image
extrasolar giant planets, using the metric of expected number of planets detected.
This has the dual effect of maximizing the possibility of detecting a planet (given
the best assumptions for populations of giant planets at the time the survey is
being planned), and setting up the survey in such a way that even a null result is
of great scientific interest, by placing strong constraints on the models of planet
23
populations that informed the survey design (Chapters 5 and 4 discuss how null
results can be used to maximal advantage).
Maximizing the chances of detecting planets is paramount, as null results,
while setting strong constraints on allowable models of planet populations, have
limited ability to differentiate between different models of planet populations
(and so theories of formation and evolution). For a given model (for example, the
extension of radial velocity power law distributions to large separations, with no
spectral type dependence on planet distributions or frequency), a null result can
set limits on the parameters of that model (in this example, at 68% confidence,
giant planets should not be found past 23 AU). And this can be done for any general type of model. But determining which model correctly describes planet populations at large separations requires actual detections. Additionally, the wealth
of knowledge that can be gained by taking spectra of even a handful of directly
imaged planets is strong motivation to construct surveys with the greatest likelihood of discovering plants, and in Chapter 7 I discuss future directions for direct
imaging surveys. A unified distribution of planet populations is the ultimate
goal, and direct imaging surveys are the tool we will use to reach it. At this point,
it is just a matter of determining the optimal survey design for future surveys to
maximize the science we get from this effort.
24
C HAPTER 2
AB DORADUS C: AGE, SPECTRAL TYPE, ORBIT, AND COMPARISON
TO EVOLUTIONARY MODELS
We expand upon the results of Close et al. (2005) regarding the young, low-mass
object AB Dor C and its role as a calibration point for theoretical tracks. We
present an improved spectral reduction of the VLT NACO spectrum of AB Dor C,
and a new orbital solution with two additional epochs. Our improved reduction
suggests a confirmation of our spectral type of M8 (±1) and mass of 0.090 ±0.003
M⊙ for AB Dor C.
An analysis of a new spectrum, taken with the SINFONI instrument at the
VLT, produces a better-quality spectrum that correctly preserves the continuum
shape of AB Dor C. Analyzing this new spectrum leads us to significantly revise
the spectral type of M8 suggested by the VLT NACO spectrum, and instead assign an earlier spectral type of M5.5 ±1. This places AB Dor C in good agreement
with the DUSTY models. The significant change in spectral type from the new
spectrum points to the superiority of IFU spectra over AO slit spectroscopy in
determining a accurate spectral type of a high contrast close companion.
The material in this Chapter was first published in Nielsen et al. (2005), Close
et al. (2007a), and Thatte et al. (2007).
2.1 Introduction
The study of young, low-mass objects has been yielding increasingly fruitful science, yet the field remains dependent on evolutionary models to properly interpret the data that are collected from these objects. In particular, mass, while a
fundamental property, is very rarely measured directly, and instead must be in-
25
ferred from theoretical tracks (e.g., Burrows et al. (2003), Chabrier et al. (2000)).
It is thus of great interest to find calibrating objects that can link a dynamically
measured mass with observables such as NIR (1-2 µm) fluxes and spectral types.
In our previous work (Close et al., 2005), we reported the direct detection of
the low-mass companion to the young star AB Dor A, along with measurements
of the JHKs fluxes, spectral type, and dynamically determined mass of AB Dor
C. Upon comparing these results with the predictions of Chabrier et al. (2000),
we found the models to be systematically over-predicting the fluxes and temperature of AB Dor C, given an age of the system of 50 Myr. Put another way, the
model masses seem to be underestimating the mass of a low-mass object given its
age, NIR fluxes, and spectral type. Since the publication of these results, another
calibrating object has been reported by Reiners et al. (2005): USco CTIO 5. While
this equal-mass binary is younger (∼8 Myr) and more massive (total mass ≥0.64
M⊙ ) than AB Dor C, Reiners et al. (2005) find the same trend of models underpredicting masses based simply on photometric and spectroscopic data applied
to the HR diagram. A similar trend for such masses was previously noted by Hillenbrand & White (2004). Moreover, this trend has been theoretically predicted
for higher masses by Mohanty et al. (2004), and by Marley et al. (2007) for planetary masses.
In this Chapter, we seek to expand on our earlier results from Close et al.
(2005), using an improved spectral reduction and a more robust determination
of the spectral type. We also present an improved orbital fit based on additional
astrometric data, as well as address concerns raised by Luhman et al. (2005) regarding the age of the AB Dor system.
26
2.2 An Improved Spectral Reduction
As described in Close et al. (2005), in February 2004 we obtained 20 minutes of
K-band spectra using the Very Large Telescope (VLT), following our initial detection of AB Dor C. We used the R ≈ 1200-1500 (2-2.5 µm) grism and the 0.027”
pixel camera of NACO (see Lenzen et al. (2004)), aligning the 0.086” slit along
the centers of both AB Dor A and C. The observations themselves consisted of
eight deep exposures, intentionally saturating the inner pixels of the spectral PSF
(point-spread function), with the two objects (A and C) nodded along the slit
between exposures. An additional eight exposures were obtained with a 180◦ rotation of the derotator, flipping the relative positions of A and C. The FWHM of
the spectral PSF was approximately 3 pixels.
Given our measured separation of A and C of 0.156” (5.78 pixels), and a flux
ratio at Ks of 80, the signal from AB Dor C lies beneath the wings of the PSF of
A. Relying on the relative stability of the NACO PSF, we subtracted a 0◦ image
from one at 180◦ , removing the signal from A while leaving a positive and negative spectrum of AB Dor C, which can then be extracted easily using the standard
Image Reduction and Analysis Facility (IRAF) routines. This aligning of the PSFs
is complicated by sub-pixel variations in the order position and orientation from
image to image, as well as by variations in the total flux across different exposures.
To prepare for this subtraction, the first step is to align the 0◦ and 180◦ images.
This pair of images is considered one dispersion pixel at a time (that is, we consider the 1024 spatial pixels along the chip corresponding to a single wavelength
element), where one image undergoes a series of sub-pixel shifts before the two
one-dimensional segments are subtracted. A series of reference pixels between
9 and 12 pixels (0.24” and 0.32”) from the center of the PSF is chosen so as to
27
avoid the saturated central pixels, and any signal from AB Dor C (which would
be positive in the 0◦ images and negative in the 180◦ images, and so would not
produce an accurate alignment). The minimum variance in these reference pixels
after subtraction is taken to correspond to the best shift. This process is repeated
for each of the 1024 dispersion pixels, a second-order polynomial (polynomial
order chosen based on visually inspecting the 1024 individual shift offsets) is fit
to these 1024 “best offsets”, and this fit is used to prepare the final subtraction.
We continue this procedure iteratively with various values of a global flux
scaling of one of the two images, again minimizing the variance in the reference
pixels to find the best fit. An example of this subtraction of a 0◦ and 180◦ image
is shown in Figure 2.1. Each point represents a sum across all 1024 dispersion
pixels corresponding to a given spatial pixel, with the dashed lines indicating the
location of AB Dor C. The inner, saturated pixels show a large amount of noise
as would be expected, but at the position of AB Dor C are obvious negative and
positive peaks. We repeat these steps for each possible pairing of the eight 0◦
and eight 180◦ spectra, eliminating pairs where the routine did not converge, and
choosing the best subtraction; this yields a total of 13 spectra (out of 16 possible),
which are then combined.
We note that while there are many pairs where this process fails to converge,
we never see a “false-positive” signal. That is, while for many of our spectra we
see a positive peak to the right and a negative peak to the left, as seen in Figure 2.1, not even once (out of 64 trials) do we see a positive peak on the left or
a negative peak on the right at the position of AB Dor A. This leaves us confident that we have extracted the signal from AB Dor C, rather than spurious light.
Additionally, these 13 independent extractions of the spectra are all qualitatively
similar; each appears as a late-M spectrum, clearly distinguishable from the spec-
28
Figure 2.1 An example of a subtraction of a 0◦ image from a 180◦ , with each spatial
pixel along the x-axis representing a sum along the dispersion direction. The
expected positions of AB Dor C on either side are marked with dashed lines; the
clear positive and negative signals at this location indicate a good subtraction
of AB Dor A. We note there is still some random noise in this subtraction, as
the positive and negative peaks of AB Dor C have different amplitudes (at the
∼12% level), which we mitigate by median-combining spectra extracted from
multiple images. The spectrum is extracted from both the positive peak on the
right, as well as the negative peak on the left. The marked central region (where
the data are not plotted) indicate the saturated pixels which were ignored during
the reduction.
29
trum of AB Dor A.
Observations of a standard star (HIP 24153, G3V) taken within a half hour of
the AB Dor images are used to remove telluric lines, and a modified solar spectrum compensates for stellar features from the standard (Maiolino et al., 1996).
The final spectrum is shown plotted against two young, late-M templates in
Figures 2.2 and 2.3. Since we were unable to preserve the continuum of AB Dor C
through our data reduction, we simply remove the continuum from our spectrum
as well as that of the template (using polynomial fits of the same order). Judging by the depth of the CO breaks, and the strength of the Na I line at 2.21 µm,
these templates constrain the spectral type of AB Dor C between M7 and M9.5 at
the 1σ level, as was previously reported in Close et al. (2005). Additionally, we
found four features in the spectrum that do not seem consistent with any late-M.
We compared our unsaturated spectrum of AB Dor A to other K1 spectra, and
finding these features present in A as well, we determined these lines to be telluric features that were not fully removed, hence we have not plotted these small
segments of the spectra.
We note in Figures 2.2 and 2.3 that while both AB Dor A and C show a Na
I line at 2.21 µm and CO features between 2.3 and 2.4 µm, AB Dor A shows a
strong 2.26 µm Ca I triplet absorption feature while AB Dor C does not. Similarly,
there is no correlation between the strength of the Mg I line (2.28 µm) or the
Al I doublet (2.11 µm) between A and C, as would occur if our spectrum were
dominated by spurious light from AB Dor A. Comparing the line strengths, we
find the equivalent width of the Na I 2.21 µm doublet in C to be ∼1.5 times that
of A. Meanwhile, the Ca I 2.26 µm feature equivalent width for C is less than 5%
of A. This leaves us confident that the amount of contamination from AB Dor A
is ≤5%, with similar results obtained from analysis of the Al I doublet.
30
Figure 2.2 The spectrum of AB Dor C (upper solid line) shown against that of
USco 100 (dashed line), a young (∼8 Myr) M7 (Gorlova et al. 2003), with the
continuum of both objects removed. Features arising from an incomplete removal
of telluric lines are marked, and are not plotted in the AB Dor C spectrum. The
strength of C’s sodium line at 2.21 µm and the depth of the H2 O absorption and
the first CO break at 2.3 µm suggest AB Dor C is cooler than an M7, at the 1σ level
of the observational noise, as indicated in the figure (this noise, 0.015, was found
by taking the standard deviation of the AB Dor C spectrum between 2.13 and
2.18 µm, a featureless section of spectrum between the Al I and Na I doublets).
The spectrum of AB Dor A (which was used as a reference for poorly-removed
telluric features) is also shown at the bottom of the plot.
31
Figure 2.3 The spectrum of AB Dor C, this time plotted with GSC 8047-0232, a
young (∼ 30 Myr) M9.5 (Chauvin et al., 2005). The sodium and CO features of
the template now appear cooler than those of AB Dor C, bounding the spectral
type between M7 and and M9.5, at the 1σ level.
32
2.3 Improved Orbit
Our earlier paper (Close et al., 2005) was based on observations conducted at the
VLT in February of 2004. Since this work was published, we have reduced additional Simultaneous Differential Imaging (SDI, see Lenzen et al. (2004)) data from
September and November of 2004. While data through the narrow-band SDI
filters do not provide us with any improved photometric information (beyond
confirmation that between AB Dor A and C, ∆H = 5.20), these images do give
us additional astrometric data points, allowing us to refine the orbit. To measure
positions, we have replaced the saturated pixels of AB Dor A using unsaturated
acquisition images. We then did standard PSF fitting to find the relative offsets
between A and C in the pre-subtracted SDI images. As acquisition images from
NACO SDI datasets are obtained within 10 minutes of the science data, using
the same observing mode but a shorter exposure time, they provide an accurate measure of the shape of the peak of the PSF. We have used this method to
measure the photometry of AB Dor Ba/Bb, finding agreement with the 2MASS
flux ration between AB Dor A and Ba/Bb at the 1% level, further validating this
method. Since each SDI exposure gives us four images, we did astrometry on
each of these four images of A and C (which gave us an estimate of the accuracy,
∼5mas, though varying between the three observational epochs), then averaged
the results. Lenzen et al. (2004) has used observations of binaries to measure the
NACO SDI platescale to better than 0.1% accuracy (much smaller than the 5 mas
/ 218 mas = 2% error we measure for AB Dor C’s position), so we adopt our measurement precision as the accuracy of the position of AB Dor C. We present these
measurements in Table 2.1. In Figure 2.4 we show the subtracted SDI images at
each epoch where we measured the position of AB Dor C with respect to A.
We fit our three VLT SDI data points for the relative position between AB
33
Figure 2.4 The different epochs of AB Dor C measured during 2004 with the VLT
SDI device. Each of the numbered panels shows an individual epoch of SDI observations, with images at position angles of 0◦ and 33◦ subtracted from each
other, showing a positive and negative signal from AB Dor C. The inner pixels
of AB Dor A have been intentionally saturated, and have been removed from the
image. The orbital motion of the companion can clearly be seen over this span of
time. The bottom-right panel shows these locations against a plot of the full orbit of AB Dor C. The 11 additional VLBI/Hipparchos measurements of the reflex
motion of AB Dor A (which went into finding the orbital solution) are not shown
on this plot (Close et al., 2005).
34
Figure 2.5 Detail of the reflex orbit of AB Dor A for the time period of our SDI
observations. The previous orbit (Close et al., 2005) is also shown.
35
Table 2.1 Astrometry from our three epochs of SDI observations, with the offset of
AB Dor C given with respect to AB Dor A. Errors in position are 10, 5, and 3 mas
in the first, second, and third epochs, respectively. For astrometric measurements
of AB Dor A at previous epochs, see Guirado et al. (1997).
Epoch
RA Offset (mas)
Dec offset (mas)
Position Angle
2004.096
125
-94
127
2004.825
106
-191
151
2004.877
106
-192
151.1
Dor A and C along with the existing VLBI/Hipparcos astrometry for AB Dor
A (Guirado et al., 1997) to obtain an improved orbit of the reflex motion of AB
Dor A. For this fit, we followed the procedure described in Guirado et al. (2006).
The new orbital elements are shown in Table 2.2, and are mostly similar to those
published in Close et al. 2005. The two orbits are compared with respect to the
three 2004 epochs of SDI observations in Figure 2.5.
The most immediate consequence of our new orbital fit is that the mass of AB
Dor C remains at 0.090 M⊙ . As reported in Guirado et al. (2006), we notice that
the error bars shrink from 0.005 M⊙ to 0.003 M⊙ . This confidence with which
we know the mass of AB Dor C makes it an ideal object for calibrating theoretical
evolutionary tracks.
2.4 Discussion
2.4.1 Spectral Type
Using our new spectrum, we attempt to refine the determination of the spectral
type of AB Dor C. Rather than use field objects as our standards (as we did in
Close et al. (2005)), we choose young objects (with lower surface gravities) to
36
Table 2.2 Our Improved Parameters for the Reflex Motion of AB Dor A.
Parameter
Value
Error
Units
Period
11.74
0.07
years
Semi-Major Axis
0.0319
0.0008
“
Semi-Major Axis
0.476
0.012
AU
Eccentricity
0.61
0.03
Inclination
66
2
deg.
Argument of Periastron
110
3
deg.
Position Angle of Node
133
2
deg.
Epoch of Periastron Passage
1991.92
0.03
years
Mass of AB Dor C
0.090
0.003
M⊙
constrain the spectral type. Figure 2.6 shows our AB Dor C spectrum plotted
against a variety of young, late-M spectra (WL 14, USco 67, USco 66, and USco
100 from Gorlova et al. (2003), GSC 8047-0232 from Chauvin et al. (2005)). Again,
since AB Dor C lacks a continuum, we have removed the continuum of all the
objects (using the same order of polynomial fit) for comparison purposes. Trends
across the sequence are clearly visible: as we move to later spectral types, the
strengths of the Na line, CO breaks, and H2 O absorption increases, while the Ca
line weakens. For all these features, AB Dor C seems best bound between the
M9.5 and M7 templates at 1σ, agreeing with the J-Ks ∼ 1.3 ± 0.4 magnitude color
reported in Close et al. (2005).
All of the templates used in Figure 2.6 are significantly younger than AB Dor
C. To properly bound the spectral type, we consider field objects, as we did in
Close et al. (2005). Figure 2.7 again shows AB Dor C, now with templates of
higher surface gravity (spectra from Cushing et al. (2005); since these spectra
37
Figure 2.6 The spectrum of AB Dor C shown against a number of young (∼10
Myr), low-surface gravity objects. The features seem to be bound between the
M7 and M9.5 templates.
38
were taken at higher resolution, we have smoothed them to match the resolution
of AB Dor C). The spectra no longer fit as nicely (especially the shapes of the CO
features), but as before, the spectrum seems to fit best in the sequence between
an M7 and an M9.
2.4.2 The Age of AB Dor
In Close et al. (2005) it was argued that due to the excess luminosity of AB Dor
A and C compared to the Pleiades, and A’s large Li equivalent width and very
fast rotation, that the age of the system was 30-100 Myr. An age of 50 (-20, +50)
Myr was adopted, which was consistent with the 50 Myr published age of the AB
Dor moving group (Zuckerman et al., 2004). Recently Luhman et al. (2005) have
suggested a slightly older age of 70-150 Myr. However, as Luhman et al. (2005)
note, the AB Dor moving group is systematically over-luminous compared to the
Pleiades (age 100-120 Myr) by ∼0.1 magnitudes in MKs vs. V-Ks plots (see their
Figure 1).
We have found similar results with a near-infrared color magnitude diagram,
as seen in Figure 2.8. While the two groups of stars appear similar for the earlytype members (where the isochrones overlap), beyond a color of J-Ks ∼0.4, the
lower main sequence of the AB Dor Moving group appears to be above that of
the Pleiades by about 0.15 magnitudes. We have run a series of simulations that
suggest that only ∼10% of the time would a group of Pleiades aged stars appear
0.15 magnitudes above the single-star locus as is observed for all the AB Dor
group members.
We note that a 0.15 magnitude offset from the Pleiades single star locus suggests a group age of ∼70 Myr from the Lyon group’s models (Baraffe et al., 1998).
We adopt an average age of 70 ± 30 Myr with 1σ error bars. Hence, there is a
∼10% chance that the AB Dor moving group is as old as the Pleiades based on
39
Figure 2.7 The spectrum of AB Dor C, this time plotted against field M dwarfs
(∼ 5 Gyr), with higher surface gravities. Again, a spectral type of M8±1 (1σ)
seems most consistent with our spectrum (we find the 1 subclass error from visual
inspection, noting that template spectra beyond this range are an increasingly
poor fit to our AB Dor C spectrum).
40
Figure 2.8 A NIR color-magnitude diagram of medium-mass members of the
Pleiades (compiled from the literature) and the AB Dor moving group (Zuckerman et al., 2004), with the theoretical isochrones of Baraffe et al. (1998). The offset
between the single star locus of the two groups redward of J-Ks ∼0.4 suggests a
younger age for the AB Dor moving group, closer to 70 Myr.
41
these color-magnitude diagrams.
Luhman et al. (2005) conclude that their increase in the age of the system (from
50 to 120 Myr) implies that the luminosity is correctly predicted by the models.
But, as we will see in Section 2.4.3, even if the luminosity is close to the predicted
value at an age of 100 Myr and 0.09 M⊙ , there is still a very large error in the
temperature. Hence, the models will overestimate the temperature (or underestimate the mass) of young, low-mass objects in the HR diagram regardless of the
70 or 120 Myr age of AB Dor.
2.4.3 HR Diagram and Evolutionary Models
In order to further compare our observations of AB Dor C with the theoretical
models, we consider an HR diagram with our measured values and the DUSTY
models. Using our spectral type of M8 and the absolute Ks from Close et al.
(2005), we can derive an effective temperature and bolometric luminosity for AB
Dor C. We plot AB Dor C in such an HR diagram in Figure 2.9, along with the
DUSTY tracks, AB Dor Ba/Bb, and low-mass members of the Pleiades. We compile Pleiades members from Martı́n et al. (2000), as well as from other sources in
the literature (Cluster identifications and spectral types from Briggs & Pye (2004),
Pinfield et al. (2003), Terndrup et al. (1999), Festin (1998), Martin et al. (1996), and
Ks-band fluxes from the 2MASS catalog) The bolometric luminosities and temperatures for all these objects (AB Dor Ba/Bb, C, and the Pleiades members) are
derived using Allen et al. (2003) and Luhman (1999) (dwarf scale), respectively.
As is seen in Figure 2.9, AB Dor C is overluminous, above the Pleiades sequence (as expected from a younger object, ∼70 Myr). We also show an arrow to
its position in the HR diagram predicted by the DUSTY models appropriate to its
age and mass.
It has been suggested that this overluminosity could be explained if AB Dor
42
Figure 2.9 HR diagram showing low-mass Pleiades objects from Martin et al.
2000 (open stars), other low-mass members of the Pleiades taken from the literature (open triangles), and AB Dor Ba/Bb (filled boxes). Both AB Dor Ba/Bb
and PPL 15 A/B are shown both as individual objects and as a single, blended
source (rings). The dotted vertical lines are iso-mass contours for the DUSTY
models (from left to right, 0.09, 0.07,0.05, and 0.04 M⊙ ), while the more horizontal, dashed lines are the DUSTY isochrones (top to bottom, 10, 50, 100, 120, 500,
1000 Myr). Note that the DUSTY models predict a 70-100 Myr object of 0.09 M⊙
should be ∼400 K hotter than observed. From the location of AB Dor C on the HR
diagram, one would derive a mass of 0.04 M⊙ , a factor of 2 underestimate in mass. As
the temperatures and luminosities of the Pleiades objects in this plot were determined in the same manner used for AB Dor C, and these Pleiades points mostly
fall along the appropriate 120 Myr DUSTY isochrone, we are assured that our
temperature scale and bolometric correction are reasonable. With 1σ error bars,
there is a ∼99% chance that the DUSTY models underestimate the mass of AB
Dor C from the HR diagram.
43
C were a close, unresolved binary (Martin private communication; Marois et al.
(2005)). Were this the case, AB Dor C would split into two points in Figure 2.9,
and move downward (as AB Dor Ba/Bb and PPL 15 do when deblended), appearing consistent with the Pleiades locus. While this interpretation cannot be
currently ruled out, we will address this issue in more depth in Close et al. (2006).
Briefly, however, we note that an AB Dor Ca/Cb system could only be stable with
a maximum aphelion distance of 0.138 AU (Hoenig private communication 2005),
else these proposed binary brown dwarfs would be disturbed by close passage
to the K1 star AB Dor A. Based on the Reid et al. (2002) survey for spectroscopic
binaries among low mass field dwarfs, we estimate the likelihood that AB Dor C
is a binary system with such a separation to be <5%.
Finally, we note an overall trend for young, low-mass objects where dynamic
masses have been measured, as shown in Figure 2.10. There is a global offset to
higher luminosities and temperatures for AB Dor C, USco CTIO 5, and Gl 569
Ba/Bb (in this last case, however, with an older object, the offset is within the
measurement errors). These results suggest that further work must be done to
bring theoretical evolutionary tracks in line with observations.
2.5 New Spectra of AB Dor C from VLT SINFONI
Since the publication of Nielsen et al. (2005), our group has obtained, reduced,
and analyzed high resolution Integral Field Spectroscopy of AB Dor C using SINFONI at the VLT (Thatte et al., 2007; Close et al., 2007a). These observations benefit both from being conducted at a phase in the AB Dor C orbit when the A-C
separation is larger (219 mas for the SINFONI data, compared to 155 mas for the
discovery epoch, when the NACO slit spectra were obtained), and also from the
superior capability of SINFONI to accurately measure spectra at high contrasts.
44
Figure 2.10 Again, an HR diagram with the Pleiades and certain other young,
low-mass objects, spanning a range of dynamical masses. The points with error
bars mark objects with dynamical masses, with the diagonal lines representing
the displacement from the measured luminosity and temperature to the values
predicted by the DUSTY and Next-Gen models. Upper Sco CTIO 5 (Reiners et al.,
2005), AB Dor C, and Gl 569 Ba/Bb (Zapatero Osorio et al., 2004) all show a
systematic trend where the measured HR diagram location is cooler and fainter
than the models’ predictions (though in the case of the older (300 Myr) Gl 569 B
system, this is within the stated 1σ uncertainties. Seen another way, the masses
predicted by the models are underestimates of the actual masses.
45
With this new spectra, we find a much earlier spectral type for AB Dor C (M5.5
±1), putting it in good agreement with the DUSTY models.
2.5.1 Further Astrometric Confirmation
In Nielsen et al. (2005), we published a new orbital fit to the AB Dor system,
which led to a more precise measurement of the mass of AB Dor C. This fit was
based on data taken through late 2004. Since then, we have obtained and reduced
an additional AB Dor dataset, an AO Ks image, from 2005.017, and our SINFONI
data of 2006.066 provides an even later measurement of the orbit. These new
datapoints essentially double the length of the time baseline for following the
orbit of AB Dor C. Table 2.3 shows the astrometric measurements from all five
epochs. In Fig. 2.11 and 2.12, we see that the orbit of Nielsen et al. (2005) is an
excellent fit to subsequent astrometric data, as each measurement is within 1 σ of
the predicted value. This analysis gives us even greater confidence in the validity
of the astrometrically determined mass of AB Dor C, and strengthens the use of
AB Dor C as a calibrator of theoretical evolution models for young, low-mass
stellar objects.
Table 2.3 Astrometry of AB Dor C, expanded out to all five epochs of measurement at the VLT. Final two epochs from Close et al. (2007a).
Epoch
Separation offset (mas)
Position Angle
2004.096
156
127
2004.825
218
151
2004.877
219
151.1
2005.0170
219
156
2006.0660
202
181
46
Figure 2.11 Orbit of AB Dor C, using the fit of Nielsen et al. (2005). The SINFONI astrometric measurement shows that AB Dor C is continuing to follow the
predicted path, giving us greater confidence in the mass estimate of the system.
Figure from Close et al. (2007a).
47
Figure 2.12 Orbit of AB Dor C, using the fit of Nielsen et al. (2005), now with RA
and Dec plotted against time. AB Dor C is clearly following the expected orbital
path. Figure from Close et al. (2007a).
48
2.5.2 Spectral Fit and a New Spectral Type
Taking the reduced spectra of AB Dor C (the observations and data reduction
are described in depth in Thatte et al. (2007)), we proceed to analyze this spectra
to determine the precise spectra type of this low-mass companion. With H and
K spectra, including an accurate continuum shape, we are in a much stronger
position to properly place AB Dor C in context among other low-mass templates.
In Fig. 2.13, we plot a smoothed version of the AB Dor C spectrum against
three young late-M objects in Upper Sco (Gorlova et al., 2003). The templates
are generally a good fit for AB Dor C, though we note that the low resolution
(and uncertainty in the extinction correction to these Upper Sco objects) makes
finding a precise spectral type difficult. In order to overcome this, we turn to the
IRTF standard spectra of Cushing et al. (2005). While these spectra are at higher
resolution, they represent field objects, which are a good deal older than AB Dor
C (∼5 Gyr, instead of 70 Myr). As a result, when comparing spectra we must be
careful to note the disparate surface gravity between templates and AB Dor C.
Looking at the template spectra of field objects, we note that the continuum
shape across H and K is best fit by the M5 and M6 templates, and the strength
of the CO breaks are consistent with and M4 to M5 spectral types. The best fit to
the H-band continuum seems to be the M5 template, while the Magnesium and
Aluminum lines redward of 1.65 µm are best fit to the M6 template. Combining
these data, we adopt a spectral type for AB Dor C of M5.5 ±1.
We note that this new spectral type is a significant departure from the spectral
type of M8 ±1 presented in Close et al. (2005) and Nielsen et al. (2005), and is
outside the 1σ error bars of the previous spectral type. We believe this mismatch
came about as a result of our previous work underestimating the systematic effect of finding a best-fit template spectrum without a preserved continuum. By
49
Figure 2.13 SINFONI spectra of AB Dor C plotted against young template spectra from Gorlova et al. (2003). The resolution of the Upper Sco objects is much
lower than our SINFONI spectra, so the AB Dor C spectrum has been Gaussian
smoothed to match the resolution of the templates. The shape of the continuum,
and the sodium doublet and carbon monoxide bands, are well-fit with a M5.5 M6 spectrum. Residuals are shown in the bottom of the plot, figure from Close
et al. (2007a).
50
Figure 2.14 K band spectra of AB Dor C, plotted against higher surface gravity
(older) late-M template spectra from the IRTF standard catalog (Cushing et al.,
2005). The continuum shape is best fit by the M5 and M6 templates, and the shape
of the CO breaks (which do not depend on surface gravity) are consistent with
an M4-5 (the sodium doublet is gravity-dependent, and so we do not consider it
here). Figure from Close et al. (2007a).
51
Figure 2.15 AB Dor C compared to the IRTF standards again, now with the H
band shown. The continuum shows a poor fit to the M3 and M7 templates, and a
better fit to the M5 and M6 spectra, as compared to the somewhat poorer quality
fit to the M4 template. Combining this with the K-band plot, and the comparison
to young standards, we converge on a spectral type of M5.5 ±1 for AB Dor C.
Figure from Close et al. (2007a).
52
relying only on spectral features, and then comparing our spectrum to only to
high-gravity templates, we not only arrived at an incorrect spectral type, but presented error bars on our measurement that were smaller than the actual uncertainty. With the SINFONI spectrum, and its preserved continuum, we considered
template spectra at ages (and so surface gravities) that bracket AB Dor C, and so
we believe this M5.5 ±1 spectral type and error region to be much more robust
than our previous estimate.
2.5.3 Validation of the DUSTY models
A spectral type of AB Dor C of M5.5 ±1 is an unexpected departure from the later
spectral type of M8 ±1 reported in Close et al. (2005) and Nielsen et al. (2005). The
disagreement between the parameters of AB Dor C and the predictions of the
DUSTY models hinged primarily on the age of the system (we adopted 50 Myr
in Close et al. (2005), later revised upward to 70 Myr in Nielsen et al. (2005)) and
the spectral type. With a revised spectral type of M5.5 and age of 70 Myr, AB Dor
C is behaving very much in line with the theoretical DUSTY models. Using the
spectral type conversion of Leggett et al. (1996), we find an effective temperature
for AB Dor C of 2925+170
−140 K.
In Fig. 2.16, we compare our new parameters for AB Dor C to the theoretical
DUSTY tracks of Baraffe et al. (1998). We also plot the analysis of the 2004 VLT
NACO data (the dataset used by us in Close et al. (2005) and Nielsen et al. (2005))
by Luhman & Potter (2006). We suggest a younger age for the AB Dor system
than Luhman & Potter (2006), but nevertheless both sets of analyses agree well
with the relevant DUSTY iso-mass contours. The DUSTY models still predict
brighter H and J luminosity than is observed, though we note that it is more
difficult to accurately measure high contrast photometry at J band, where the
Strehl is not as favorable as it is at longer wavelengths. In all, the NIR photometry
53
Figure 2.16 AB Dor C (solid square) compared to the theoretical DUSTY models
of Baraffe et al. (1998), and analysis of Luhman & Potter (2006) (open triangles).
The Tef f and Ks plots show much better agreement to the models than was found
in Close et al. (2005), though the H and J plots still show an underluminous AB
Dor C, compared to model predictions. Figure from Close et al. (2007a).
54
Figure 2.17 Comparison of AB Dor C to other low-mass objects with dynamical
mass measurements, and the DUSTY models. There is general agreement between the mass measurements and the predictions of the DUSTY models. Figure
from Close et al. (2007a).
and spectra of AB Dor C put it in good agreement with the predictions of the
DUSTY models.
Fig. 2.17 shows that in general, there is good agreement between the DUSTY
models and low mass objects with dynamical mass measurements. AB Dor C
follows a trend of the DUSTY models accurately predicting masses given the
position in the HR diagram, for brown dwarfs and low-mass stars. It is important to note, however, that such mass calibrators are much more rare at the
lowest mass and age regime. In particular, there are no calibrators of the mass
for self-luminous planetary-mass objects, so it is important to be careful when
55
using models in an area of parameter space where they have not been adequately
calibrated.
2.6 Acknowledgements
We thank Gael Chauvin for providing an electronic copy of the spectrum of GSC
8047-0232, and Nadja Gorlova for providing spectra of many young, low-mass
objects. We also thank the organizers of the ULMF conference for the chance to
present this work.
This publication makes use of data products from the Two micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared
Processing and Analysis Center/California Institute of Technology, funded by the
National Aeronautics and Space Administration and the National Science Foundation.
56
C HAPTER 3
DESIGNING DIRECT IMAGING SURVEYS THROUGH SIMULATIONS
OF EXTRASOLAR PLANET POPULATIONS
As direct imaging surveys are being designed and carried out to detect extrasolar planets around young, nearby stars it is important to carefully evaluate the
criteria for selection of target stars, as well as the predicted success of a given
system. We have developed a routine to simulate an ensemble of a large number
of planets around each potential target star, and to determine what fraction can
be reliably detected using a system’s predicted or observed sensitivity curve (the
maximum flux ratio between the parent star and a detectable planet as a function
of projected radius). Each planet has a randomly assigned semi-major axis, mass,
and eccentricity (following extrapolations of detected radial velocity planets), as
well as viewing angles and orbital phase. The orbital parameters give a projected
separation for each planet, while the mass is converted into a flux ratio in the appropriate bandpass of the detector using the models of Burrows et al. (2003); this
allows the simulated planets to be directly evaluated against the system’s sensitivity curve. Since this method requires basic parameters (age, distance, spectral
type, apparent magnitude) for each target star, a target list can be constructed that
maximizes the likelihood of detecting planets, or competing instrument designs
can be evaluated with respect to their predicted success for a given survey. We are
already employing this method to select targets for our Simultaneous Differential
Imaging surveys (Biller et al., 2004), now underway at the VLT and MMT.
This Chapter is based on material originally published in Nielsen et al. (2006).
57
3.1 Introduction
With the number of detected extrasolar planets continuing to climb well over one
hundred, astronomers are finally in a position to begin to characterize the process
of planet formation, as well as give statistical descriptions of planet populations
around nearby stars. A significant gap, however, exists in our knowledge for
planets with orbits beyond that of Jupiter: the widest orbit known for a confirmed
extrasolar planet is 6 AU, for 55 Cnc d (Marcy et al., 2002). Since this limit is set by
the time baseline of radial velocity surveys, this threshold will march out slowly;
it will take another 15 years to close an orbit equivalent to Saturn’s (9.5 AU).
Radial velocity detections of planets in this regime will be further hampered by
the fact that the amplitude of the velocity declines with the inverse square root of
the semi-major axis.
Direct imaging, then, serves as a completely complementary detection method
to radial velocity surveys, as it is most sensitive to planets with large separations
from their parent stars, with no real upper limit to detectable semi-major axes.
If the two techniques could be brought together at intermediate separations, we
will be able to start building up a complete picture of the distribution of planets.
Again, since radial velocity surveys are slow to move outward, direct imaging is
well-situated to close the gap.
SDI, or Simultaneous Differential Imaging, is a technique to achieve very high
contrast images at small angular separations. By obtaining images simultaneously through narrow-band filters centered at the 1.6 µm methane bandhead, we
can greatly attenuate speckle noise from the star, and achieve very high contrasts
for objects with a strong methane signature (most giant planets). We are currently
conducting a survey for planets around young, nearby stars using SDI cameras
installed at the VLT and MMT. For further information on SDI and the progress
58
of our survey, see Lenzen et al. (2004) and Biller et al. (2004).
3.2 Monte Carlo Simulations
The ability of a survey instrument to detect self-luminous, giant extrasolar planets is typically given in the form of a contrast curve: the minimum magnitude
(expressed in relation to the magnitude of the parent star) at which a companion
can be significantly detected, given as a function of the angular separation between the two objects. Here, we express contrast ratio in terms of ∆H, where ∆H
= mH,planet − mH,star , comparing the H-band flux from the planet to the H-band
flux from the star. When computing this quantity from images, we calculate the
5σ contrast curve by measuring the residual noise in regions of varying angular
separation from the star (see Section 3.3 of Biller et al. (2004) for a detailed explanation of this process). We have assembled a set of four sensitivity curves in
order to illustrate the nature of our simulations, as shown in Fig. 3.1.
VLT NACO SDI represents a currently available system, on the 8.2m VLT telescope with a 200 element Shack-Hartmann wavefront sensor, using four-channel
SDI optics to reduce speckle noise (Lenzen et al., 2004; Biller et al., 2004). This
contrast curve was taken from observations of a star meant to represent median
conditions for our survey, in terms of observing conditions, target star spectral
type, and target brightness. We note that SDI contrast curves are actually measured in a narrowband filter within the H band, at 1.575 µm; we convert to ∆H
here (and through subsequent analysis) by assuming a constant conversion consistent with our NACO SDI observations of Gl 229 B (Biller et al., 2004).
Gemini NICI is expected to come on-line by 2006, utilizing the H85 AO systems, an 85 element curvature wavefront sensor, along with a coronagraph and
two-channel SDI optics (NICI Request for Proposal , 2005). The contrast curve
59
used here is given by the NICI Request for Proposals (used as the baseline for
teams competing for the NICI Planet-Finding Campaign). It represents the assumption of NICI’s performance (prior to being tested at the telescope) for median seeing, with a V=13 guide star (assumed strehl of 30%), of spectral type K or
earlier. In this study, we scale the contrast curve by the assumed strehl for stars of
later spectral type, as well as adjusting the minimum H-band flux level at which
point sources can be detected. As with SDI, this contrast curve assumes a narrowband filter within the H band, at 1.6 µm with a width of 1%, and we assume
a constant conversion from narrowband to broadband.
We also include potential designs for Extreme Adaptive Optics Coronagraphs
(ExAOC) at an 8m-class telescope, or at the proposed 24m Giant Magellan Telescope (Johns et al. , 2004). In either case, the instrument design consists of
a spatially-filtered Shack-Hartmann wavefront sensor (750 element for the 8m
telescope, 4000 for the GMT), a coronagraph, a focal-plane wavefront sensor for
speckle suppression (Codona & Angel, 2004), and SDI optics for added contrasts
(Codona et al. , 2005). We note that this represent a proposed system (“GemSDI”)
for an ExAOC system at Gemini South, a proposal that was not ultimately accepted. Assumptions for the ExAOC curves are similar to that for the NICI curve,
attempting to reproduce median conditions, in terms of seeing and target star
properties. We again scale this curve according to expected strehl, given the V
magnitude of each target star. For the 24m GMT case, we take a very conservative estimate of system performance, simply scaling up the 8m simulations to
a larger telescope size. While this decreases the inner working angle, the outer
working angle stays fixed, given our assumption about the number of actuators
in the AO system producing the dark hole.
All contrast curves, for each instrument design, represent 5σ sensitivity to
60
planets.
Figure 3.1 Sensitivity curves for the four planet-finding instruments we consider
here. The curves represent the 5σ level of detection for a companion at a given
angular distance from the parent star.
While the contrast curves of Fig. 3.1 describe the comparative abilities to image faint companions of the four systems, it is not immediately apparent how
these curves translate into the figure of merit about which we’re most concerned:
the number of planets each system could detect from a survey. In order to evaluate this, we have constructed a Monte Carlo simulation to create an ensemble
of planets, compute their projected separation and H-magnitude, then compare
them to these contrast curves to determine what fraction can be detected with a
given system.
For each target star, we simulate 100,000 planets, randomly generating six
quantities for each planet: mass, semi-major axis, eccentricity, inclination angle, longitude of periastron, and orbital phase. Mass and semi-major axis are
61
Figure 3.2 The assumed distributions of mass and semi-major axis of extrasolar
giant planets, plotted against histograms of known planets from radial velocity
surveys.
assumed to be governed by simple power-law distributions, with indices chosen
to fit the population of known radial velocity planets, as shown in Fig. 3.2 (similar distributions were inferred by Lineweaver and Grether (2003) for mass and
Graham et al. (2002) for semi-major axis). Distributions of extrasolar planets are
taken from California & Carnegie Planet Search Almanac of Planets (2005). High
and low mass cut-offs are imposed on the power law distribution at 0.5 and 14
MJup , and the semi-major axis distribution is truncated at 0.037 AU (orbital radius of the innermost known extrasolar planet, HD 73256) and 20 AU. This final
value is uncertain, as the data from extrasolar planet surveys become incomplete
beyond ∼ 3 AU, and no data exist for extrasolar planets further out than 6 AU.
We take 20 AU (the orbit of Uranus) as a conservative upper limit (Since the publication of Nielsen et al. (2006), the imaging of planets at much larger separations,
including the HR 8799 planets (Marois et al., 2008), shows that this is likely too
62
stringent a constraint). The distribution for eccentricity is taken as a simple polynomial fit to the histogram of eccentricities of radial velocity planets.
It should be noted that we have assumed three independent distributions for
mass, semi-major axis, and eccentricity for planets, which is almost certainly incorrect. With only 137 known planets, however, the statistics are not sufficient
to suggest a more complex distribution. Additionally, our simulations allow for
the possibility of multiple-planet systems, though we do not treat them explicitly. The Monte Carlo Simulations create a similar ensemble of simulated planets
around each target star, with the assumption that a detected planet will represent a single simulated planet. Should there be a discovery of multiple planets,
however, we would then assume that two of the simulated planets around the
target star represent the actual discoveries. In fact, the RV planets used to build
the power law distributions of planet populations include multiple planet systems, though as with our simulations, each planet is considered independent of
any other planet orbiting the star. Again, this simplistic assumption is likely to be
incorrect, as the presence of a single planet will strongly constrain the allowable
masses and orbits of other planets. Nevertheless, we treat each simulated planet
as independent, which should be a safe starting point for our analysis, to first
order.
We also assign an inclination angle for the orbit (uniform in cos(i)), longitude
of periastron (uniform between 0 and 2π), and orbital phase (uniform random
variable is time; between 0 and 1 orbital periods). From these six quantities we
can solve for the instantaneous separation between planet and star, as viewed
from the observer on earth. The distance to the target star can then be used to
solve for angular separation. With the planet models of Burrows et al. (2003),
the planet’s mass (along with the age of the target star) are converted into an H-
63
magnitude, which we use to solve for ∆H, given the distance and 2MASS fluxes
of the target star. Then, it is determined whether or not each planet can be detected, given the sensitivity curve of Fig. 3.1.
We show examples of these simulations for a single target star in Fig. 3.3. In
addition to the sensitivity limit, we consider if the apparent magnitude of the
planet is sufficient to be detected by photon noise arguments alone, and whether
the planet is too massive to have a significant methane feature (SDI is most effective when there is a strong drop in the planet’s spectrum at the methane bandhead, Tef f < 1200K). We note that there are planets beyond 20 AU, since the 20
AU cut is in orbital semi-major axis, while the plot shows observed planet-star
separation (given the assumed eccentricity distribution of exoplanets, for planets
with 20 AU in semi-major axis, separations can be <40 AU). We can now directly
compare two systems by their ability to find planets: VLT NACO SDI should
have a 6% chance of finding a planet around this star, while GMT ExAOC will be
at 35%.
3.3 Target Selection
The ideal target star for a direct imaging survey for self-luminous extrasolar planets is characterized by three traits: the star should be young so the planet’s luminosity is larger, the star should be nearby so the angular separation between
primary and companion is greater, and the star should be of a late spectral type
so that the inherent luminosity of the star does not overwhelm the planet’s light.
It is not trivial to find a balance between these factors to select an observing list
for a survey. In particular, there is a lack of very young stars (<30 Myr) very
close (<20 pc) to the sun, so compromises must be made. It is through the simulations described in this paper that we seek to disentangle these target star traits,
64
Figure 3.3 Example simulations for a particular target star with the VLT NACO
SDI (left) and GMT ExAOC (right) systems. Each point represents a single simulated planet, out of a total of 100,000 in the simulation run. Detected planets lie
above the sensitivity curve (solid line), the detection threshold (dashed line), and
below the methane limit (dotted line). The detection threshold is the minimum
detectable flux given the observation, regardless of the presence of a stellar halo.
For VLT NACO SDI, 6% of these planets are detected; GMT ExAOC can detect
35%. The GMT ExAOC curve is generated assuming the use of simultaneous
differential imaging, so it too has an upper methane cut-off.
65
so that every potential target gets a quantitative ranking. By constructing a survey that maximizes the expected number of planets detected, our results (even
null results) become more meaningful.
We note that as we move to younger target stars, it is important to consider the
effects of circumstellar dust upon the sensitivity of direct imaging observations
to planets. For the planet-finding systems considered here, it is unlikely to be a
major effect, as stars on the target list we use for this analysis are generally older
than 10 Myr. Nevertheless, brighter disks can produce an additional noise source;
we do not address this issue in the analysis presented here (of our target list, only
AU Mic has a bright debris disk), however surveys focused on stars with disk will
have to more properly account for this complication. A more accurate consideration of future very-high-contrast ground-based (and space based) planet-finding
instruments will have to carefully weigh the effects of circumstellar dust, as these
instruments become sensitive to fainter and fainter planets; however such higher
order effects are beyond the scope of our considerations here.
Another important consideration (especially for higher-order AO systems such
as ExAOC) is the limiting magnitude at which the adaptive optics can efficiently
operate. More complex AO systems (more wavefront measurements, and more
actuators to control) require more photons from the guide star (the target star
in most cases), with declining Strehl ratios (and so contrasts) for fainter guide
stars. Since our simulations indicate a preference for younger, further-out stars
over older, nearby targets, a planet-finding system with a limiting magnitude
that is too bright will exclude many of the best targets. For example, of the 40
best targets from our list of 153 (which we have compiled from the literature),
the median V magnitude is 9.75; a next-generation AO system that can’t lock
onto targets fainter than 9th magnitude will simply not be an efficient planet
66
finder, as half the potential targets are eliminated before the survey begins. This
effect can be mitigated by allowing the AO system’s performance to be modulated depending on the target star (having the wavefront sensor integrate longer
on fainter stars, for example), at the expense of contrasts. In any event, when
designing future adaptive optics systems with the primary goal of detecting extrasolar planets, one must be keenly aware of the nature of the available science
targets when evaluating potential instrument designs. The number of target stars
for direct imaging surveys for self-luminous extrasolar planets is limited, and an
instrument that cannot reach most of them would not be competitive.
3.4 Simulation Results
We now consider the implications of our simulation results for the selection of
target stars. In Fig. 3.4 we examine the fraction of planets that can be detected
around target stars of various ages and distances. As expected, younger, nearby
targets are more likely to harbor detectable planets. The probability of detecting a
planet around an older, or more distant, star drops quickly. We also look at results
of the simulation for all 153 of our target stars, plotting the median separation
of the detected planets (See Fig. 3.3) against the percentage of planets that are
detectable. With the more sophisticated planet-finding systems, we see the most
important aspect of the system design in the inner working radius, as we would
expect most planets to lie at small angular separations from their parent stars.
We also consider the predicted results of a planet-search campaign, directed at
our target list, using the four systems. Since the simulations return the probability
of detecting a planet around a given star, the sum of these probabilities for many
stars should give us the total number of planets we’d expect to detect at the end
of a survey. In Fig. 3.5 we have grouped our targets by detection probability
67
Figure 3.4 Basic results from the simulation. Top left shows the fraction of simulated planets detected (the detection probability) for target stars of different ages.
As expected, younger stars are the preferred targets for finding self-luminous
planets, and there is very little value in observing older target stars. Bottom left
is a similar plot, only with distance being varied. In the right panel, we consider
the properties of the simulated planets that can be detected with each system. For
each of the 153 target stars, we plot the fraction of planets that can be detected (yaxis) against the median projected separation between primary and companion
for those planets that can be detected. The pile-up at small separations underscores the importance of the inner working radius of any planet-finding system.
68
(so the highest-quality targets are observed first), and show the expected yield
of planets from surveys of various sizes. Clearly, the best targets are observed
first, and adding lesser-quality target stars to the observing campaign results in a
slower gain in planets. The break in these curves, between rapid return of planets
and a more gradual increase, depends on the nature of the instrument.
3.5 Conclusions
With these simple Monte Carlo simulations, extrapolating from populations of
known extrasolar planets, we have a method to quantitatively rank stars in a
target list for a planet search campaign, or to directly compare competing instrument designs for future planet finding systems. Our basic results suggest that
there are a limited number of target stars suitable for direct imaging searches for
self-luminous planets, a fact that must be considered when planning a survey or
designing a new instrument.
Finally, we consider one of our basic assumptions: that each of our target
stars has a planet described by the power laws of Fig. 3.2. While there is a lack of
data for planet populations at large separations, we can make an estimate of total
populations based on our initial assumptions and results from radial velocity
surveys. Fischer & Valenti (2005) determine that in a volume-limited sample,
about 6% of stars show the radial velocity signature of a massive planet with
an orbital period shorter than 4 years (2.5 AU for a solar mass primary). Given
this, we can then integrate our assumed semi-major axis distribution (dN/da =
a−0.5 ), to give the total number of planets between 0.03 and 20 AU (which we
simulate), compared to the fraction found by Fischer & Valenti (2005) between
0.03 and 2.5 AU. From this argument, we’d expect 18% of all stars to have a giant
planet, or 40% for stars of solar metallicity or greater. This simplistic argument
69
Figure 3.5 The number of planets expected to be detected, as a function of the
number of stars in the survey. In each case, once the best targets are observed,
there is a slow gain in planets detected as lower-quality targets are added to the
survey. The location of this break, however, depends on the ability of the instrument.
70
does not take into account possible effects of changing planet populations (or
overall frequency) with spectral type of the parent star, an issue that is still being
studied. Nevertheless, as these simulations make real predictions about survey
results, they place us in a strong position to interpret any results as they relate to
the overall populations of extrasolar planets.
3.6 Acknowledgments
This work was performed in part under contract with the Jet Propulsion Laboratory (JPL) funded by NASA through the Michelson Fellowship Program. JPL is
managed for NASA by the California Institute of Technology
71
C HAPTER 4
CONSTRAINTS ON EXTRASOLAR PLANET POPULATIONS FROM VLT
NACO/SDI AND MMT SDI AND DIRECT ADAPTIVE OPTICS
IMAGING SURVEYS: GIANT PLANETS ARE RARE AT LARGE
SEPARATIONS
We examine the implications for the distribution of extrasolar planets based on
the null results from two of the largest direct imaging surveys published to date.
Combining the measured contrast curves from 22 of the stars observed with the
VLT NACO adaptive optics system by Masciadri et al. (2005), and 48 of the stars
observed with the VLT NACO SDI and MMT SDI devices by Biller et al. (2007)
(for a total of 60 unique stars: the median star for our survey is a 30 Myr K2 star
at 25 pc), we consider what distributions of planet masses and semi-major axes
can be ruled out by these data, based on Monte Carlo simulations of planet populations. We can set the following upper limit with 95% confidence: the fraction of
stars with planets with semi-major axis between 20 and 100 AU, and mass above
4 MJup , is 20% or less. Also, with a distribution of planet mass of
dN
dM
∝ M −1.16 in
the range of 0.5-13 MJup , we can rule out a power-law distribution for semi-major
∝ aα ) with index 0 and upper cut-off of 18 AU, and index -0.5 with an
axis ( dN
da
upper cut-off of 48 AU. For the distribution suggested by Cumming et al. (2008),
a power-law of index -0.61, we can place an upper limit of 75 AU on the semimajor axis distribution. At the 68% confidence level, these upper limits state that
fewer than 8% of stars have a planet of mass >4 MJup between 20 and 100 AU,
and a power-law distribution for semi-major axis with index 0, -0.5, and -0.61
cannot have giant planets beyond 12, 23, and 29 AU, respectively. In general, we
find that even null results from direct imaging surveys are very powerful in con-
72
straining the distributions of giant planets (0.5-13 MJup ) at large separations, but
more work needs to be done to close the gap between planets that can be detected
by direct imaging, and those to which the radial velocity method is sensitive.
This Chapter is based on material originally published in Nielsen et al. (2008).
4.1 Introduction
There are currently well over 200 known extrasolar planets, the bulk of which
were discovered by radial velocity surveys (e.g. Butler et al. (2006)). While this
field has initially been dominated by the study of the relatively easy-to-find Hot
Jupiters (planets with orbital periods of order days), over the past several years
there has been an increasing amount of data describing planets in larger orbits.
In particular, Fischer & Valenti (2005) compared radial velocity target stars with
known planets to stars that had been monitored but did not show signs of planets;
they concluded that about 5% of stars had planets of mass greater than 1.6MJup ,
in orbits shorter than 4 years (within 2.5 AU). Additionally, they determined
that planet fraction increased with the host star’s metal abundance. Butler et al.
(2006) have also considered the distributions of semi-major axis and planet mass
of known radial velocity planets, and found that both distributions are well-fit
by power laws. Cumming et al. (2008) have examined the biases of the radial velocity technique, and found that the semi-major axis distribution found by Butler
et al. (2006),
dN
dP
∝ P −1 , should be modified in light of the decreasing sensitivity of
the radial velocity method with orbital distance, and suggest a power law index
of -0.74 for period, instead (for solar-like stars, this corresponds to a power law
distribution for semi-major axis where
dN
da
∝ a−0.61 ).
A careful consideration of sensitivity of microlensing observations to planets
by Gould et al. (2006) suggests that for certain lensing geometries, at projected
73
separations of ∼1-4 AU, the lower limit for the frequency of Neptune-mass planets is 16%, making low-mass planets more common than giant planets in the inner
solar system (though we note that the range of separations probed by Gould et al.
(2006) and Fischer & Valenti (2005) do not precisely overlap, and the target star
samples are not uniform between the two surveys). Additionally, Gaudi et al.
(2002) found that from existing microlensing data, a third or less of M dwarfs in
the galactic bulge have 1 MJup planets in orbits between 1.5 and 4 AU, and ≤45%
of M dwarfs have planets between 1 and 7 AU of mass 3 MJup .
One outstanding question is how the abundance of planets varies as one considers planets in longer orbits. Raymond (2006) has studied the dynamics of
terrestrial planet formation in systems with giant planets, and found from numerical simulations that giant planets impede the formation of earth-like planets
when the giant planet orbits within 2.5 AU, and that water delivery to a terrestrial
planet is only possible in significant amounts when the giant planet is beyond 3.5
AU. The full extent to which giant planets impede (or encourage) water-rich terrestrial planet formation is still unknown. A greater understanding of the distribution of giant planets is a precursor to investigating the conditions under which
habitable terrestrial planets form and evolve.
The global distribution of giant planets has also been considered from the
theoretical direction. Ida & Lin (2004) have produced distributions of planets
forming in disks by core accretion, showing a continuation of a power law from
the radial velocity regime (within 2.5 AU) for giant planets, out to about 10 AU,
then trailing off at larger radii. It is possible that the lack of outer planets in
these simulations may be due (at least in part) to the fact that these models do
not consider the effects of planet-planet scattering after planets are formed, or it
may simply be a function of the initial conditions of the simulation. In order to
74
constrain such models it is necessary to measure the distribution of giant planets
in longer orbits, so as to fully sample parameter space.
With the advent of adaptive optics (AO) systems on large (∼8m) telescopes,
the ability to detect and characterize planets by directly imaging the companion
is becoming increasingly viable. Already planetary mass companions (in most
cases ∼13 MJup at 40-300 AU, or even lower mass objects with brown dwarf
hosts) have been detected in certain favorable circumstances (e.g. companions
to 2MASS1207: Chauvin et al. (2004), AB Pic: Chauvin et al. (2005), Oph 1622:
Brandeker et al. (2006), Luhman et al. (2007), Close et al. (2007), CHXR 73: Luhman et al. (2006), and DH Tau: Itoh et al. (2005)), and numerous surveys are
underway for planets around nearby, young stars (since a self-luminous planet is
brightest at young ages). While the paucity of traditional planets (that is, planets
<13 MJup and <40 AU orbiting a star) detected by this method has been disappointing, in this Chapter we consider how even a null result from these direct
imaging surveys can be used to set constraints on the population of giant planets. As the sensitivity of radial velocity surveys to planets at larger separations
decreases (due both to the smaller radial velocity signal, and the much longer
orbital period requiring a longer time baseline of observations to adequately constrain the orbital parameters), at orbits wider than 10 AU only direct imaging is
efficient at characterizing the extrasolar planet population.
Janson et al. (2007) used VLT SDI data (part of the data considered in this
work) for the known planet host star ǫ Eridani, to search for the radial velocity
planet, given its predicted position from the astrometric orbit of Benedict et al.
(2006). Though upper limits were found for the planet of MH ∼19, the predicted
flux of the planet could be up to 10 magnitudes fainter, given the likely age of the
system of 800 Myr. While this is young compared to the rest of the radial velocity
75
planet host stars, it is quite old by the standards of direct imaging planet searches,
so the inability to detect this planet’s flux is unsurprising. Previous work has been
done by Kasper et al. (2007) to study the region of parameter space unprobed
by the radial velocity method, large orbital separations, by observing 22 young,
nearby stars in the L-band from the VLT. The null result from this survey was
used to set constraints on combinations of power-law index and upper cut-off
for the distribution of the observed separation (not semi-major axis) of extrasolar
planets.
Masciadri et al. (2005) conducted a survey of 28 young, nearby stars, with
a null result for planets. They found that their observations were sufficient to
detect a 5 MJup planet at projected separations greater than 14 AU around 14 of
their target stars, and above 65 AU for all 28 stars. Similarly, their observations
would have been sensitive to a 10 MJup planet with a projected separation of 8.5
AU or beyond for half their sample, and greater than 36 AU for the full sample.
These results (obtained by adopting published ages for the target stars, and using
the appropriate planet models of Baraffe et al. (2003)) point to a rarity of giant
planets at large separations from their parent stars.
Lowrance et al. (2005) conducted a survey of similar scope to this VLT survey,
looking at 45 stars with HST NICMOS, though they considered a range of spectral
types, while Masciadri et al. (2005) considered only target stars of spectral types K
and M. Since direct imaging surveys are more sensitive to planets around fainter
target stars, the NICMOS survey could detect an object more massive than 30
MJup between 15 and 200 AU around the median target star, and 5 MJup beyond
30 AU for 36(Lowrance et al., 2005). The results, then, from both surveys are
similar, that there is a rarity of giant planets at large separations.
In this Chapter we enlarge the sample beyond that considered by Masciadri
76
et al. (2005), and consider the implications of our null result with respect to the
full orbital parameters of potential planets. We aim to set quantitative limits
on the distribution of planets in semi-major axis space, and statistically rule out
models of planet populations.
4.2 Observations
We begin with contrast plots (sensitivity to faint companions as a function of
angular separation from the target star) from two surveys for extrasolar planets, using large telescopes and adaptive optics. Masciadri et al. (2005) carried
out a survey of 28 young, nearby, late-type stars with the NACO adaptive optics system at the 8.2 meter Very Large Telescope (VLT). These observations have
exposure times of order 30 minutes, with stars being observed in the H or Ks
bands. Subsequent to these observations, a survey of 54 young, nearby stars of
a variety of spectral types (between A and M) was conducted between 2003 and
2005, with the results reported in Biller et al. (2007). This second survey used
the Simultaneous Differential Imager (SDI) at the 6.5 meter MMT and the 8 meter VLT, an adaptive optics observational mode that allows higher contrasts by
imaging simultaneously in narrow wavelength regions surrounding the 1.6 µm
methane feature seen in cool brown dwarfs and expected in extrasolar planets
(Lenzen et al., 2004; Close et al., 2005). This allows the light from a hypothetical
companion planet to be more easily distinguishable from the speckle noise floor
(uncorrected starlight), as the two will have very different spectral signatures in
this region. This translates to higher sensitivity at smaller separations than the
observations of Masciadri et al. (2005), which were conducted before the VLT SDI
device was commissioned (see Fig. 14 of Biller et al. (2007) for a more detailed
comparison of the two surveys). For most of these SDI targets, the star was ob-
77
served for a total of 40 minutes of integration time, which includes a 33 degree
roll in the telescope’s rotation angle, in order to separate super speckles–which
are created within the instrument, and so will not rotate–from a physical companion, which will rotate on the sky (Biller et al., 2006).
For both sets of target stars, contrast curves have been produced which give
the 5σ 1 noise in the final images as a function of radius from the target stars,
and thus an upper limit on the flux of an unseen planet in the given filter of the
observations. As no planets were detected in either survey at the 5σ level, we use
these contrast curves to set upper limits on the population of extrasolar planets
around young, nearby stars.
4.2.1 Target Stars
We construct a target list using 22 stars from the Masciadri et al. (2005) survey,
and 48 stars from the survey of Biller et al. (2007), for a total of 60 targets (10
stars were observed by both surveys). This first cut was made by considering
stars from the two surveys that had contrast curves, and stars whose age could
be determined by at least one of: group membership, lithium abundance, and
the activity indicator R’HK (in three cases, ages from the literature were used,
though these are stars that are generally older than our sample as a whole, and
so uncertainties in the assumed ages will not adversely affect our results). Ages
are determined by taking the age of the moving group to which the target star
belongs; if the star does not belong to a group, the lithium or R’HK age is used, or
the two are averaged if both are available. Lithium ages are found by comparing
to lithium abundances of members of clusters of known ages, and similarly for
R’HK (Mamajek, 2007). We give the full target list in Table 4.1, and details on the
1
We note that for the SDI observations this threshold corresponds to independent 5σ measurements in both the 0◦ and 33◦ images, see Biller et al. (2007) for details.
78
Figure 4.1 The 60 target stars from our two surveys (though five stars are too
old to appear on this plot). These stars are some of the youngest, nearest stars
known, spanning a range of spectral type. The size of the plotting symbol and
the color is proportional to the absolute H magnitude of the star: a bigger, bluer
symbol corresponds to a brighter and hotter star. The legend gives approximate
spectral type conversions for main sequence stars, but we note that these stars
have been plotted by their 2MASS H-band fluxes, and as a result their actual
spectral type can vary from that shown in the legend. See Table 4.1 for more
complete properties of these stars. The median target star is a 30 Myr K2 star at
25 pc.
79
age determination in Table 4.2. We also plot our target stars in Fig. 4.1. Overall,
our median survey object is a 30 Myr K2 star at 25 pc.
80
Table 4.1. Target Stars
Target
RA1
Dec1
Distance (pc)2
Sp. Type
Age (Myr)
V1
H3
Ks3
Obs. Mode4
Biller et al. (2007)
HIP 1481
00 18 26.1
-63 28 39.0
40.95
F8/G0V
30
7.46
6.25
6.15
VLT SDI
HD 8558
01 23 21.2
-57 28 50.7
49.29
G6V
30
8.54
6.95
6.85
VLT SDI
HD 9054
01 28 08.7
-52 38 19.2
37.15
K1V
30
9.35
6.94
6.83
VLT SDI
HIP 9141
01 57 48.9
-21 54 05.0
42.35
G3/G5V
30
8.11
6.55
6.47
VLT SDI
BD+05 378
02 41 25.9
+05 59 18.4
40.54
M0
12
10.20
7.23
7.07
VLT SDI
HD 17925
02 52 32.1
-12 46 11.0
10.38
K1V
115
6.05
4.23
4.17
VLT SDI
Eps Eri
03 32 55.8
-09 27 29.7
3.22
K2V
800
3.73
1.88
1.78
VLT SDI
V577 Per A
03 33 13.5
+46 15 26.5
33.77
G5IV/V
70
8.35
6.46
6.37
MMT SDI
GJ 174
04 41 18.9
+20 54 05.4
13.49
K3V
160
7.98
5.31
5.15
VLT SDI
GJ 182
04 59 34.8
+01 47 00.7
26.67
M1Ve
12
10.10
6.45
6.26
VLT SDI/Ks
VLT SDI/Ks
HIP 23309
05 00 47.1
-57 15 25.5
26.26
M0/1
12
10.09
6.43
6.24
AB Dor
05 28 44.8
-65 26 54.9
14.94
K1III
70
6.93
4.84
4.69
VLT SDI
GJ 207.1
05 33 44.8
+01 56 43.4
16.82
M2.5e
100
9.50
7.15
6.86
VLT SDI
UY Pic
05 36 56.8
-47 57 52.9
23.87
K0V
70
7.95
5.93
5.81
VLT SDI
AO Men
06 18 28.2
-72 02 41.4
38.48
K6/7
12
10.99
6.98
6.81
VLT SDI/Ks
HIP 30030
06 19 08.1
-03 26 20.0
52.36
G0V
30
8.00
6.59
6.55
MMT SDI
HIP 30034
06 19 12.9
-58 03 16.0
45.52
K2V
30
9.10
7.09
6.98
VLT SDI
HD 45270
06 22 30.9
-60 13 07.1
23.50
G1V
70
6.50
5.16
5.05
VLT SDI
HD 48189 A
06 38 00.4
-61 32 00.2
21.67
G1/G2V
70
6.15
4.75
4.54
VLT SDI
pi01 UMa
08 39 11.7
+65 01 15.3
14.27
G1.5V
210
5.63
4.28
4.17
MMT SDI
HD 81040
09 23 47.1
+20 21 52.0
32.56
G0V
2500
7.74
6.27
6.16
MMT SDI
LQ Hya
09 32 25.6
-11 11 04.7
18.34
K0V
13
7.82
5.60
5.45
MMT/VLT SDI/Ks
DX Leo
09 32 43.7
+26 59 18.7
17.75
K0V
115
7.01
5.24
5.12
MMT/VLT SDI
HD 92945
10 43 28.3
-29 03 51.4
21.57
K1V
70
7.76
5.77
5.66
VLT SDI
GJ 417
11 12 32.4
+35 48 50.7
21.72
G0V
115
6.41
5.02
4.96
MMT SDI
TWA 14
11 13 26.5
-45 23 43.0
46.005
M0
10
13.00
8.73
8.49
VLT SDI
TWA 25
12 15 30.8
-39 48 42.0
44.005
M0
10
11.40
7.50
7.31
VLT SDI
VLT SDI
RXJ1224.8-7503
12 24 47.3
-75 03 09.4
24.17
K2
16
10.51
7.84
7.71
HD 114613
13 12 03.2
-37 48 10.9
20.48
G3V
4200
4.85
3.35
3.30
VLT SDI
HD 128311
14 36 00.6
+09 44 47.5
16.57
K0
630
7.51
5.30
5.14
MMT SDI
EK Dra
14 39 00.2
+64 17 30.0
33.94
G0
70
7.60
6.01
5.91
MMT SDI
HD 135363
15 07 56.3
+76 12 02.7
29.44
G5V
3
8.72
6.33
6.19
MMT SDI
KW Lup
15 45 47.6
-30 20 55.7
40.92
K2V
2
9.37
6.64
6.46
VLT SDI
HD 155555 AB
17 17 25.5
-66 57 04.0
30.03
G5IV
12
7.20
4.91
4.70
VLT SDI/Ks
HD 155555 C
17 17 27.7
-66 57 00.0
30.03
M4.5
12
12.70
7.92
7.63
VLT SDI/Ks
HD 166435
18 09 21.4
+29 57 06.2
25.24
G0
100
6.85
5.39
5.32
MMT SDI
HD 172555 A
18 45 26.9
-64 52 16.5
29.23
A5IV/V
12
4.80
4.25
4.30
VLT SDI
CD -64 1208
18 45 37.0
-64 51 44.6
34.21
K7
12
10.12
6.32
6.10
VLT SDI/Ks
HD 181321
19 21 29.8
-34 59 00.5
20.86
G1/G2V
160
6.48
5.05
4.93
VLT SDI
HD 186704
19 45 57.3
+04 14 54.6
30.26
G0
200
7.03
5.62
5.52
MMT SDI
GJ 799B
20 41 51.1
-32 26 09.0
10.22
M4.5e
12
11.00
0.00
-99.00
VLT SDI/Ks
GJ 799A
20 41 51.2
-32 26 06.6
10.22
M4.5e
12
10.25
5.20
4.94
VLT SDI/Ks
GJ 803
20 45 09.5
-31 20 27.1
9.94
M0Ve
12
8.81
4.83
4.53
VLT SDI/Ks
HD 201091
21 06 53.9
+38 44 57.9
3.48
K5Ve
2000
5.21
2.54
2.25
MMT SDI
81
Table 4.1—Continued
Target
RA1
Dec1
Distance (pc)2
Sp. Type
Age (Myr)
V1
H3
Ks3
Obs. Mode4
Eps Indi A
22 03 21.7
-56 47 09.5
3.63
K5Ve
1300
4.69
2.35
2.24
VLT SDI
GJ 862
22 29 15.2
-30 01 06.4
15.45
K5V
6300
7.65
5.28
5.11
VLT SDI
HIP 112312 A
22 44 57.8
-33 15 01.0
23.61
M4e
12
12.20
7.15
6.93
VLT SDI
HD 224228
23 56 10.7
-39 03 08.4
22.08
K3V
70
8.20
6.01
5.91
VLT SDI
VLT Ks
Masciadri et al. (2005)
HIP 2729
00 34 51.2
-61 54 58
45.91
K5V
30
9.56
6.72
6.53
BD +2 1729
06 18 28.2
-72 02 42
14.87
K7
30
9.82
6.09
5.87
VLT H
TWA 6
07 39 23.0
02 01 01
77.005
K7
30
11.62
8.18
8.04
VLT Ks
BD +1 2447
10 18 28.8
-31 50 02
7.23
M2
12
9.63
5.61
5.31
VLT H
TWA 8A
10 28 55.5
00 50 28
21.005
M2
115
12.10
7.66
7.43
VLT Ks
TWA 8B
11 32 41.5
-26 51 55
21.005
M5
100
15.20
9.28
9.01
VLT Ks
TWA 9A
11 32 41.5
-26 51 55
50.33
K5
800
11.26
8.03
7.85
VLT Ks
VLT Ks
TWA 9B
11 48 24.2
-37 28 49
50.33
M1
70
14.10
9.38
9.15
SAO 252852
11 48 24.2
-37 28 49
16.406
K5V
160
8.47
5.69
5.51
VLT H
V343 Nor
14 42 28.1
-64 58 43
39.76
K0V
12
8.14
5.99
5.85
VLT Ks
PZ Tel
15 38 57.6
-57 42 27
49.65
K0Vp
12
8.42
6.49
6.37
VLT Ks
BD-17 6128
18 53 05.9
-50 10 50
47.70
K7
70
10.60
7.25
7.04
VLT Ks
1
from the CDS Simbad service
2
derived from the Hipparcos survey Perryman et al. (1997)
3
from the 2MASS Survey Cutri et al. (2003)
4
In cases were target stars were observed by both Masciadri et al. (2005) and Biller et al. (2007), the star is listed in the Biller et al. (2007) section,
with Obs. Mode given as “VLT SDI/Ks,” for example.
5
Distance from Song et al. (2003)
6
Distance from Zuckerman et al. (2001a)
82
Table 4.2. Age Determination for Target Stars
Sp. Type∗
Li EW (mÅ)∗
Li Age (Myr)
R’HK ∗
R’HK Age
Group Membership1
Group Age1
Adopted Age
HIP 1481
F8/G0V2
1293
100
-4.3604
200
Tuc/Hor
30
30
HD 8558
G6V2
2055
13
Tuc/Hor
30
30
HD 9054
K1V2
1705
160
Tuc/Hor
30
30
HIP 9141
G3/G5V7
1818
13
Tuc/Hor
30
30
BD+05 378
M09
1510
β Pic
12
12
HD 17925
K1V7
1948
Her/Lyr
115
115
Eps Eri
K2V11
Target
Biller et al. (2007)
V577 Per A
G5IV/V
13
219
13
50
K3V14
1188
160
GJ 182
M1Ve10
28015
12
AB Dor
K1III2
2678
10
GJ 207.1
M2.5e16
HIP 23309
M0/118
29418
-4.5986
1300
-4.0666
<100
-3.8806
<100
-4.2346
6
-3.7556
HD 45270
G1V2
1495
G1/G2V2
1458
25
8
2
219
-4.2686
<100
100
HIP 30034
K2V2
pi01 UMa
G1.5V21
1358
100
-4.40022
320
K0V21
1808
100
-4.2346
<100
21
70
70
160
12
10
35718
DX Leo
80012
AB Dor
-3.8936
K6/718
G0V
200
12
AO Men
HIP 30030
263
8
K0V
20
-4.3576
AB Dor
70
70
10017
UY Pic
HD 48189 A
<100
3
GJ 174
19
-4.2366
24
23
β Pic
12
12
AB Dor
70
70
β Pic
12
12
AB Dor
70
70
AB Dor
70
70
Tuc/Hor
30
30
Tuc/Hor
30
30
210
Her/Lyr
115
2500
115
HD 81040
G0V
2500
LQ Hya
K0V21
2478
13
HD 92945
K1V21
1388
160
-4.3936
320
AB Dor
70
70
GJ 417
G0V24
7625
250
-4.36826
250
Her/Lyr
115
115
TWA 14
M027
60027
8
TW Hya
10
10
28
25028
16
TW Hya
10
13
RXJ1224.8-7503
K2
TWA 25
M09
49429
10
HD 114613
G3V30
10031
400
-5.1186
7900
EK Dra
G032
2128
2
-4.18022
<100
HD 128311
K021
-4.48926
630
HD 135363
G5V21
2208
3
KW Lup
K2V30
43033
2
HD 155555 AB
G5IV18
2058
6
HD 155555 C
M4.518
CD -64 1208
K718
58018
5
HD 166435
G034
HD 172555 A
A5IV/V2
HD 181321
G1/G2V30
HD 186704
G035
16
AB Dor
79
70
70
630
3
2
-3.9656
<100
-4.27022
100
-4.3726
250
-4.35022
200
β Pic
12
12
β Pic
12
12
β Pic
12
12
100
β Pic
1318
10
4200
12
12
160
200
GJ 799A
M4.5e
16
β Pic
12
12
GJ 799B
M4.5e16
β Pic
12
12
GJ 803
M0Ve16
β Pic
12
HD 201091
K5Ve16
518
30
-4.7046
2000+
12
2000
83
4.3 Monte Carlo Simulations
In order to place constraints on the properties of planets from our null results,
we run a series of Monte Carlo simulations of an ensemble of extrasolar planets
around each target star. Each simulated planet is given full orbital parameters,
an instantaneous orbital phase, and a mass, then the planet’s magnitude in the
observational band is determined from these properties (using the target star’s
age and distance, and theoretical mass-luminosity relations) as is its projected
separation from the star. Finally, this magnitude is compared to the measured
contrast curve to see if such a planet could be detected. Determining which simulated planets were detected, and which were not, allows us to interpret the null
result in terms of what models of extrasolar planet populations are excluded by
our survey’s results.
4.3.1 Completeness Plots
As in Biller et al. (2007), we use completeness plots to illustrate the sensitivity
to planets as a function of planet mass and semi-major axis. To do this, for each
target star, we create a grid of semi-major axis and planet mass. At each grid location we simulate 104 planets, and then compute what fraction could be detected
with the contrast curve for that star.
In general, most orbital parameters are given by well-known distributions.
Inclination angle has a constant distribution in sin(i), while the longitude of the
ascending node and the mean anomaly are given by uniform distributions between 0 and 2π. Since contrast plots are given in terms of radius alone, it is not
necessary to consider the argument of periastron in the simulations.
To simulate the eccentricities of the planet orbits, we examine the orbital parameters of known extrasolar planets from radial velocity surveys. We consider
84
Table 4.2—Continued
Target
Sp. Type∗
Eps Indi A
K5Ve16
GJ 862
K5V16
HIP 112312 A
M4e9
HD 224228
K3V30
Li EW (mÅ)∗
Li Age (Myr)
515
538
630
R’HK ∗
R’HK Age
-4.8516
4000
-4.9836
6300+
-4.4686
500
Group Membership1
Group Age1
Adopted Age
130036
6300
β Pic
12
12
AB Dor
70
70
Masciadri et al. (2005)
HIP 2729
BD +2 1729
K5V2
Tuc/Hor
30
30
K721
Her/Lyr
115
115
TWA 6
K737
BD +1 2447
M238
TWA 8A
M237
53037
TWA 8B
M5
37
56037
TWA 9A
K537
TWA 9B
M137
SAO 252852
K5V39
V343 Nor
K0V2
PZ Tel
BD-17 6128
1
K0Vp
19
K741
56037
3
TW Hya
10
10
TW Hya
150
150
3
TW Hya
10
10
3
TW Hya
10
10
46037
3
TW Hya
10
10
48037
3
TW Hya
10
10
Her/Lyr
115
115
12
30031
5
β Pic
12
26740
20
β Pic
12
12
40042
3
β Pic
12
12
Group Membership for TWA, β Pic, Tuc/Hor, and AB Dor from Zuckerman & Song (2004), Her/Lyr from López-Santiago et al. (2006). Group Ages from
Zuckerman & Song (2004) (TWA, β Pic, and Tuc/Hor), Nielsen et al. (2005) (AB Dor), and López-Santiago et al. (2006) (Her/Lyr)
∗
Measurement References: 2: Houk & Cowley (1975), 3: Waite et al. (2005), 4: Henry et al. (1996), 5: Torres et al. (2000), 6: Gray et al. (2006b), 7: Houk &
Smith-Moore (1988), 8: Wichmann et al. (2003), 9: Zuckerman & Song (2004), 10: Favata et al. (1995), 11: Cowley et al. (1967), 12: Benedict et al. (2006), 13:
Christian & Mathioudakis (2002), 14: Leaton & Pagel (1960), 15: Favata et al. (1997), 16: Gliese & Jahreiss (1991), 17: Lowrance et al. (2005), 18: Zuckerman et al.
(2001a), 19: Houk (1978), 20: Cutispoto et al. (1995), 21: Montes et al. (2001), 22: Wright et al. (2004), 23: Sozzetti et al. (2006), 24: Bidelman (1951), 25: Gaidos et al.
(2000), 26: Gray et al. (2003b), 27: Zuckerman et al. (2001b), 28: Alcala et al. (1995), 29: Song et al. (2003), 30: Houk (1982), 31: Randich et al. (1993), 32: Gliese &
Jahreiß (1979), 33: Neuhauser & Brandner (1998), 34: Eggen (1996), 35: Abt (1985), 36: Lachaume et al. (1999), 37: Webb et al. (1999), 38: Vyssotsky et al. (1946),
39: Evans (1961), 40: Soderblom et al. (1998), 41: Nesterov et al. (1995), 42: Mathioudakis et al. (1995)
+
In general, we have only determined Ca R’HK ages for stars with spectral types K1 or earlier, but in the case of these two K5 stars, we have only the R’HK
measurement on which to rely for age determination. The calibration of Mt. Wilson S-index to R’HK for K5 stars (B-V ∼ 1.1 mag) has not been well-defined
(Noyes et al. (1984); specifically the photospheric subtraction), and hence applying a R’HK vs. age relation for K5 stars is unlikely to yield useful ages. Although
we adopt specific values for the ages of these stars, it would be more accurate to state simply that these stars have ages >1 Gyr. As a result, almost all simulated
planets are too faint to detect around these stars, so the precise error in the age does not significantly affect our final results.
85
Figure 4.2 The assumed distribution for the orbital eccentricities of extrasolar
planets. The datapoints represent the histograms for planets found to date with
the radial velocity method (Butler et al., 2006), with error bars as 1-sigma Poisson
noise based on the number of planets per bin. Planets are divided to separate
“Hot Jupiters,” based on a period cut at 21 days; long period planets are divided
into linear bins, short-period ones into logarithmic bins. In both cases, a simple
linear fit is a good representation of the data.
86
the orbits of planets given by Butler et al. (2006), and show their distribution of
eccentricities in Fig. 4.2. By dividing the sample into two populations, based on
a cut at an orbital period of 21 days, we can separate out the population of Hot
Jupiters, which we expect to have experienced orbital circularization as a result
of their proximity to their host stars. For both sets of populations, we fit a simple
straight line to the distributions (the logarithmic bins for the Hot Jupiter population means this line translates to a quadratic fit). We note that the Hot Jupiter
fit is plagued by small number statistics, and so the fit is likely to be less reliable than that for long period planets. Additionally, the choice of 21 days as the
cut-off is a result of the RV sample being comprised almost entire of solar-type
(FGK) stars, and were we to consider planets around target stars of a wide range
of masses, this cut-off would likely prove to be a function of stellar mass, as the
circularization radius will ultimately depend on the gravitational force felt by the
planet. However, even for our closest target stars, such an orbital period gives
star-planet separations less than 0.1”, a regime where our contrast curves show
we are not sensitive to planets. As a result, the manner in which the orbits of Hot
Jupiters are simulated has effectively no impact on our final results.
For each simulated planet, the on-sky separation is determined at the given
orbital phase, and mass is converted into absolute H or Ks magnitude, following the mass-luminosity relations of both Burrows et al. (2003) and Baraffe et al.
(2003); both of these sets of models have shown success at predicting the properties of young brown dwarfs (e.g. Stassun et al. (2007) and Close et al. (2007a)).
In the case of the models of Burrows et al. (2003), we use a Vega spectrum to
convert the various model spectra into absolute H and Ks magnitudes. We also
note that the Burrows et al. (2003) models only cover a range of planet masses
greater than 1 MJup , and ages above 100 Myr. Since the range of ages of our tar-
87
get stars extends down to 2 Myr, and we wish to consider planets down to masses
of 0.5 MJup , we perform a simple extrapolation of the magnitudes to these lower
ages and masses. While this solution is clearly not ideal, and will not reflect the
complicated physical changes in these objects as a function of mass and age, we
feel that this method provides a good estimation of how the Burrows et al. (2003)
models apply to our survey.
At this point, we use the distance to the target star, as well as its 2MASS flux
density in either H or Ks, to find the delta-magnitude of each simulated planet.
With this, and the projected separation in the plane of the sky, we can compare
each simulated planet to the 5σ contrast curve, and determine which planets can
be detected, and which cannot. We also apply a minimum flux limit, based on
the exposure time of the observation, as to what apparent magnitude for a planet
is required for it to be detected, regardless of its distance from the parent star. For
the SDI observations, which make use of optimized (compared to basic H-band
observing) methane filters, we add an additional factor of ∆H=0.6 magnitudes
(appropriate for a T6 spectral type, a conservative estimate for young planets;
see Biller et al. (2007) for details on this factor). Also, for these SDI observations,
we place an upper cut-off on masses where, for the age of the system, the planet
reaches an effective temperature of 1400 K. Above this temperature, methane in
the atmosphere of the planet is destroyed, and the methane feature disappears,
so that the SDI subtraction now attenuates any planets, as well as stellar speckles. While non-methane objects further out than 0.2” are not totally removed in
the image (e.g. Fig. 4 of Nielsen et al. (2005)), for consistency we ignore this
possibility when considering upper limits.
In many cases in our survey, a single target star was observed at several
epochs, in some cases with different observational parameters (such as VLT NACO
88
SDI and VLT NACO Ks broadband) or even different telescopes (MMT and VLT).
As a result, to be considered a null detection, a simulated planet must lie below
the 5σ detection threshold at each observational epoch, and this threshold must
reflect the appropriate contrast curve for the given observation. To account for
this, for target stars with multiple observations, an ensemble of simulated planets
is created for the earliest observational epoch, as described above, and compared
to the contrast curve for that observation. The simulated planets then retain all
the same orbital parameters, except for orbital phase which is advanced forward
by the elapsed time to the next observational epoch, and the simulated planets
are now compared to the contrast curve from the later epoch (and so on for every available contrast curve). A planet that lies above the contrast curve at any
epoch is considered detectable. Typically this elapsed time is about a year, and so
is a minor effect for planets with long-period orbits; we nevertheless include this
complexity for completeness. The major benefit of this method is that for stars
observed both with SDI (Biller et al., 2007) and at H or Ks (Masciadri et al., 2005),
it is possible to leverage both the higher contrasts at smaller separations with SDI
and the insensitivity to the methane feature of broadband imaging, which allows
planets of higher masses to be accessed. The epochs used when considering each
observation are those given in Table 3 of Masciadri et al. (2005) and Tables 2 and
3 of Biller et al. (2007).
We plot an example of this simulation at a single grid point in mass and semimajor axis in Fig. 4.3, for the target star GJ 182, the 18th best target star in our
survey, using the planet models of Burrows et al. (2003). 104 simulated planets
(only 100 are plotted in this figure, for clarity) are given a single value of mass
(6.5 MJup ) and semi-major axis (10 AU). Since each planet has unique orbital parameters (eccentricity, viewing angle, and orbital phase), the projected separation
89
Figure 4.3 The results of a single simulation of 104 planets around the SDI target
star GJ 182 (for clarity, only 100 points are plotted here) (Biller et al., 2007). Each
planet has a mass of 6.5 MJup , and a semi-major axis of 10 AU. Due to various
values of eccentricity, viewing angle, and orbital phase, the projected separation
of each simulated planet departs from the semi-major axis, and the points smear
across the horizontal direction, with projected separation running between 0 and
14 AU. Planets that are above the contrast curve are detected (blue dots), while
those below are not (red dots). In this case, 20% of these simulated planets were
detected. By running this simulation over multiple grid points of mass and semimajor axis, we produce a full completeness plot, such as Fig. 4.4.
90
varies from planet to planet, so some are above the 5σ detection threshold of the
contrast curve (the blue dots in the figure), while others are not (the red dots). For
this particular target star and simulated planets of mass 6.5 MJup and semi-major
axis 10 AU, 20% of these planets can be detected.
To produce a complete contour plot, we consider a full grid of mass (100
points, between 0.5 and 17 MJup ) and semi-major axis (200 points, between 1 and
4000 AU), running a simulation as in Fig. 4.3 at each of the 20,000 grid points.
We then plot contours showing what fraction of planets we can detect that have
a given mass and semi-major axis, in Fig. 4.4, again for the target star GJ 182. The
hard upper limit is set by the methane cut-off, where the planet mass becomes
high enough (for the age of the given target star) for the effective temperature
to exceed 1400 K, at which point the methane feature is much less prominent in
the planet’s spectrum. Although there exists a Ks dataset for the star GJ 182, and
additional observational epochs with SDI, for clarity we only use a single SDI
contrast curve to produce this figure; the full dataset is used for subsequent analysis. If GJ 182 had a planet with mass and semi-major axis such that it would fall
within the innermost contour of Fig. 4.4, we would have an 80% chance of detecting it. Obviously, these plots make no statements about whether these stars
have planets of the given parameters, but instead simply express our chances of
detecting such a planet if it did exist.
4.3.2 Detection Probabilities Given an Assumed Distribution of Mass and Semimajor Axis of Extrasolar Planets
With the large number of currently-known extrasolar planets, it is possible to
assume simple power-law representations of the distributions of mass and semimajor axis of giant planets, which allows for a more quantitative interpretation of
our null result. Butler et al. (2006) suggest a power law of the form
dN
dM
∝ M −1.16
91
Figure 4.4 A full completeness plot for the target star GJ 182. As a function of
planet mass and semi-major axis (with grid points between 0.5 and 17 MJup for
mass, and semi-major axis between 1 and 4000 AU, though only the inner 210
AU are plotted here), the contours give the probability of detecting a planet with
those parameters given the available contrast curve. At each grid point, 104 planets are simulated, as shown in Fig. 4.3, and the fraction that can be detected is
returned. The left edge is strongly influenced by the shape of the contrast curve,
while the right edge depends mainly on the projected field of view of the observation. The hard upper limit at 9 MJup is set by the methane cut-off imposed by
the SDI method, when the simulated planets exceed 1400 K and cease to have
a strong methane signature in the spectrum. The fact that the contours do not
precisely line up at this limit is simply a result of the interpolation used to plot
the contours. Completeness plots for all 60 survey stars are available online at
http://exoplanet.as.arizona.edu/%7Elclose/exoplanet.html
92
Figure 4.5 The assumed mass distribution of extrasolar planets, plotted against
the histogram of known planets detected by the radial velocity method (as of May
2007). Throughout this Chapter we adopt a power law of the form
dN
dM
∝ M −1.16 ,
as suggested by Butler et al. (2006), and the data shown here are well-represented
by this power-law fit.
93
Figure 4.6 The distributions that we consider for semi-major axis of extrasolar
planets, again with the histogram of known radial velocity planets, detected as
of May 2007. We adopt the observed distribution of Cumming et al. (2008), with
dN
da
∝ a−0.61 , which is suggestive of the existence of wider planets, given that
radial velocity surveys should be especially sensitive to hot Jupiters (producing
an over-abundance at small separations) and less sensitive to long-period orbits
(resulting in a decline in detected planets at larger separations).
94
for mass, while Cumming et al. (2008) use the power law
dN
da
∝ a−0.61 for semi-
major axis, in order to describe the distributions of known extrasolar planets. We
make histograms for mass (Fig. 4.5) and semi-major axis (Fig. 4.6) from the parameters of all currently-known extrasolar planets (parameters taken from the
Catalog of Nearby Exoplanets, http://exoplanets.org, in May 2007). In both
cases, the power laws do a reasonable job of fitting the data, above 1.6 MJup and
within 3.5 AU. For smaller planets, or longer periods, we would expect the observational biases of the radial velocity method to make the sample incomplete,
thus accounting for the drop-off of planets from what would be predicted by
the power law. We echo the caution of Butler et al. (2006) that these planets are
drawn from many inhomogeneous samples, but we believe with the relatively
large numbers the derived distributions are not far off from the actual distributions.
In general, then, if one assumes that these power laws are universal to all stars,
and that the semi-major axis power law continues to larger separations with the
same index, the only outstanding question is to what outer limit (or “cut-off”)
this distribution continues before it is truncated. This cut-off is a term that can be
uniquely well constrained by the null results from our survey. We return to this
issue, after considering the results from our survey, in Section 4.4.3.
For the Monte Carlo simulations using these assumptions, in addition to the
other orbital parameters, we obtain mass and semi-major axis through random
variables that follow the given power law distributions, and again find what fraction of planets can be detected given the contrast curve for that particular target
star. An example of this simulation, again for GJ 182, is given in Fig. 4.7, showing
that with an assumed upper limit for semi-major axis of 70 AU, and a power law
with index -0.61, and mass power law index of -1.16 between 0.5 and 13 MJup , we
95
Figure 4.7 105 simulated planets around the SDI target star GJ 182, following the
dN
distributions for mass ( dM
∝ M −1.16 ) of Butler et al. (2006) and semi-major axis
( dN
∝ a−0.61 ) of Cumming et al. (2008), with mass running from 0.5 to 13 MJup ,
da
and semi-major axis cut off at 70 AU (since there is a range of eccentricities for
the simulated planets, instantaneous projected separation can exceed the semimajor axis cut-off of 70 AU, and so some planets are seen at observed separations
beyond 70 AU). Detected planets (blue dots) are those that lie above the contrast
curve, above the minimum flux level, and below the methane cut-off. In this case,
10% of the simulated planets could be detected with this observation. Using the
metric of completeness to planets with this mass and semi-major axis distribution, GJ 182 is the 18th best target star in our sample.
96
would be able to detect 10% of the simulated planets. Again, for this figure, we
simply show the results using the models of Burrows et al. (2003).
4.4 Analysis
Having developed the tools to produce completeness plots, as well as compute
the fraction of detected planets for various assumed models of semi-major axis,
we proceed to combine the results over all our target stars in order to place constraints on the populations of extrasolar planets from these two surveys.
4.4.1 Planet Fraction
A simplistic description of the number of planets expected to be detected is given
by the expression
N(a, M) =
N
obs
X
fp (a, M)Pi (a, M)
(4.1)
i=1
That is, the number of planets one expects to detect at a certain semi-major axis
and mass is given by the product of the detection probability (Pi ) for a planet of
that mass (M) and semi-major axis (a), and the fraction of stars (fp ) that contain
such a planet (or “planet fraction”), summed over all target stars (in this case,
Nobs = 60). In this treatment, we ignore two major effects: we assume that there
is no change in the mass or separation distribution of planets, or their overall
frequency, as a function of spectral type of the primary; we also do not consider
any metallicity dependence on the planet fraction. While these assumptions are
clearly incorrect (e.g. Johnson et al. (2007), Fischer & Valenti (2005)), it is a good
starting point for considering what constraints can be placed on the population of
extrasolar planets. Also, we note that our sample includes 24 binaries, which may
inhibit planet formation, though most of these binaries have separations greater
than 200 AU. This leaves only ten binaries with separations in the range of likely
97
planet orbits that might potentially contaminate our results. For simplicity, we
leave these binaries in our sample, and we will return to this issue in Section 4.4.3.
Using the contrast curves from each of our 60 targets stars (as in Fig. 4.4), we
simply sum the fraction of detectable planets at each grid points for all of our
stars. This gives the predicted number of detectable planets at each combination
of mass and semi-major axis, assuming each target star has one planet of that
mass and semi-major axis (fp (a, M)=1).
More instructively, if we assume a uniform value of the planet fraction for all
target stars, we can solve for fp . Then by assuming a particular value for the predicted number of planets (ΣPi ), our null result allows us to place an upper limit
on the planet fraction at a corresponding confidence level, since our survey measured a value of N(a,M)=0. In a Poisson distribution, the probability of obtaining
ν
a certain value is given by P = e−µ µν! , which for the case of a null result, ν = 0,
becomes P = e−µ , so a 95% confidence level requires an expectation value, µ, of
3 planets. We can thus rewrite Eq. 4.1, using ΣPi = 3, as
fp (a, M) ≤ PNobs
i=0
3
Pi (a, M)
(4.2)
Put another way, if we expected, from our 5σ contrast curves, to detect 12 planets
(ΣP=12, for fp = 1), in order to have actually detected 0 planets from our entire
survey (N=0), the planet fraction must be less than
3
12
= 25% (fp <0.25), at the
95% confidence level. Doing this at each point in the grid of our completeness
plots allows for an upper limit on the planet fraction as a function of mass and
semi-major axis.
We plot the contours of this upper limit in Fig. 4.8, using the planet models
of Burrows et al. (2003). A general result from these data is that, again at the
95% confdience level, we would expect fewer than 20% of stars to have planets
of mass greater than 4MJup with semi-major axis between 20 and 100 AU. There
98
Figure 4.8 The upper limit on the fraction of stars with planets (fp ), as a function
of mass and semi-major axis (see Eq. 4.2), using the planet models of Burrows
et al. (2003), with the 95% confidence level plotted as thin blue lines. We also plot
in thicker red lines the 68% confidence level contours. Given the results of our
survey, we would expect, for example, less than 20% (as indicated by the thin
dashed blue line) of stars to have a planet of mass greater than 4 MJup in an orbit
20 < a < 100 AU, and less than 50% of stars (the dot-dashed thin blue line, which
falls almost on top of the thick red dashed line) to have planets more massive than
4 MJup with semi-major axes between 8 and 250 AU, at the 95% confidence level.
Also plotted in the solid circles are known extrasolar planets. There is still a gap
between planets probed by direct imaging surveys (such as the ones described in
this work), and those using the radial velocity method.
99
appears to be no “oasis” of giant planets (more massive than Jupiter) in longperiod orbits: at the 85% confidence level, this upper limit on the fraction of stars
with giant planets drops to less than 10%.
We present the same plot, this time using the COND models of Baraffe et al.
(2003), in Fig. 4.9. As the two sets of models predict quite similar planet NIR
magnitudes, the plots are virtually the same. The main difference between these
models is that, given the age distribution of our target stars, higher mass planets appear slightly brighter in the Baraffe et al. (2003) models, with the trend
reversing and lower mass planets becoming fainter, as compared to the models
of Burrows et al. (2003). Marley et al. (2007) have recently produced a third set of
models, which globally predict lower luminosities for giant planets. Since synthetic spectra for these models are not currently available, we do not examine
the consequences of these models here, though we discuss possible effects in Section 4.5. But we note that while at 30 Myr and at 4 MJup there is only a ∼3X
decrease in the luminosity predicted by Marley et al. (2007) compared to Burrows et al. (2003), the temperature of these objects is lower, therefore increasing
the number of planets with methane that can be detected using SDI. As a result,
even with the future use of the Marley et al. (2007) models, our results will not
change dramatically, with respect to the total number of planets to which we are
sensitive.
4.4.2 Host Star Spectral Type Effects
From the perspective of direct imaging searches for extrasolar planets, M-stars
are especially appealing: their lower intrinsic luminosity means a given achievable contrast ratio allows fainter companions to be detected, and so makes the
detection of planet-mass companions seem more likely. Nevertheless, there appears to be mounting evidence that even if the fraction of stars with planets does
100
Figure 4.9 The same as Fig. 4.8, but instead using the models of Baraffe et al.
(2003) to convert between planet mass and NIR magnitudes. The COND models
generally predict brighter planets for higher masses, but fainter planets at lower
masses, compared to the Burrows et al. (2003) models. Nevertheless, the two sets
of models predict similar overall results.
101
not decline when moving to later spectral types (and the work of Johnson et al.
(2007) suggests this fraction does decrease for M stars), the mean planet mass is
likely to decrease (e.g. Butler et al. (2004), Bonfils et al. (2005)). While it seems
natural that the initial mass of the circumstantial disk (and so the mass of formed
planets) should scale with the mass of the parent star, such a relation is not easily
quantified for planets at all orbital separations. Additionally, it is problematic for
us to model planet distributions for M star hosts on radial velocity planets, when
these planets are almost entirely in systems observationally biased with a host
star of spectral type F, G, or K.
In order to investigate this effect, we divide our stars by spectral type, then
recompute what limits we can set on the planet fraction. In Fig. 4.10 and 4.11
we plot the upper limit on the planet fraction for only the solar-like stars (K or
earlier) in our survey (45 of our 60 target stars, this includes the one A star in
our survey, HD 172555 A). As we would expect, the statistics in the inner contour
remain largely the same, but the contours move upward and to the right, as less
massive and closer-in planets become harder to detect against the glare of earliertype stars.
We also consider the fifteen M stars in our sample, in Fig. 4.12 and 4.13. The
effect of the smaller number of stars is apparent, though the shape of the contours is again roughly the same. If, as is suggested by Johnson et al. (2007), giant
planets are less common around low mass stars, or less massive stars harbor less
massive planets, it becomes difficult to probe the population of M star planets
with surveys such as these.
4.4.3 Constraining the Semi-Major Axis Distribution
We now consider what constraints can be placed on planet populations if we assume a basic form to the distributions. In particular, if we take the mass power-
102
Figure 4.10 The 95% and 68% confidence upper limit on planet fraction, limited
only to stars of spectral type A through K, using the Burrows et al. (2003) models.
Since with earlier spectral types the parent star is intrinsically brighter, it becomes
more difficult to access planets of smaller masses or smaller separations. For
AFGK stars we can only say, at the 95% confidence level, that less than 20% of
stars have M > 7MJup planets at 30-70 AU, or a limit of 50% for planets with
masses above 6 MJup at 10-200 AU.
103
Figure 4.11 The same as Fig. 4.10, but with the Baraffe et al. (2003) models used
to find planet masses.
104
Figure 4.12 Now using only our 15 M stars, we again plot the 95% and 68% confidence level upper limit on planet fraction, using the Burrows et al. (2003) models.
While the plot follows the shape of Fig. 4.8, the removal of about three-quarters
of the target stars reduces the upper limit that can be set on the planet fraction.
Hence less than 50% of M stars should have planets with M > 4MJup from 10 to
80 AU, at 95% confidence. The analysis of microlensing results by Gaudi et al.
(2002) sets upper limits on the planet fraction of M dwarfs in the galactic bulge of
45% for 3 MJup planets between 1 and 7 AU, and 33% for 1 MJup planets between
1.5 and 4 AU. While even our 50% contour (at the 68% confidence level) does not
probe the area of parameter space considered by Gaudi et al. (2002), which places
upper limits on 1 MJup planets between 1.5 and 4 AU around M dwarfs of ≤33%,
and ≤45% for 3 MJup planets between 1 and 7 AU, the microlensing upper limits
are unsurprising given our limits at somewhat larger separations for planets of
the same mass. Though we note that the composition (especially in terms of stellar metallicity) is likely to differ greatly between the two samples. Also, we again
draw attention to the fact that Johnson et al. (2007) have shown that for M stars,
giant planets at small radii are less common than around more massive stars.
105
Figure 4.13 As with Fig. 4.12, only now with the Baraffe et al. (2003) models used
to find planet masses.
106
law from currently-known extrasolar planets,
dN
dM
∝ M −1.16 (Butler et al., 2006),
we can constrain what types of power laws for semi-major axis are allowed by
our survey null result. To accomplish this, we simulate planets using a grid of
power law indices and upper cut-offs for semi-major axis for each of our target
stars. Then, the sum of the detection fractions over the entire survey gives the
expected number of detected planets, assuming each star has one planet (for example, if for 10 stars, we had a 50% chance of detecting a planet around each star,
we’d expect to detect 5 planets after observing all 10 stars). Since we’ve set the
distribution of planets, we can determine the actual planet fraction: radial velocity surveys tell us this value is 5.5% for planets more massive than 1.6 MJup and
with periods shorter than 4 years (closer-in than 2.5 AU) (Fischer & Valenti, 2005).
We can then use the mass and semi-major axis power laws to find the planet fraction for planets down to 0.5 Jupiter masses and out to the given semi-major axis
cut-off, while always preserving the value of 5.5% for the planet fraction for planets >1.6 MJup and <2.5 AU. Then, by multiplying this planet fraction by the sum
of detection probabilities, we find the expected number of planets we’d detect
given each distribution. At this point, we can again use the Poisson distribution
to convert this to a confidence level (CL) for rejecting the model, given our null
result: CL = 1 − e−µ , where µ is the expected number of planets for that model.
Since stellar multiplicity can disrupt planet formation, especially for small binary separations, we exclude all known stellar binaries from our target list with
projected separations less than 200 AU. Since our results deal mainly with the
inner 100 AU around our target stars, binaries that are any closer would greatly
influence the formation of planets at these radii, creating an entirely different
population. Bonavita & Desidera (2007) have shown that while the overall planet
fraction (for radial velocity planets, as taken from the volume limited sample of
107
Fischer & Valenti (2005)) is similar between single stars and wide binaries, it decreases for stars in tight binary systems. Our inner cut-off on binary separation is
at a larger separation than that noted in Bonavita & Desidera (2007), but we consider planets in much wider orbits than those detectable with the radial velocity
method. Additionally, it has been shown by Quintana et al. (2002) and Holman
& Wiegert (1999) that terrestrial planets could form and survive in the α Cen AB
system, despite the relatively tight (23 AU), high eccentricity (0.5) orbit. Holman
& Wiegert (1999) also found that for most cases, a planet is stable in a binary
system if its orbital radius is less than ∼10-20% of the binary separation. Applying this additional condition to our sample, we remove 1 star from the Masciadri
et al. (2005) survey, and 9 from the Biller et al. (2007) sample, leaving 50 stars in
our sample. We give further details on the binaries in our sample in Table 4.3.
In Fig. 4.14 and 4.15, we plot the confidence with which we can reject the
model for various combinations of power law index and upper cut-off for the
semi-major axis distribution. For the favored model of a power law distribution
given by
dN
da
∝ a−0.61 , we can place, at the 95% confidence level, an upper-limit
on the semi-major axis cut-off of 75 AU (94 AU using the models of Baraffe et al.
(2003) instead of those of Burrows et al. (2003)). In other words, if the power law
index has a value of -0.61, there can be no planets in orbits beyond a=75 AU at
the 95% confidence level (29 AU at the 68% confidence level). In Fig. 4.16, we
show how these assumptions of power law index compare with the distributions
of known radial velocity planets, as well as to what confidence we can exclude
various models.
4.4.4 Testing Core Accretion Models
We also consider more sophisticated models of planet populations, namely the
core accretion models of Ida & Lin (2004). Using their Fig. 12, we extract all the
108
Table 4.3. Binaries
Target
Sep (“)
Sep. (AU)
Reference
Companion Type
0.15
6.38
Biller et al. (2007)
7
230
Pounds et al. (1993)
M0
AB Dor
9 (Ba/Bb)
134 (Ba/Bb)
Close et al. (2005)
Binary M stars
AB Dor
0.15 (C)
2.24 (C)
Close et al. (2005)
Very low-mass M Star
5.5
250
Chauvin et al. (2005)
Planet/Brown Dwarf
HD 48189 A
0.76 (B)
16.5
Fabricius & Makarov (2000)
K star
HD 48189 A
0.14
3.03
Biller et al. (2007)
DX Leo
65
1200
Lowrance et al. (2005)
M5.5
EK Dra
SB
SB
Metchev & Hillenbrand (2004)
M2
0.26
7.65
Biller et al. (2007)
Biller et al. (2007)
HIP 9141
V577 Per A
HIP 30034
HD 135363
HD 155555 AB
SB (AB)
SB (AB)
Bennett et al. (1967)
G5 and K0 SB
HD 155555 AB
18 (C)
1060 (C)
Zuckerman et al. (2001a)
Target Star 155555 C, M4.5
HD 172555 A
71
2100
Simon & Drake (1993)
Target Star CD -64 1208, K7
HD 186704
13
380
Aitken & Doolittle (1932)
GJ 799A
3.6
36
Wilson (1954)
HD 201091
16
55
Baize (1950)
K5
Eps Indi A
400
1500
McCaughrean et al. (2004)
Binary Brown Dwarf
HIP 112312
100
2400
Song et al. (2002)
M4.5
TWA 8A
13
270
Jayawardhana et al. (1999)
Target Star TWA 8B, M5
TWA 9A
9
576
Jayawardhana et al. (1999)
Target Star TWA 9B, M1
15.7
260
Poveda et al. (1994)
HD 128898, Ap
V343 Nor
10
432
Song et al. (2003)
M4.5
BD-17 6128
2
100
Neuhäuser et al. (2002)
M2
Target Star GJ 799B, M4.5
Masciadri et al. (2005)
SAO 252852
109
Figure 4.14 The confidence level with which we can reject models of planet populations, assuming a power-law distribution for semi-major axes ( dN
∝ aα ), as
da
a function of the power law index and upper cut-off (N(a)=0 for a ≥ aCut−of f ).
The expected power-law index from the radial velocity distribution (see Fig 4.6)
is -0.61 (Cumming et al., 2008), and given these data we can place a 95% confidence limit on the upper cut-off of 75 AU. At 68% confidence, there cannot be
giant planets in orbits beyond 29 AU, for this choice of power law index. For this
figure, we use the models of Burrows et al. (2003)
110
Figure 4.15 The same as Fig. 4.14, but using the models of Baraffe et al. (2003).
The 95% confidence upper cut-off for semi-major axis for the
moves to 94 AU.
dN
da
∝ aα model now
111
Figure 4.16 The histogram (in blue) of the distribution of known extrasolar giant
planets found with the radial velocity method, plotted against a series of power
laws considered in Fig. 4.14 and 4.15. Since radial velocity observations are only
complete to about 2.5 AU, a less steep drop-off of planets with semi-major axis is
possible. We give the confidence with which we can rule out various combinations of power law index and upper cut-off (the percentages in red), for indices of
-1, -0.61, -0.25, and upper cut-offs of 10 AU, 20 AU, 40 AU, and 80 AU. While we
have insufficient statistics to place strong constraints on the power law of index
-1, we can rule out the other two with increasing confidence as larger values of
the upper limit are considered. For example, a power law of the form
dN
da
∝ a−0.25
must cut-off at 26 AU (95% confidence), while the most likely power law of index
-0.61 must have its cut-off at 75 AU (also at the 95% confidence level).
112
non-Hot-Jupiter giant planets, and of the 200-300 resulting planets, we run our
Monte Carlo simulation by, for each simulated planet, randomly selecting one
planet from this figure, adopting its values of mass and semi-major axis, then
assigning it the other orbital elements as usual. We consider each of the three
cases modeled by Ida & Lin (2004).
In Fig. 4.17 we plot the predicted number of planets detected from these three
distributions. Again, the planet fraction for each curve is set to match the planet
fraction of Fischer & Valenti (2005) for planets above 1.6 MJup and within 2.5 AU.
Since the predicted total number of planets detected range between about 0.6 and
0.7 at the end of our survey, we cannot place any strong constraints on these models from our null result. For the three cases of Ida & Lin (2004), A, B, and C, we
can only “rule them out” at the confidence levels of 45%, 49%, and 50% respectively, and again only after leaving all binaries in the sample. Additionally, since
we are considering target stars of all spectral type, we are not staying faithful to
the original simulations of Ida & Lin (2004), which consider only solar mass host
stars. In summary, the core-accretion simulations of Ida & Lin (2004) are quite
consistent with our results.
4.5 Discussion: Systematic Effects of Models on Results and Other Work
We underscore the dependence of these results upon the accuracy of the massluminosity relations of Burrows et al. (2003) and Baraffe et al. (2003). In particular, these models utilize the “Hot Start” method for giant planet formation, at
odds with the core accretion mechanism suggested by the planet-metallicity relation of Fischer & Valenti (2005). The giant planet models of Marley et al. (2007)
incorporate formation by core accretion, and predict systematically fainter fluxes
for these young planets (typically ∼3 times fainter for a 30 Myr, 4 MJup planet,
113
Figure 4.17 The number of planets we would expect to detect at the end of the
survey, as a function of the number of target stars observed, out of our total sample of 60. Stars are divided into bins based on binarity, and within each bin the
stars are arranged so that the best targets are observed first. The first four models
use power laws with
dN
da
∝ a−0.61 , with the upper cut-off given. These models can
be ruled out with increasing confidence with cut-offs beyond 40 AU as increasingly close binaries are added to the sample. Since the three Ida & Lin (2004)
models predict less than one planet from our survey, we can only place very limited constraints on these models at this time, namely that cases A, B, and C are
inconsistent with our null result at the 45%, 49%, and 50% confidence levels, respectively, if all binaries are included in our sample.
114
yet the overall effect is difficult to predict without detailed models and spectra).
Another result of moving to these models, however, would be that these planets
are also cooler, so that the SDI method (limited to objects with effective temperatures lower than 1400 K) will likely reach planets of higher masses than would
be predicted by the models of Burrows et al. (2003) and Baraffe et al. (2003).
It is possible to envision a scenario with extrasolar planets being built by both
disk instability (e.g. Boss (2007)) and core accretion, with the two types of planets segregated in orbital distance: inner planets being more common in orbit
around metal-rich stars, consistent with core accretion, while outer planets (the
type to which the surveys discussed here are sensitive) form by disk instability.
In that case, the use of the Hot Start models would be entirely reasonable, as these
models have been shown to be mostly consistent with young, low-mass objects
that likely form in this way (e.g. Stassun et al. (2007), Close et al. (2007a)). This
possibility (which we again note is pure speculation) endangers any conclusions
drawn from Fig. 4.14 and 4.15, which assume a single, consistent population of
planets, not allowing for the possibility of two overlapping populations (such as
one described by broken power laws). Our results for the upper limit on planet
fraction would remain valid, however, since these make no assumptions on extrasolar planet populations beyond the eccentricity distribution (a minor factor)
and the mass-luminosity relation.
Clearly, these constraints would be stronger with a larger sample size to improve our statistics. Such an increase in sample size is hampered by the limited
number of young, nearby stars: observing older targets tends to require an order of magnitude increase in number of targets so as to assure a similar number
of detected planets. The greatest improvement in these results is likely to come
with more advanced planet-finding instruments, which increase the contrast and
115
inner working angle to which one can detect planets close to their parent stars.
Two such Extreme AO systems, slated to come online in the next several years,
are VLT-SPHERE and the Gemini Planet Imager (GPI). Surveys of a sample of
young, nearby stars (likely very similar to the target list of this work) with these
planet-finders should be able to greatly close the gap between the sensitivities to
planets of direct imaging and radial velocity surveys.
Additionally, new observing techniques, such as Angular Differential Imaging (Marois et al., 2008), or better data reduction techniques like LOCI (Lafrenière
et al., 2007), will further improve achievable contrasts. Indeed, the power of LOCI
to improve contrasts from high contrast imaging data suggests the possibility of
re-reducing existing direct imaging datasets. The improved contrasts could potentially lead to discoveries of previously undetectable companions or, failing
that, provide increased constraints on planet populations.
While radial velocity surveys continue to have great success in finding planets, the limiting factor is orbital time: a planet at 10 AU takes over 30 years to
complete a single orbit, and radial velocity planets are generally not confirmable
until at least one orbit has elapsed. As a result, the onus on determining the
characteristics of giant planets beyond ∼10 AU is largely upon direct imaging
surveys.
A survey planned for the immediate future uses the NICI (Near Infrared
Coronographic Imager) instrument currently being commissioned on the Gemini South Telescope, with plans for a 50-night survey for extrasolar giant planets.
It is hoped, of course, that these future surveys will produce actual detections,
not just more null results, which when considered alongside the targets that were
not found to harbor planets, should continue to constrain parameter space on the
distribution of outer extrasolar giant planets.
116
Another direct imaging survey for giant planets has recently been completed,
searching for companions to 79 young, nearby stars: the Gemini Deep Planet Survey (Lafrenière et al., 2007). For completeness, we run an extra set of simulations
to compare our results to theirs. Lafrenière et al. (2007) consider the case of planets with masses between 0.5 and 13 MJup , governed by a power law of index -1.2
(quite similar to our value of -1.16), and with a power law of index -1 for semimajor axis. They then set an upper limit on the planet fraction in three ranges of
semi-major axis: 28% for 10-25 AU, 13% for 25-50 AU, and 9.3% for 50-200 AU,
all at the 95% confidence level, using the models of Baraffe et al. (2003). Adopting these same simulation parameters, we find upper limits on planet fractions
of 37%, 24%, and 28%, respectively. We attribute our somewhat lower sensitivity
to the increased number of stars in the Lafrenière et al. (2007) survey, as well as
their increased field of view (9” compared to the 2.2” for SDI), which makes their
method better-suited to detecting planets at the very large orbital radii of the last
two bins. Also, the Lafrenière et al. (2007) survey was more consciously focused
on closer stars: all 85 of their target stars are within 35 parsecs, 18 of our 60 stars
are beyond 35 pc. The overall results of both our work and that of Lafrenière et al.
(2007), however, are in good agreement for the case of planets in shorter orbits:
for example, we reach the same upper limits as Lafrenière et al. (2007) reached
at the 95% confidence level, if we degrade our confidence level to 89% for 10-25
AU, 80% for 25-50 AU, and 63% for 50-200 AU. Hence the conclusions from both
works are the same: giant planets are rare at large separations.
We also note that the value of the planet fraction in these intervals can be estimated from the uniform detectability sample of Fischer & Valenti (2005), which
gives 5.5% of stars having planets within 2.5 AU, and more massive than 1.6
MJup . When using a model of planet mass with index -1.2, and semi-major axis
117
power law index -1, as above, the planet fractions for the semi-major axis bins
10-25 AU, 25-50 AU, and 50-200 AU become 2.1%, 1.6%, and 3.2%, respectively.
It should be noted that the samples of Fischer & Valenti (2005) and Lafrenière
et al. (2007) (as well as the one discussed in this Chapter, for that matter) are not
directly comparable, as the Fischer & Valenti (2005) sample is made up primarily
of older stars (>1 Gyr), and exclusively FGK spectral types, whereas the sample of Lafrenière et al. (2007) is made up of younger stars, and contains stars of
M spectral type. These two effects push the planet fractions in opposite directions: younger stars are more likely to be metal-rich2 , and so have a higher planet
fraction (Fischer & Valenti, 2005), whereas M stars are less likely to harbor giant
planets (Johnson et al., 2007). Overall, then, the upper limits from both works
are consistent with the predictions from radial velocity detections, with respect
to this particular model of planet populations.
Finally, we note that although four of our target stars do, in fact, harbor extrasolar planets (HIP 30034 (AB Pic) has a wide (5.5”) companion at the planet/brown
dwarf boundary, while Eps Eri, HD 81040, and HD 128311 all have radial velocity
planets), our survey can be regarded as a null result. Even though these planets
were orbiting our target stars, we were unable to detect them, as they were either outside our field of view (as with AB Pic B), or too faint (due to their host
star’s age) to be detected from our images, as was the case with the radial velocity planets. The motivation behind our simulations is to find what population of
hidden (undetected) planets are consistent with a lack of planet detections, and
the knowledge of existing planets around some target stars does not change this.
2
Although Table 1 of Lafrenière et al. (2007) gives the metallicity for most of their target stars,
which give a median value of [Fe/H] = 0, more metal poor than the overall sample of Fischer &
Valenti (2005) by ∼0.1 dex, it is notoriously difficult to make accurate metallicity measurements
of young stars. As a result, it is likely that these reported metallicities are systematically lower
than their actual values.
118
4.6 Conclusion
Even without detecting extrasolar planets from our surveys, the null results provide a basis for setting limits on the allowable distribution of giant planets. From
our data, using the planet models of Burrows et al. (2003), we can exclude any
model for planet distributions where more than 20% of stars of all spectral types
have planets more massive than 4MJup between 20 and 100 AU, at 95% confidence
(this upper limit becomes 8% of stars with such planets at the 68% confidence
level). If we create simple models of planet populations with the semi-major axis
distribution governed by the power law
dN
da
∝ aα , and mass by
dN
dM
∝ M −1.16 , we
can exclude giant planets in the case of α = 0 beyond 18 AU, and with α = −0.5
beyond 48 AU. Using the distribution of Cumming et al. (2008), based on radial
velocity observations, with α = −0.61, there can be no giant planets beyond 75
AU. All these statements are at the 95% confidence level; for the 68% confidence
level, these upper limits for the outer cut-offs of giant planets become 12 AU, 23
AU, and 29 AU, for power law indices of 0, -0.5, and -0.61, respectively. With our
data, the most we can say of the models of Ida & Lin (2004) is that they are consistent with our observations at the ∼50% confidence level. We again note that these
conclusions are highly dependent on the models of planet luminosity as a function of the planet’s age and mass. Additionally, we caution that since our sample
differs from the volume-limited sample of Fischer & Valenti (2005), known correlations of planet fraction with stellar mass and metallicity will likely shift our
results from the values reported here. Nevertheless, the analysis presented here is
an important first step in constraining the populations of extrasolar giant planets.
119
4.7 Acknowledgments
We thank the anonymous referee for many helpful comments that have improved
the quality of this work. We thank Eric Mamajek for a great deal of assistance
both in selecting targets for the SDI survey, and determining the ages of our target stars. We thank Remi Soummer for the idea of presenting sensitivity to planets as a grid of mass and semi-major axis points, and we thank Daniel Apai for
presenting the idea of constructing a grid of semi-major axis power law indices
and cut-offs. We also thank Thomas Henning and Wolfgang Brandner for their
important work in the original data gathering, and helpful comments over the
course of the project. This work makes use of data from the European Southern
Observatory, under Program 70.C - 0777D, 70.C - 0777E, 71.C-0029A, 74.C-0548,
74.C-0549, and 76.C-0094. Observations reported here were obtained at the MMT
Observatory, a joint facility of the University of Arizona and the Smithsonian
Institution. This publication makes use of data products from the Two Micron
All-Sky Survey, which is a joint project of the University of Massachusetts and
the Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation. This research has made use of the SIMBAD database, operated at CDS, Strasburg, France. ELN is supported by a Michelson Fellowship.
LMC is supported by an NSF CAREER award and the NASA Origins of the Solar
System program. BAB is supported by the NASA GSRP grant NNG04GN95H
and NASA Origins grant NNG05GL71G.
120
C HAPTER 5
A UNIFORM ANALYSIS OF 118 STARS WITH HIGH-CONTRAST
IMAGING: LONG PERIOD EXTRASOLAR GIANT PLANETS ARE RARE
AROUND SUN-LIKE STARS
We expand on the results of Nielsen et al. (2008), using the null result for giant
extrasolar planets around the 118 target stars from the VLT NACO H and Ks
band planet search (Masciadri et al., 2005), the VLT and MMT Simultaneous Differential Imaging (SDI) survey (Biller et al., 2007), and the Gemini Deep Planet
Survey (Lafrenière et al., 2007) to set constraints on the population of giant extrasolar planets. Our analysis is extended to include the planet luminosity models
of Fortney et al. (2008), as well as the correlation between stellar mass and frequency of giant planets found by Johnson et al. (2007). Doubling the sample size
of FGKM stars strengthens our conclusions: a model for extrasolar giant planets with power-laws for mass and semi-major axis as given by Cumming et al.
(2008) cannot, with 95% confidence, have planets beyond 65 AU, compared to
the value of 94 AU reported in Nielsen et al. (2008), using the models of Baraffe
et al. (2003). When the Johnson et al. (2007) correction for stellar mass (which
gives fewer Jupiter-mass companions to M stars with respect to solar-type stars)
is applied, however, this limit moves out to 82 AU. For the relatively new Fortney
et al. (2008) models, which predict fainter planets across most of parameter space,
these upper limits, with and without a correction for stellar mass, are 180 and 230
AU, respectively.
This Chapter is based on material originally published in Nielsen & Close
(2010).
121
5.1 Introduction
There are currently close to 300 extrasolar planets known, most detected by the
radial velocity method (Mayor & Udry, 2008; Marcy et al., 2008). These planets
have provided a great deal of information on the distribution of giant planets
in short period orbits. The likelihood of a star harboring a close-in giant planet
increases with the metal abundance of the parent star (Fischer & Valenti, 2005;
Santos et al., 2004), and power laws were found to accurately represent the distributions of mass and semi-major axis of exoplanets (Cumming et al., 2008). While
radial velocity surveys have moved on to discovering and building up statistics
on smaller Neptune-mass planets, direct imaging surveys continue to struggle to
reach even the highest mass planets.
Many observing campaigns have been conducted in the last decade to detect
and characterize planets through direct imaging, especially aimed at young target stars, when the self-luminosity of hosted planets is large enough to overcome
the glare of the parent star. Improvements in adaptive optics and instrumentation designed solely to detect planets, as well as specialized observing techniques,
have improved the contrasts achievable close to the target star. This has allowed
a large increase in sensitivity to planets, and resulted in the discovery of several
planetary-mass (<13 MJup ) objects, including companions to 2MASS 1207-3932
(Chauvin et al., 2004), HIP 30034 (AB Pic) (Chauvin et al., 2005), Oph 1622 (Close
et al., 2007; Brandeker et al., 2006; Luhman et al., 2007), and DH Tau (Itoh et al.,
2005). These objects were discovered with projected separations of 42, 260, 243,
and 330 AU, respectively. Few, if any, of these wide companions (>200 AU for objects found around stars) are likely to have formed in the primordial circumstellar
disk of the primary.
Recently there have been exciting discoveries of planetary-mass objects around
122
the higher-mass A stars: HR 8799, Fomalhaut, and β Pic (Marois et al., 2008; Kalas
et al., 2008; Lagrange et al., 2009). In the case of the triple planet system HR 8799,
we know that the largest separation planet (HR 8799 b, with a projected separation of 68 AU) has the same parallax as the primary (Close & Males, 2009) and
so it (and very likely HR 8799 c and d) formed together around the A5 star HR
8799. While this is an amazing system, in this study we concentrate on lower
mass stars, more similar to the Sun.
Nielsen et al. (2008) presented null results from the direct imaging surveys
for extrasolar giant planets of Masciadri et al. (2005) and Biller et al. (2007), using the contrast curves for each of 60 unique target stars to set constraints on
the populations of extrasolar planets. We concluded that extrasolar giant planets are rare at large separations (>60 AU). Just prior to the publication of our
work, Lafrenière et al. (2007) published the null results from the Gemini Deep
Planet Survey (GDPS) for 85 stars, reaching conclusions very similar to ours. In
this Chapter, we combine the samples from these three surveys, to improve the
statistical constraints we can place on extrasolar giant planet populations.
Also since these past publications, two papers directly relevant to this analysis
have been published, Johnson et al. (2007) compared radial velocity target stars
of different masses, and found that less massive stars have a lower likelihood of
hosting a giant planet (>0.8 MJup ). Since direct imaging surveys lean heavily on
the M stars in their samples (as these are intrinsically fainter, making the detection of close-in planets easier), we attempt here to estimate the corresponding
decrease in the strength of earlier null results. Also, a new set of planet luminosity models has been published by Fortney et al. (2008), which differs from the
popular “hot start” models of Burrows et al. (2003) and Baraffe et al. (2003) which
had been previously utilized in such work. These new models are based heavily
123
on the “core accretion” model of planet formation, and tend to predict consistently fainter fluxes for giant planets, especially at the youngest ages and largest
planet masses. In addition to significantly enlarging the sample, this Chapter
takes into account the stellar mass dependence of planet frequency, and the new
core accretion models of Fortney et al. (2008), to present more realistic constraints
on the distribution of extrasolar giant planets around Sun-like stars.
5.2 Observations
5.2.1 VLT NACO H and Ks Imaging
Masciadri et al. (2005) carried out a survey of 28 young, nearby, late-type stars
with the NACO adaptive optics system at the 8.2 meter Very Large Telescope
(VLT). These observations have exposure times of order 30 minutes, with stars
being observed in the H or Ks bands. For the 22 stars used (see Section 5.2.4)
from the VLT NACO survey of Masciadri et al. (2005), the median target star is a
12 Myr old K7 star at 30 pc.
5.2.2 VLT NACO and MMT SDI
A survey of 54 young, nearby stars of a variety of spectral types (between A and
M) was conducted between 2003 and 2005, with the results reported in Biller et al.
(2007). This second survey used the Simultaneous Differential Imager (SDI) at
the 6.5 meter MMT and the 8 meter VLT, an adaptive optics observational mode
that allows higher contrasts by imaging simultaneously in narrow wavelength
regions surrounding the 1.6 µm methane feature seen in cool brown dwarfs and
expected in extrasolar planets (Lenzen et al., 2004; Close et al., 2005) (Swain et al.
(2008) have recently detected methane in the atmosphere of the transiting extrasolar planet HD 189733b). This allows the light from a hypothetical companion
planet to be more easily distinguishable from the speckle noise floor (uncorrected
124
starlight), as the two will have very different spectral signatures in this region.
This translates to higher sensitivity at smaller separations than the observations
of Masciadri et al. (2005), which were conducted before the VLT SDI device was
commissioned (see Fig. 14 of Biller et al. (2007) for a more detailed comparison
of the two surveys). For most of these SDI targets, the star was observed for
a total of 40 minutes of integration time, which includes a 33 degree roll in the
telescope’s rotation angle, in order to separate super speckles–which are created
within the instrument, and so will not rotate–from a physical companion, which
will rotate on the sky (Biller et al., 2006) (this technique has been previously used
frequently with HST observations, e.g. Schneider & Silverstone (2003)). The 50
stars used from the Biller et al. (2007) SDI survey have a median age, distance,
and spectral type of 70 Myr, 24 pc, and K1, respectively.
5.2.3 Gemini Deep Planet Survey
At about the same time as the Biller et al. (2007) SDI survey, a direct imaging
campaign was underway from the Gemini North telescope using the Altair AO
system and NIRI camera, imaging in a narrow-band H filter with transmission
between 1.54-1.65 µm. The observations were done using the Angular Differential Imaging (ADI) technique, which leaves the Cassegrain instrument rotator off
during a sequence of exposures on the star, so that instrumental effects like super speckles will stay fixed, while physical companions (like planets) will rotate
throughout the observation (Liu, 2004; Marois et al., 2006; Lafrenière et al., 2007).
This technique is most effective at producing high contrasts at larger star-planet
angular separations, with the contrasts achieved exceeding those with SDI (Biller
et al., 2007) beyond ∼0.7”. For the 71 of the 85 stars from the GDPS survey of
Lafrenière et al. (2007) which we consider here, the median target star is a K0 star
at a distance of 22 pc, with an age of 250 Myr. Hence, the target stars of this sur-
125
vey are somewhat closer and older, whereas the southern VLT SDI survey was
focused on more distant, though younger, stars.
5.2.4 Target Stars
Between the three surveys listed above, our analysis considers 118 distinct target
stars, with some overlap between surveys. General properties of the target stars,
including name, position, distance, spectral type, age, fluxes, and observation
method are given in Table 5.1. We attempt to derive ages in a uniform manner
for all target stars, using the same method as in Nielsen et al. (2008). If the star
is a member of a known moving group, the age of that group is adopted as the
age of the star. We limit moving group identifications to the well-studied and
established groups AB Dor, Her/Lyr, Tuc/Hor, β Pic, and TW Hya. Membership
in more controversial associations, such as the Local Association and IC 2391
(e.g. Fernández et al. (2008)), are not adopted here. If the star is not a member
of a group, but has a measured value of the calcium emission indicator R’HK
and a measurement of the equivalent width of the lithium absorption at 6708
Å, the average of the ages from the two methods is used. If only one of these
two spectral age indicators is available, the age from that measurement is used.
If a star from any of the three surveys has none of these three sources for an age
estimate, it is simply not used in this work. As a result, 6 stars from the Masciadri
et al. (2005) survey, 1 star from the Biller et al. (2007) survey, and 14 stars from the
Lafrenière et al. (2007) survey were dropped.
126
Table 5.1. Target Stars
Target
RA1
Dec1
Distance (pc)2
Sp. Type
Age (Myr)
V1
H3
Ks3
Obs. Mode4
Biller et al. (2007)
HIP 1481
00 18 26.1
-63 28 39.0
40.95
F8/G0V
30
7.46
6.25
6.15
VLT SDI
HD 8558
01 23 21.2
-57 28 50.7
49.29
G6V
30
8.54
6.95
6.85
VLT SDI
HD 9054
01 28 08.7
-52 38 19.2
37.15
K1V
30
9.35
6.94
6.83
VLT SDI
HIP 9141
01 57 48.9
-21 54 05.0
42.35
G3/G5V
30
8.11
6.55
6.47
VLT SDI
BD+05 378
02 41 25.9
+05 59 18.4
40.54
M0
12
10.20
7.23
7.07
VLT SDI
HD 17925
02 52 32.1
-12 46 11.0
10.38
K1V
200
6.05
4.23
4.17
VLT SDI/GDPS
Eps Eri
03 32 55.8
-09 27 29.7
3.22
K2V
1100
3.73
1.88
1.78
VLT SDI/GDPS
V577 Per A
03 33 13.5
+46 15 26.5
33.77
G5IV/V
70
8.35
6.46
6.37
MMT SDI
GJ 174
04 41 18.9
+20 54 05.4
13.49
K3V
280
7.98
5.31
5.15
VLT SDI
GJ 182
04 59 34.8
+01 47 00.7
26.67
M1Ve
12
10.10
6.45
6.26
VLT SDI/Ks/GDPS
HIP 23309
05 00 47.1
-57 15 25.5
26.26
M0/1
12
10.09
6.43
6.24
VLT SDI/Ks
AB Dor
05 28 44.8
-65 26 54.9
14.94
K2Vk
70
6.93
4.84
4.69
VLT SDI
UY Pic
05 36 56.8
-47 57 52.9
23.87
K0V
70
7.95
5.93
5.81
VLT SDI
AO Men
06 18 28.2
-72 02 41.4
38.48
K6/7
12
10.99
6.98
6.81
VLT SDI/Ks
HIP 30030
06 19 08.1
-03 26 20.0
52.36
G0V
30
8.00
6.59
6.55
MMT SDI
HIP 30034
06 19 12.9
-58 03 16.0
45.52
K2V
30
9.10
7.09
6.98
VLT SDI
HD 45270
06 22 30.9
-60 13 07.1
23.50
G1V
70
6.50
5.16
5.05
VLT SDI
HD 48189 A
06 38 00.4
-61 32 00.2
21.67
G1/G2V
70
6.15
4.75
4.54
VLT SDI
pi01 UMa
08 39 11.7
+65 01 15.3
14.27
G1.5V
200
5.63
4.28
4.17
MMT SDI/GDPS
HD 81040
09 23 47.1
+20 21 52.0
32.56
G0V
2500
7.74
6.27
6.16
MMT SDI
LQ Hya
09 32 25.6
-11 11 04.7
18.34
K0V
13
7.82
5.60
5.45
MMT/VLT SDI/Ks/GDPS
DX Leo
09 32 43.7
+26 59 18.7
17.75
K0V
200
7.01
5.24
5.12
MMT/VLT SDI/GDPS
HD 92945
10 43 28.3
-29 03 51.4
21.57
K1V
70
7.76
5.77
5.66
VLT SDI/GDPS
GJ 417
11 12 32.4
+35 48 50.7
21.72
G0V
200
6.41
5.02
4.96
MMT SDI/GDPS
TWA 14
11 13 26.5
-45 23 43.0
46.005
M0
10
13.00
8.73
8.49
VLT SDI
TWA 25
12 15 30.8
-39 48 42.0
44.005
M0
10
11.40
7.50
7.31
VLT SDI
RXJ1224.8-7503
12 24 47.3
-75 03 09.4
24.17
K2
16
10.51
7.84
7.71
VLT SDI
HD 114613
13 12 03.2
-37 48 10.9
20.48
G3V
8800
4.85
3.35
3.30
VLT SDI
HD 128311
14 36 00.6
+09 44 47.5
16.57
K0
630
7.51
5.30
5.14
MMT SDI
EK Dra
14 39 00.2
+64 17 30.0
33.94
G0
70
7.60
6.01
5.91
MMT SDI/GDPS
HD 135363
15 07 56.3
+76 12 02.7
29.44
G5V
3
8.72
6.33
6.19
MMT SDI/GDPS
KW Lup
15 45 47.6
-30 20 55.7
40.92
K2V
2
9.37
6.64
6.46
VLT SDI
HD 155555 AB
17 17 25.5
-66 57 04.0
30.03
G5IV
12
7.20
4.91
4.70
VLT SDI/Ks
HD 155555 C
17 17 27.7
-66 57 00.0
30.03
M4.5
12
12.70
7.92
7.63
VLT SDI/Ks
HD 166435
18 09 21.4
+29 57 06.2
25.24
G0
110
6.85
5.39
5.32
MMT SDI
HD 172555 A6
18 45 26.9
-64 52 16.5
29.23
A5IV/V
12
4.80
4.25
4.30
VLT SDI
CD -64 1208
18 45 37.0
-64 51 44.6
34.21
K7
12
10.12
6.32
6.10
VLT SDI/Ks
HD 181321
19 21 29.8
-34 59 00.5
20.86
G1/G2V
160
6.48
5.05
4.93
VLT SDI
HD 186704
19 45 57.3
+04 14 54.6
30.26
G0
210
7.03
5.62
5.52
MMT SDI
GJ 799B
20 41 51.1
-32 26 09.0
10.22
M4.5e
12
11.00
5.20
-99.00
VLT SDI/Ks
GJ 799A
20 41 51.2
-32 26 06.6
10.22
M4.5e
12
10.25
5.20
4.94
VLT SDI/Ks
GJ 803
20 45 09.5
-31 20 27.1
9.94
M0Ve
12
8.81
4.83
4.53
VLT SDI/Ks/GDPS
HD 201091
21 06 53.9
+38 44 57.9
3.48
K5Ve
2000
5.21
2.54
2.25
MMT SDI
Eps Indi A
22 03 21.7
-56 47 09.5
3.63
K5Ve
4000
4.69
2.35
2.24
VLT SDI
127
Table 5.1—Continued
Target
RA1
Dec1
Distance (pc)2
Sp. Type
Age (Myr)
V1
H3
Ks3
Obs. Mode4
VLT SDI
GJ 862
22 29 15.2
-30 01 06.4
15.45
K5V
6300
7.65
5.28
5.11
HIP 112312 A
22 44 57.8
-33 15 01.0
23.61
M4e
12
12.20
7.15
6.93
VLT SDI
HD 224228
23 56 10.7
-39 03 08.4
22.08
K3V
70
8.20
6.01
5.91
VLT SDI
HIP 2729
00 34 51.2
-61 54 58
45.91
K5V
30
9.56
6.72
6.53
VLT Ks
BD +2 1729
07 39 23.0
02 11 01
14.87
K7
200
9.82
6.09
5.87
VLT H/GDPS
TWA 6
10 18 28.8
-31 50 02
77.005
K7
10
11.62
8.18
8.04
VLT Ks
BD +1 2447
10 28 55.5
00 50 28
7.23
M2
70
9.63
5.61
5.31
VLT H/GDPS
TWA 8A
11 32 41.5
-26 51 55
21.005
M2
10
12.10
7.66
7.43
VLT Ks
TWA 8B
11 32 41.5
-26 51 55
21.005
M5
10
15.20
9.28
9.01
VLT Ks
TWA 9A
11 48 24.2
-37 28 49
50.33
K5
10
11.26
8.03
7.85
VLT Ks
TWA 9B
11 48 24.2
-37 28 49
50.33
M1
10
14.10
9.38
9.15
VLT Ks
SAO 252852
14 42 28.1
-64 58 43
16.407
K5V
200
8.47
5.69
5.51
VLT H
V343 Nor
15 38 57.6
-57 42 27
39.76
K0V
12
8.14
5.99
5.85
VLT Ks
PZ Tel
18 53 05.9
-50 10 50
49.65
K0Vp
12
8.42
6.49
6.37
VLT Ks
BD-17 6128
20 56 02.7
-17 10 54
47.70
K7
12
10.60
7.25
7.04
VLT Ks
HD 166
00 06 36.7839
+29 01 17.406
13.70
K0V
200
6.13
4.63
4.31
GDPS
HD 691
00 11 22.4380
+30 26 58.470
34.10
K0V
260
7.96
6.26
6.18
GDPS
HD 1405
00 18 20.890
+30 57 22.23
30.60
K2V
70
8.60
6.51
6.39
GDPS
HD 5996
01 02 57.2224
+69 13 37.415
25.80
G5V
440
7.67
5.98
5.90
GDPS
HD 9540
01 33 15.8087
-24 10 40.662
19.50
K0V
2900
6.96
5.27
5.16
GDPS
HD 10008
01 37 35.4661
-06 45 37.525
23.60
G5V
200
7.66
5.90
5.75
GDPS
HD 14802
02 22 32.5468
-23 48 58.774
21.90
G0V
5200
5.19
3.71
3.74
GDPS
HD 16765
02 41 13.9985
-00 41 44.351
21.60
F7IV
290
5.71
4.64
4.51
GDPS
HD 17190
02 46 15.2071
+25 38 59.636
25.70
K1IV
4300
7.81
6.00
5.87
GDPS
HD 17382
02 48 09.1429
+27 04 07.075
22.40
K1V
430
7.62
5.69
5.61
GDPS
HD 18803
03 02 26.0271
+26 36 33.263
21.20
G8V
4400
6.72
5.02
4.95
GDPS
HD 19994
03 12 46.4365
-01 11 45.964
22.40
F8V
6200
5.06
3.77
3.75
GDPS
HD 20367
03 17 40.0461
+31 07 37.372
27.10
G0V
380
6.41
5.12
5.04
GDPS
Masciadri et al. (2005)
Lafrenière et al. (2007)
2E 759
03 20 49.50
-19 16 10.0
27.00
K7V
200
10.26
7.66
7.53
GDPS
HIP 17695
03 47 23.3451
-01 58 19.927
16.30
M3e
70
11.59
7.17
6.93
GDPS
HD 25457
04 02 36.7449
-00 16 08.123
19.20
F5V
70
5.38
4.34
4.18
GDPS
HD 283750
04 36 48.2425
+27 07 55.897
17.90
K2
300
8.42
5.40
5.24
GDPS
HD 30652
04 49 50.4106
+06 57 40.592
8.00
F6V
4500
3.19
1.76
1.60
GDPS
HD 75332
08 50 32.2234
+33 17 06.189
28.70
F7V
270
6.22
5.03
4.96
GDPS
HD 77407
09 03 27.0820
+37 50 27.520
30.10
G0
120
7.10
5.53
5.44
GDPS
HD 78141
09 07 18.0765
+22 52 21.566
21.40
K0
270
7.99
5.92
5.78
GDPS
HD 90905
10 29 42.2296
+01 29 28.025
31.60
G0V
230
6.90
5.60
5.52
GDPS
HD 91901
10 36 30.7915
-13 50 35.817
31.60
K2V
1000
8.75
6.64
6.57
GDPS
HD 93528
10 47 31.1553
-22 20 52.927
34.90
K1V
310
8.36
6.56
6.51
GDPS
HIP 53020
10 50 52.0645
+06 48 29.336
5.60
M4
200
11.66
6.71
6.37
GDPS
HD 96064
11 04 41.4733
-04 13 15.924
24.60
G8V
250
8.41
5.90
5.80
GDPS
HD 102392
11 47 03.8343
-11 49 26.573
24.60
K4.5V
3400
9.05
6.36
6.19
GDPS
HD 105631
12 09 37.2563
+40 15 07.399
24.30
K0V
1500
8.26
5.70
5.60
GDPS
128
In order to determine ages from the R’HK value, we utilize the polynomial fit
derived by Mamajek & Hillenbrand (2008). The authors derive their relation from
R’HK values of young clusters, and find a precision of 0.2 dex for ages derived
from this relation.
For lithium values, we compare the equivalent width of the 6707 Å lithium
line and effective temperature of the star to a set of young stellar clusters. For
each cluster (NGC 2264 - 3 Myr (Soderblom et al., 1999), IC 2602 - 50 Myr (Randich
et al., 2001), Pleiades - 125 Myr (Soderblom et al., 1993a), M34 - 250 Myr (Jones
et al., 1997), Ursa Majoris - 300 Myr (Soderblom et al., 1993b), M67 - 5200 Myr
(Jones et al., 1999)), the mean lithium equivalent width is fit as a function of effective temperature. Then, for our target stars, we interpolate between the fits to
each cluster for that star’s effective temperature, and the lithium value gives us
the age (E. Mamajek private communication).
For target stars with both a lithium and an R’HK age measurement, the median scatter between the two is a factor of 3. When we consider stars in our target
list that belong to a single moving group (e.g. AB Dor or β Pic), and compute
their ages using only the lithium or R’HK method (that is, we temporarily ignore
their membership in a group), we find the scatter in the computed age, between
members of the same moving group, to also be about a factor of 3. This suggests that the noise in our age measurements is primarily astrophysical in nature.
While finding a precise age for any single target star is notoriously difficult, our
hope is that by using a large sample of stars the individual errors will average
out of our final results.
129
Table 5.1—Continued
RA1
Dec1
Distance (pc)2
Sp. Type
Age (Myr)
V1
H3
Ks3
Obs. Mode4
HD 107146
12 19 06.5015
+16 32 53.869
28.50
G2V
190
7.07
5.61
5.54
GDPS
HD 108767 B
12 29 50.908
-16 31 14.99
26.90
K2V
140
8.51
6.37
6.24
GDPS
HD 109085
12 32 04.2270
-16 11 45.627
18.20
F2V
100
4.31
3.37
3.37
GDPS
Target
BD +60 1417
12 43 33.2724
+60 00 52.656
17.70
K0
270
9.40
7.36
7.29
GDPS
HD 111395
12 48 47.0484
+24 50 24.813
17.20
G5V
1000
6.31
4.70
4.64
GDPS
HD 113449
13 03 49.6555
-05 09 42.524
22.10
K1V
70
7.69
5.67
5.51
GDPS
HD 116956
13 25 45.5321
+56 58 13.776
21.90
G9V
710
7.29
5.48
5.41
GDPS
HD 118100
13 34 43.2057
-08 20 31.333
19.80
K4.5V
280
9.31
6.31
6.12
GDPS
HD 124106
14 11 46.1709
-12 36 42.358
23.10
K1V
1700
7.92
5.95
5.86
GDPS
HD 130004
14 45 24.1821
+13 50 46.734
19.50
K2.5V
5100
7.60
5.67
5.61
GDPS
HD 130322
14 47 32.7269
-00 16 53.314
29.80
KOIII
2900
8.05
6.32
6.23
GDPS
HD 130948
14 50 15.8112
+23 54 42.639
17.90
G2V
420
5.88
4.69
4.46
GDPS
HD 139813
15 29 23.5924
+80 27 00.961
21.70
G5
270
7.31
5.56
5.45
GDPS
HD 141272
15 48 09.4630
+01 34 18.262
21.30
G9V
280
7.44
5.61
5.50
GDPS
HIP 81084
16 33 41.6081
-09 33 11.954
31.93
K9Vkee
70
11.29
7.78
7.55
GDPS
HD 160934
17 38 39.6261
+61 14 16.125
24.54
K7
70
10.18
7.00
6.81
GDPS
GDPS
HD 166181
18 08 16.030
+29 41 28.12
32.58
G5V
60
7.70
5.61
5.61
HD 167605
18 09 55.5001
+69 40 49.788
30.96
K2V
500
8.60
6.45
6.33
GDPS
HD 187748
19 48 15.4478
+59 25 22.446
28.37
G0
140
6.66
5.32
5.26
GDPS
HD 201651
21 06 56.3893
+69 40 28.548
32.84
K0
6800
8.20
6.41
6.34
GDPS
HD 202575
21 16 32.4674
+09 23 37.772
16.17
K3V
700
7.91
5.53
5.39
GDPS
HIP 106231
21 31 01.7137
+23 20 07.374
25.06
K3Vke
70
9.24
6.52
6.38
GDPS
HD 206860
21 44 31.3299
+14 46 18.981
18.39
G0VCH-0.5
200
6.00
4.60
4.56
GDPS
HD 208313
21 54 45.0401
+32 19 42.851
20.32
K2V
6400
7.78
5.68
5.59
GDPS
V383 Lac
22 20 07.0258
+49 30 11.763
10.68
K0
40
8.57
6.58
6.51
GDPS
HD 213845
22 34 41.6369
-20 42 29.577
22.74
F5V
200
5.20
4.27
4.33
GDPS
HIP 114066
23 06 04.8428
+63 55 34.359
24.94
M0
70
10.87
7.17
6.98
GDPS
HD 220140
23 19 26.6320
+79 00 12.666
19.74
K2Vk
85
7.73
5.51
5.40
GDPS
HD 221503
23 32 49.3999
-16 50 44.307
13.95
K6Vk
550
8.60
5.61
5.47
GDPS
HIP 117410
23 48 25.6931
-12 59 14.849
27.06
K5Vke
55
9.57
6.49
6.29
GDPS
1
from the CDS Simbad service
2
derived from the Hipparcos survey Perryman et al. (1997)
3
from the 2MASS Survey Cutri et al. (2003)
4
In cases where target stars were observed by multiple surveys, the star is listed only in the first section of this table where it appears, either
in the Biller et al. (2007) or Masciadri et al. (2005) section, with Observing Mode given as “VLT SDI/Ks” or “VLT H/GDPS,” for example.
5
Distance from Song et al. (2003)
6
As this is the only star in our sample earlier than F2, we consider this work to be a survey of FGKM stars.
7
Distance from Zuckerman et al. (2001a)
130
Table 5.2. Age Determination for Target Stars
Sp. Type∗
Li EW (mÅ)∗
Li Age (Myr)
R’HK ∗
HIP 1481
F8/G0V2
1293
100
-4.3604
HD 8558
G6V2
2055
13
HD 9054
K1V2
1705
160
HIP 9141
G3/G5V7
1818
13
Target
R’HK Age++ Group Membership1
Group Age1
Adopted Age +++
Biller et al. (2007)
BD+05 378
M09
HD 17925
K1V7
Eps Eri
K2V10
V577 Per A
G5IV/V
1948
11
219
11
50
-4.2366
221
100
-4.3576
216
-4.5986
1129+
3
Tuc/Hor
30
30
Tuc/Hor
30
30
Tuc/Hor
30
30
Tuc/Hor
30
30
β Pic
12
12
Her/Lyr
200
200
AB Dor
70
1100
458
280
GJ 182
M1Ve14
28015
12
HIP 23309
M0/116
29416
12
-3.8936
AB Dor
K2Vk17
2678
10
-3.8806
UY Pic
K0V18
2638
10
-4.2346
AO Men
K6/716
35716
6
-3.7556
HIP 30030
G0V19
2198
2
HIP 30034
K2V2
HD 45270
G1V2
1495
90
-4.3786
254
G1/G2V2
1458
25
-4.2686
105
pi01 UMa
G1.5V20
1358
100
-4.40021
300
HD 81040
G0V20
2422
2500
LQ Hya
K0V20
2478
13
DX Leo
K0V20
1808
100
-4.2346
78
HD 92945
K1V20
1388
160
-4.3936
285
AB Dor
70
70
GJ 417
G0V23
7624
250
-4.36813
235
Her/Lyr
200
200
TWA 14
M025
60025
8
TW Hya
10
10
TWA 25
M09
49426
10
TW Hya
10
10
RXJ1224.8-7503
K227
25027
16
G3V28
10029
400
-5.1186
-4.48913
565
-4.10613
<50
HD 48189 A
HD 114613
HD 128311
K020
EK Dra
G030
2128
2
HD 135363
G5V20
2208
3
KW Lup
K2V28
43031
2
HD 155555 AB
G5IV16
2058
6
HD 155555 C
M4.516
HD 166435
G032
HD 172555 A
A5IV/V2
CD -64 1208
K716
58016
5
HD 181321
G1/G2V28
1318
79
HD 186704
G033
-4.06613
70
K3V12
GJ 174
280
12
β Pic
12
12
<50
AB Dor
70
70
78
AB Dor
70
70
β Pic
12
12
Tuc/Hor
30
30
Tuc/Hor
30
30
AB Dor
70
70
AB Dor
70
70
200
2500
13
Her/Lyr
200
200
16
7900
8800
630
AB Dor
70
70
3
2
-3.9656
<50
-4.27021
107
-4.3726
243
-4.35021
205
β Pic
12
β Pic
12
12
12
110
β Pic
12
β Pic
12
12
12
160
210
GJ 799B
M4.5e34
β Pic
12
12
GJ 799A
M4.5e34
β Pic
12
12
GJ 803
M0Ve34
β Pic
12
HD 201091
K5Ve34
-4.70413
2029+
2000
Eps Indi A
K5Ve34
-4.8516
3964+
4000
518
30
12
131
Table 5.2—Continued
Target
Sp. Type∗
GJ 862
K5V34
HIP 112312 A
M4e9
HD 224228
K3V28
Li EW (mÅ)∗
Li Age (Myr)
R’HK ∗
-4.9836
538
630
R’HK Age++ Group Membership1
Group Age1
6280+
-4.4686
Adopted Age
6300
β Pic
12
12
AB Dor
70
70
Masciadri et al. (2005)
HIP 2729
BD +2 1729
K5V2
Tuc/Hor
30
30
K720
Her/Lyr
200
200
TWA 6
K735
BD +1 2447
M236
TWA 8A
M235
53035
3
TW Hya
10
10
TWA 8B
35
56035
3
TW Hya
10
10
M5
56035
3
TW Hya
10
10
AB Dor
70
70
TWA 9A
K535
46035
3
TW Hya
10
10
TWA 9B
M135
48035
3
TW Hya
10
10
SAO 252852
K5V37
Her/Lyr
200
200
V343 Nor
K0V2
30029
5
-4.1596
40
β Pic
12
12
K0Vp18
26738
20
-3.7804
<50
β Pic
12
12
K739
40040
3
β Pic
12
12
Her/Lyr
200
200
AB Dor
70
PZ Tel
BD-17 6128
Lafrenière et al. (2007)
HD 166
K0V41
7442
290
-4.45813
460
HD 691
K0V43
1108
260
-4.38021
260
HD 1405
K2V44
27145
HD 5996
G5V46
-4.45413
440
HD 9540
K0V7
-4.7746
2900
HD 10008
G5V47
10348
280
-4.53013
740
HD 14802
G0V17
5149
4000
-4.9856
6300
HD 16765
F7IV50
7314
270
HD 17190
K1IV51
260
70
440
2900
Her/Lyr
200
200
5200
-4.40013
300
290
-4.87021
4300
4300
HD 17382
K1V51
-4.45021
430
430
HD 18803
G8V52
-4.88021
4400
4400
HD 19994
F8V53
8000
-4.88021
4400
6200
HD 20367
G0V
55
150
-4.50021
610
2E 759
K7V56
HIP 17695
M3e58
HD 25457
HD 283750
1254
113
8
6357
260
F5V59
9160
80
-4.39021
K261
338
300
-4.05713
7500
-4.65021
HD 30652
F6V
62
15
14
380
Her/Lyr
280
200
200
AB Dor
70
70
AB Dor
70
70
300
1500
4500
HD 75332
F7V50
1258
50
-4.47021
500
270
HD 77407
G063
16245
50
-4.34021
190
120
HD 78141
K064
1078
270
1368
80
-4.43021
370
230
-4.4246
360
65
270
HD 90905
G0V
HD 91901
K2V7
766
1000
HD 93528
K1V17
1008
260
HIP 53020
M467
HD 96064
G8V68
-4.37313
250
250
HD 102392
K4.5V17
-4.8116
3400+
3400
HD 105631
K0V69
-4.65021
1500
1500
1000
310
Her/Lyr
1148
250
200
200
+++
132
Table 5.2 gives details on measurements (if available) for each of the three age
determination methods used here, as well as the final adopted age, for each target
star. We also plot our targets in Fig. 5.1, giving the age, distance, and spectral type
(using absolute H magnitude as a proxy) for each star. Overall, for all 118 of the
stars considered in this Chapter, the median target star is a K1 star at a distance
of 24 pc with an age of 160 Myr.
5.3 Monte Carlo Simulations
As in Nielsen et al. (2008) we use Monte Carlo simulations of “fake” planets
around each of the target stars in the three direct imaging surveys considered
here. A large number (104 - 105 , depending on the application) of simulated planets are given random values of eccentricity, viewing angles, and orbital phase
based on the appropriate distributions. Planet mass and semi-major axis are assigned either from a grid (see Section 5.3.3), or from power-law distributions (as
in Section 5.3.4). For graphical representations of the distributions of extrasolar
planet orbital parameters, see Fig. 2, 5, and 6 of Nielsen et al. (2008), and the
discussion therein. For each observation of a given target star, the flux of each
simulated planet is computed based on the planet’s mass and the target star’s
age, using one of three planet models (see Section 5.3.1). The angular separation
between parent star and simulated planet, as well as the flux ratio between planet
and star, are then computed given the distance to the star. These are compared to
the contrast curve for the observation, which give the faintest detectable companion (at the 5σ level) to the star, in the observation band, as a function of angular
separation from the star.
In cases where the same target star is observed in multiple epochs, and sometimes among different surveys (a common occurrence, the 22, 50, and 71 stars we
133
Table 5.2—Continued
Target
HD 107146
Sp. Type∗
Li EW (mÅ)∗
Li Age (Myr)
R’HK ∗
G2V70
1258
180
-4.34021
71
100
F2V17
3773
100
BD +60 1417
K074
968
270
K1V17
HD 116956
68
G9V
190
140
HD 109085
HD 113449
190
Adopted Age +++
140
K2V
G5V52
Group Age1
72
HD 108767 B
HD 111395
175
R’HK Age++ Group Membership1
1428
270
-4.58021
1000
1000
200
-4.34013
190
24
1000
-4.44713
420
710
2515
280
-4.09013
31
AB Dor
70
70
HD 118100
K4.5V68
HD 124106
K1V17
-4.6756
1700
1700
HD 130004
K2.5V68
-4.91913
5100+
5100
HD 130322
KOIII
75
21
2900
2900
HD 130948
G2V52
1168
230
-4.50021
610
420
HD 139813
G576
1198
230
-4.40021
300
270
HD 141272
G9V68
-4.39021
280
HIP 81084
K9Vkee77
-4.2106
HD 160934
K778
4079
280
HD 166181
G5V80
1868
60
60
HD 167605
K2V81
1457
500
500
HD 187748
G063
1148
140
HD 201651
K047
HD 202575
K3V68
HIP 106231
K3Vke
68
HD 206860
G0VCH-0.517
HD 208313
K2V68
V383 Lac
K083
HD 213845
F5V17
-4.780
140
8
280
280
AB Dor
70
70
AB Dor
70
70
140
-5.01021
6800
-4.52213
700+
13
180
-3.906
11082
190
-4.4006
300
-4.98713
6400+
2598
40
-4.5476
830
6800
700
AB Dor
70
70
Her/Lyr
200
200
6400
40
Her/Lyr
200
200
AB Dor
70
70
HIP 114066
M078
HD 220140
K2Vk68
HD 221503
K6Vk17
-4.4866
550+
550
HIP 117410
K5Vke17
-4.1946
55+
55
1
2188
85
-4.07413
85
Group Membership for TWA, β Pic, Tuc/Hor, and AB Dor from Zuckerman & Song (2004), Her/Lyr from López-Santiago et al. (2006). Group Ages
from Zuckerman & Song (2004) (TWA, β Pic, and Tuc/Hor), Nielsen et al. (2005) (AB Dor), and López-Santiago et al. (2006) (Her/Lyr)
∗
Measurement References: 2: Houk & Cowley (1975), 3: Waite et al. (2005), 4: Henry et al. (1996), 5: Torres et al. (2000), 6: Gray et al. (2006b), 7: Houk &
Smith-Moore (1988), 8: Wichmann et al. (2003), 9: Zuckerman & Song (2004), 10: Cowley et al. (1967), 11: Christian & Mathioudakis (2002), 12: Leaton &
Pagel (1960), 13: Gray et al. (2003b), 14: Favata et al. (1995), 15: Favata et al. (1997), 16: Zuckerman et al. (2001a), 17: Gray et al. (2006b), 18: Houk (1978), 19:
Cutispoto et al. (1995), 20: Montes et al. (2001), 21: Wright et al. (2004), 22: Sozzetti et al. (2006), 23: Bidelman (1951), 24: Gaidos et al. (2000), 25: Zuckerman
et al. (2001b), 26: Song et al. (2003), 27: Alcala et al. (1995), 28: Houk (1982), 29: Randich et al. (1993), 30: Gliese & Jahreiß (1979), 31: Neuhauser & Brandner
(1998), 32: Eggen (1996), 33: Abt (1985), 34: Gliese & Jahreiss (1991), 35: Webb et al. (1999), 36: Vyssotsky et al. (1946), 37: Evans (1961), 38: Soderblom et al.
(1998), 39: Nesterov et al. (1995), 40: Mathioudakis et al. (1995), 41: Rufener & Bartholdi (1982), 42: Zboril et al. (1997), 43: Eggen (1962), 44: Ambruster
et al. (1998), 45: Montes et al. (2001a), 46: Helmer et al. (1983), 47: Perryman et al. (1997), 48: López-Santiago et al. (2006), 49: Pasquini et al. (1994), 50:
Cowley (1976), 51: Heard (1956), 52: Harlan & Taylor (1970b), 53: Herbig & Spalding (1955), 54: Israelian et al. (2004), 55: Sato & Kuji (1990), 56: Fleming
et al. (1989), 57: Favata et al. (1993), 58: Appenzeller et al. (1998), 59: Malaroda (1975), 60: Lambert & Reddy (2004), 61: Oswalt et al. (1988), 62: Morgan &
Keenan (1973), 63: Perry (1969), 64: Schwope et al. (2000), 65: Harlan (1974), 66: Strassmeier et al. (2000), 67: Bidelman (1985), 68: Gray et al. (2003b), 69:
Schild (1973), 70: Harlan & Taylor (1970a), 71: Mora et al. (2001), 72: Pallavicini et al. (1992), 73: Mallik et al. (2003), 74: Roeser & Bastian (1988), 75: Upgren
& Staron (1970), 76: Pye et al. (1995), 77: Fan et al. (2006), 78: Reid et al. (1995), 79: Zuckerman et al. (2004), 80: Eggen (1964), 81: Stocke et al. (1991), 82:
Chen et al. (2001), 83: Bowyer et al. (1996)
+
In general, we have only determined Ca R’HK ages for stars with spectral types K1 or earlier, but in the case of these K2-K6 stars, we have only the
R’HK measurement on which to rely for age determination. The calibration of Mt. Wilson S-index to R’HK for K5 stars (B-V ∼ 1.1 mag) has not been
well-defined (Noyes et al. (1984); specifically the photospheric subtraction), and hence applying a R’HK vs. age relation for K5 stars is unlikely to yield
accurate ages.
++
Using Eq. 3 of Mamajek & Hillenbrand (2008) to convert R’HK into age
+++
In general, ages derived from lithium and/or calcium alone are likely accurate to within a factor of ∼2
134
Figure 5.1 The 118 unique stars used in this Chapter, collected from the direct
imaging planet surveys of Masciadri et al. (2005) (squares), Biller et al. (2007)
(circles), and Lafrenière et al. (2007) (Triangles). Table 5.1 gives other properties
of these stars, and Table 5.2 provides details on how the individual ages were
determined. The median target star is a 160 Myr K1 star at 24 pc. The size and
color of the plotting symbols indicates the spectral type of each target star. The
top legend gives the conversion between size and color of the plotting symbol
and spectral type: the color scheme follows the visible spectrum, with early-type
stars represented by large dark purple symbols, while late-type stars are small
red symbols.
135
use in this work would suggest a sample size of 143 target stars, but there are only
118 unique target stars between these three surveys with reliable age estimates),
the additional elapsed time is taken into account. Simulated planets are generated at the earliest epoch as usual, and compared to that contrast curve. Their
parameters are then used again, with orbital phase advanced forward by the time
between observations (often a small effect for the planets to which these surveys
are sensitive, a 30 AU orbit around a solar-type star has a 160 year period, and
the typical time span between observations is at most about 3 years), the fluxes of
the simulated planets are now computed in the new observation band, and compared to the new contrast curve. The process is repeated for each observational
epoch for the given target star, and a simulated planet that is detectable in any
of the observational epochs is considered detectable. Again, Nielsen et al. (2008)
provides more details on these simulations, in particular their Fig. 3, 4, and 7.
5.3.1 Theoretical Models of Giant Planet Fluxes
In order to use the measured contrast curves for each observed target star to determine which simulated planets could be detected, it is necessary to have a conversion from planet mass and age to NIR flux. As in Nielsen et al. (2008), we use
the theoretical models of Burrows et al. (2003) and Baraffe et al. (2003) for the calculation of exoplanet flux, using the mass of each simulated planet and the age
of the host target star, determining the flux density in the filter band (H or Ks)
appropriate for the particular observation. In the cases of the GDPS (Lafrenière
et al., 2007) and SDI (Biller et al., 2007) surveys, where the observation band was
a specialized filter instead of the standard H bandpass, a correction factor is applied (see Section 5.3.2 for details). Though these two “hot start” models provide
basically similar predictions, we perform our calculations with both, as the two
models can predict significantly different NIR fluxes for exoplanets, depending
136
Figure 5.2 A plot of the age and H magnitude of planets, for different masses,
as predicted by the Baraffe et al. (2003) and Burrows et al. (2003) models, represented by the thin blue lines and the thick red lines, respectively. The diamonds
and circles are the H magnitudes given by the models themselves, while the lines
show the interpolation and extrapolations beyond these points that we use when
assigning H magnitudes to the simulated planets. The COND models of Baraffe
et al. (2003) required very little extrapolation to fill the range of parameter space
shown here, while far more extrapolation is required for the Burrows et al. (2003)
models, especially at young ages and small masses.
137
on planet mass and stellar age, as shown in Fig. 5.2.
Since the publication of Nielsen et al. (2008), an additional set of theoretical models has been published by Fortney et al. (2008) for extrasolar planets for
a range of masses and ages. The major difference between these new models
and those from Burrows et al. (2003) and Baraffe et al. (2003) is that the Fortney
et al. (2008) models are based heavily on the “core accretion” theory of planet
formation (e.g. Hubickyj et al. (2005)), where giant planets are formed from an
initial ∼10 M⊕ core accreting gas from the protoplanetary disk. After the brief
luminous accretion phase, these models predict consistently fainter NIR fluxes
than the “hot start” models (until ∼100 Myr to ∼1 Gyr, when the models overlap
nicely, see Fig. 1 of Fortney et al. (2008)), which do not base their initial conditions
on planetary core accretion models. For more detail, consult Figure 8, and Tables
1 and 2, of Fortney et al. (2008).
As is the case with the Burrows et al. (2003) models, the Fortney et al. (2008)
models do not cover the full range of planet parameters we consider here (masses
between 0.5 and 15 MJup , ages from 1 Myr to 10 Gyr), since Fortney et al. (2008)
limit their calculations to planets with Tef f >400K, leaving the consideration of
cooler planets to future work. As a result, we extrapolate the models to masses
below 1 MJup and above 10 MJup , and at larger ages (the age a planet cools below
400 K depends on the mass of the planet, ∼30 Myr for a 1 MJup planet, and ∼1
Gyr for a 10 MJup planet). While not an ideal solution, as we are ignoring the
complicated physical processes taking places in planets as we cross these boundaries in exchange for simple relationships between NIR fluxes and age and mass,
we believe that this method provides a good overall picture of the fluxes of extrasolar planets as predicted by the Fortney et al. (2008) models. In Fig. 5.2, we
plot the initial gridpoints of both the Baraffe et al. (2003) and Burrows et al. (2003)
138
Figure 5.3 As with Fig. 5.2, a plot of the predicted fluxes of extrasolar planets
of Baraffe et al. (2003), again represented by blue lines and open diamonds, this
time plotted against the core accretion models of Fortney et al. (2008), the red
lines with filled circles. In order to fill the parameter space of planet mass and
stellar age we consider, it is necessary to extrapolate the Fortney et al. (2008) H
magnitudes beyond the grid points of the models themselves, especially at larger
ages and smaller masses.
139
models, as well as our extrapolations to the full range of parameter space. A similar plot comparing the predicted fluxes for the Baraffe et al. (2003) and Fortney
et al. (2008) models is shown in Fig. 5.3. Our effort to map additional areas of
model parameter space is worthwhile since this work is the first to apply these
new core accretion models to the field of high contrast imaging surveys.
5.3.2 Narrowband to Broadband Colors
When we considered stars observed with the SDI method in Nielsen et al. (2008),
we used a constant conversion from the broadband H magnitude predicted by
the models to the measured contrast in the narrowband “off-methane” filter (SDI
F1, 2% bandpass, centered at 1.575 µm (Close et al., 2005)). While this conversion factor was consistent with observed T6 objects (Biller et al., 2007), it would
be expected to vary across a broad range of planet temperatures, corresponding to the large differences in ages and masses of the simulated planets. In this
work, we used template spectra from the SpeX instrument of 132 low-mass objects, spanning spectral types from L0 to T8, to compute the difference between
broadband H and narrowband filters as a function of effective temperature (M.
Liu, private communication). Spectral types are converted to effective temperature by the polynomial fit of Golimowski et al. (2004), their Table 4. SpeX spectra
were obtained from the online SpeX Prism Spectral Libraries (e.g. Cruz et al.
(2004), Kirkpatrick et al. (2006), and Burgasser (2007)). Since the reliability of the
models at reproducing the methane band when modeling planet atmospheres is
still uncertain, we prefer this method to purely using the synthetic spectra from
the models to make this color correction.
For GDPS target stars, we use this conversion for the NIRI CH4-short filter,
to convert the model’s prediction of planetary H-band flux to this 6.5% bandpass
filter, centered at 1.58 µm. For SDI target stars, we follow the steps of the data
140
reduction used in computing contrast curves, computing planet fluxes for both
the bluest “off-methane filter” (F1), and the “on methane filter” (F3) both with
a 2% bandpass, centered at 1.575 and 1.625 µm, respectively. Just as is done for
the survey images, the on-methane flux is subtracted from the off-methane flux,
providing (for each value of effective temperature) the expected final flux in the
subtracted image, as represented by the contrasts curves of Biller et al. (2007).
For both the SDI and GDPS target stars, we use the appropriate effective temperatures predicted by the models to match these color corrections to simulated
planets of each combination of age and mass.
To partially account for this effect in Nielsen et al. (2008), for SDI target stars,
we had imposed an upper cut-off on planet mass, set by where the models predicted planet effective temperatures would rise above 1400 K for a given age.
Above this temperature, the methane break would be so weak that subtracting
the “on-methane” image from the “off-methane” image would simply remove all
flux from the planet, as it is meant to do for the star. As a result, planets more
massive than this limit were simply considered undetectable. With our more
robust method that appropriately attenuates planet flux as a function of temperature, it is no longer necessary for us to impose this rather crude binary cut for
SDI targets.
In principle, an SDI observation of a non-methanated companion should not
suffer from self-subtraction of the companion signal, as the spatial scaled of these
images in the three SDI filters are rescaled by wavelength before subtraction. This
step aligns the speckles in the images (which scale as
λ
,
D
where λ is the obser-
vation wavelength and D is the diameter of the telescope), but misaligns any
physical objects (where separation from the primary star on the detector is not
a function of wavelength). As such, following subtraction of images from two
141
different filters, a real companion should appear as a “dipole:” a positive and
negative PSF, forming a radial line toward the primary star. The separation between the positive and negative parts of the dipole in the subtracted image would
be given by ∆d ∼
∆λ
d,
λ
where ∆d is the length of the dipole on the detector, ∆λ
is the difference in wavelength between the two filters, and d is the separation
on the detector between the primary star and the companion. The most extreme
shift in filters for SDI observations is between the 1.575 µm and 1.625 µm filters,
or 3%. Since the field of view for the NACO VLT SDI observations was only 2.5”,
the largest shift between positive and negative companions in the subtracted image would be 6.5 pixels. As the FWHM for these observations was typically 3.5
pixels, this dipole effect would easily be lost against the speckle background at
large separations, and almost undetectable at small separations, where positive
and negative companions would more closely overlap (Biller et al., 2007).
5.3.3 Completeness Plots
Using a similar method to Nielsen et al. (2008), we run Monte Carlo simulations
of extrasolar planets at a grid of mass and semi-major axis points for each target
star. For each star, then, we have what fraction of simulated planets could be
detected as a function of planet mass and semi-major axis. These plots, for each of
our 118 target stars, with the three sets of models we consider here, are available
in the online version of Nielsen & Close (2010). In order to combine these results
over all 118 target stars, we again make use of the concept of the “planet fraction,”
or fraction of stars with a particular type of planet, defined such that
N(a, M) =
Nobs
=118
X
fp (a, M)Pi (a, M)
(5.1)
i=1
where N(a,M) is the number of planets we would expect to detect, as a function
of semi-major axis and planet mass, Nobs is the number of stars observed, and
142
Pi (a, M) is the fraction of simulated planets, at a given combination of planet
mass and semi-major axis, we could detect around the ith star in the sample.
fp (a, M), then, is the fraction of stars that have a planet with a mass M and semimajor axis a. If every star had one Jupiter-mass planet at 5 AU, for example, then
fp (5AU, 1MJup ) = 1, and the number of these Jupiter analogs we would expect to
detect from the three surveys would simply be the sum of the detection efficiency
for these planets around all target stars. That is, if we had 10 stars in our sample
(Nobs = 10), and we had a 50% chance of detecting a Jupiter-like planet around
each star (Pi (5AU, 1MJup ) = 0.5), our expected number of detections of these
planets would be 5.
In the case of not finding planets, as was the case for the three surveys of
FGKM stars considered here, we can use the null result to set an upper limit on
the planet fraction, fp . If we assume that planet fraction is constant across all
stars in our survey (we will reexamine this assumption in Section 5.3.5), we can
remove fp from the sum of Equation 5.1. Then, utilizing the Poisson distribution,
where the probability of 0 detections given an expectation value of 3 (that is,
N(a, M) = 3), is 5%, we can set the 95% confidence level upper limit on planet
fraction with the equation
fp (a, M) ≤ PNobs
i=1
3
Pi (a, M)
(5.2)
So, with the above example, where the expectation value is 5 for Jupiter-analogs
PNobs =10
over 10 target stars (
i=1
Pi (5AU, 1MJup ) = 5), not detecting any such planets
would allow us to place a 95% confidence level upper limit of 60% on the fraction
of stars with a Jupiter-twin (fp (a, M) <
3
).
5
Doing this over the entire grid of
planet mass and semi-major axis allows us to plot what constraints can be placed
on combinations of these planet parameters.
143
Figure 5.4 The upper limit on planet fraction (fp , the fraction of stars with a planet
of a given mass and semi-major axis, see Equation 5.1), at the 95% (blue, thin
lines) and 68% (red, thick lines) confidence levels, using the theoretical models of
Baraffe et al. (2003). With 95% confidence, we can say that less than 1 in 20 stars
has a planet more massive than 8 MJup between 50 and 160 AU (constrained by
the solid blue, thin curve). We plot a horizontal fiducial bar (again, with a thick
red line and thin blue line) at 4 MJup , intersecting the fp ≤20% contour at both 68%
confidence (outer contour, thick red line) and 95% (inner contour, thin blue line).
Hence, the horizontal line at the bottom right of the figure suggests no more than
1 in 5 stars would have a planet more massive than 4 MJup from 8.1 to 911 AU
at the 68% confidence level, and between 22 and 507 AU at the 95% confidence
level. Known radial velocity planets are shown as filled circles for comparison.
144
Figure 5.5 As with Fig. 5.4, the upper limit on planet fraction only now using the
theoretical models of Burrows et al. (2003). The overall shape of the graph is quite
similar, so with 95% confidence, we can place an upper limit on planet fraction of
5% for planets larger than 8 MJup with semi-major axis between 55 and 130 AU.
As before, radial velocity planets are plotted as solid circles. The fiducial fp ≤20%
limits for 4 MJup are between 7.4 and 863 AU at 68% confidence, and 21 to 479 for
the 95% confidence level.
145
Figure 5.6 The same as Fig. 5.4 and Fig. 5.5, this time using the models of Fortney
et al. (2008) to give the upper limit on planet fraction. Overall, the theoretical
models of Fortney et al. (2008) are more pessimistic as to NIR fluxes of planets
when compared to the hot-start models (Burrows et al., 2003; Baraffe et al., 2003).
With these models, from 82 to 276 AU, less than 20% of stars can have a planet
above 4 MJup , at the 95% confidence level, and between 25 and 557 AU at 68%
confidence.
146
Table 5.3. Summary of Results.
Target Stars
Mass Correction∗
Confidence Level
Baraffe et al. (2003)
Burrows et al. (2003)
Fortney et al. (2008)
Completeness plots: semi-major axis range with fp < 20% for M > 4 MJup
All
None
68%
8.1 - 911 AU
7.4 - 863 AU
25 - 557 AU
All
None
95%
22 - 507 AU
21 - 479 AU
82 - 276 AU
M stars
None
68%
9.0 - 207 AU
8.3 - 213 AU
43 - 88 AU
M stars
None
95%
–
–
–
FGK stars
None
68%
25 - 856 AU
25 - 807 AU
59 - 497 AU
FGK stars
None
95%
38 - 469 AU
40 - 440 AU
–
All
1 M⊙
68%
13 - 849 AU
13 - 805 AU
41 - 504 AU
123 - 218 AU
All
1 M⊙
95%
30 - 466 AU
30 - 440 AU
All
0.5 M⊙
68%
9.0 - 1070 AU
8.3 - 1016 AU
26 - 656 AU
All
0.5 M⊙
95%
23 - 605 AU
22 - 573 AU
71 - 341 AU
All
None
68%
30 AU
28 AU
83 AU
All
None
95%
65 AU
56 AU
182 AU
All
Yes
68%
37 AU
36 AU
104 AU
All
Yes
95%
82 AU
82 AU
234 AU
Upper cut-off on power law distribution for semi-major axis with index -0.61
∗
The “Mass Correction” column refers to whether or not the Johnson et al. (2007) result, that more massive stars are more likely to
harbor giant planets, is used to weight the target stars by stellar mass. For the completeness plots, this correction is either not applied
(None) or set to a specific stellar mass, to determine the upper limit on the frequency of giant planets around stars of that mass. For
the limits on the upper cut-off on power law distributions, the correction is either applied (Yes) or not (None).
Fig. 5.4 gives the upper limit on planet fraction as a function of planet mass
and orbital semi-major axis, using the models of Baraffe et al. (2003), with a similar plot using the theoretical models of Burrows et al. (2003) given in Fig. 5.5.
We can place our strongest constraints on planets more massive than ∼4 MJup
between 20 and 300 AU (fewer than 5% of stars can have such planets at 68% confidence); when stars of all spectral types are considered, the lower limit probed
by direct imaging and the upper limit of the radial velocity method are still a factor of 5 apart. When we repeat the calculations using the models of Fortney et al.
(2008), the decreased NIR flux predicted for giant planets reduces constraints that
can be placed on extrasolar planets, with the “sweet spot” moving out to ∼80 AU,
as seen in Fig. 5.6.
While we continue to run calculations using all three sets of models, and re-
147
port the results here, for the sake of brevity we will henceforth only plot figures corresponding to the Baraffe et al. (2003) COND models. However, the figures appropriate to the Burrows et al. (2003) “hot-start” and Fortney et al. (2008)
core accretion models are available in our supplement, available at this URL:
http://exoplanet.as.arizona.edu/∼lclose/exoplanet2.html The supplement also
contains individual completeness plots for each of our 118 target stars, using each
of the three models of planet fluxes. Additionally, we summarize basic results for
all of our calculations in Table 5.3.
5.3.4 Testing Power Law Distributions for Extrasolar Planet Mass and SemiMajor Axis
These null results for extrasolar planets are also useful in setting constraints on
the parameters of models for planet populations that assume power law distributions for the semi-major axis and mass distributions. Cumming et al. (2008) carefully examined the sensitivity of the Keck Planet Search, and determined that,
over the range to which the radial velocity technique is sensitive (0.3 to 10 MJup ,
2-2000 day orbital periods), planets follow a double power-law distribution with
index -1.31 in mass and -0.61 in semi-major axis (-0.74 in orbital period). That is,
dN
dM
∝ M −1.31 and
to linear bins,
dN
,
da
dN
da
∝ a−0.61 (note that we define power law indices with respect
not the logarithmic bins of Cumming et al. (2008). Also, while
Cumming et al. (2008) use α and β to refer to the power law indices for mass
and period, respectively, we use α to refer to the power law index for semi-major
axis).
148
Table 5.4. Binaries
Sep (“)1
Sep. (AU)1
0.15
7
AB Dor
AB Dor
Target
Reference
Companion Type
6.38
Biller et al. (2007)
mid-G
230
Pounds et al. (1993)
M0
9 (Ba/Bb)
134 (Ba/Bb)
Close et al. (2005)
Binary M stars
0.15 (C)
2.24 (C)
Close et al. (2005)
Very low-mass M Star
5.5
250
Chauvin et al. (2005)
Planet/Brown Dwarf
HD 48189 A
0.76 (B)
16.5
Fabricius & Makarov (2000)
K star
HD 48189 A
0.14
3.03
Biller et al. (2007)
K star
DX Leo
65
1200
Lowrance et al. (2005)
M5.5
EK Dra
SB
SB
Metchev & Hillenbrand (2004)
M2
0.26
7.65
Biller et al. (2007)
late K/early M
Biller et al. (2007)
HIP 9141
V577 Per A
HIP 30034
HD 135363
HD 155555 AB
SB (AB)
SB (AB)
Bennett et al. (1967)
G5 and K0 SB
HD 155555 AB
18 (C)
1060 (C)
Zuckerman et al. (2001a)
Target Star 155555 C, M4.5
HD 172555 A
71
2100
Simon & Drake (1993)
Target Star CD -64 1208, K7
HD 186704
13
380
Aitken & Doolittle (1932)
early M
GJ 799A
3.6
36
Wilson (1954)
Target Star GJ 799B, M4.5
HD 201091
16
55
Baize (1950)
K5
Eps Indi A
400
1500
McCaughrean et al. (2004)
Binary Brown Dwarf
HIP 112312
100
2400
Song et al. (2002)
M4.5
TWA 8A
13
270
Jayawardhana et al. (1999)
Target Star TWA 8B, M5
TWA 9A
9
576
Jayawardhana et al. (1999)
Target Star TWA 9B, M1
15.7
260
Poveda et al. (1994)
HD 128898, Ap
V343 Nor
10
432
Song et al. (2003)
M4.5
BD-17 6128
2
100
Neuhäuser et al. (2002)
M2
HD 14802
0.47
10
Lafrenière et al. (2007)
K6
HD 16765
4.14
89
Holden (1977)
∼K
HD 17382
20.3
456
Lépine & Shara (2005)
M4.5
HD 19994
∼5
∼100
Hale (1994)
M3V
HD283750
124
2220
Holberg et al. (2002)
White Dwarf
Masciadri et al. (2005)
SAO 252852
Lafrenière et al. (2007)
HD 77407
1.7
50
Mugrauer et al. (2004)
∼M
HD 93528
234
8200
Perryman et al. (1997)
HIP 52776, K4.52
HD 96064
11.47
283 AU
Lippincott & MacDowall (1979)
NLTT 26194, M3
HD 102392
1.13
28
Lafrenière et al. (2007)
∼M
HD 108767 B
23.7
639
Gould & Chanamé (2004)
A0IV
HD 130948
2.64
47
Potter et al. (2002)
Binary brown dwarfs
HD 139813
31.5
683
Stephenson (1960)
G0
HD 141272
17.8
350
Eisenbeiss et al. (2007)
M3
early M, a = 4.5 AU
HD 160934
SB
SB
Hormuth et al. (2007)
HD 160934
8.69
213
Lowrance et al. (2005)
∼M
HD 166181
SB
SB
Nadal et al. (1974)
1.8 day orbit
HD 166181
0.102
3
Lafrenière et al. (2007)
∼K
HD 167605
1.2
37
Arribas et al. (1998)
M4V
HD 206860
43.2
795
Luhman et al. (2007b)
T dwarf
149
Table 5.4—Continued
Target
Sep (“)1
Sep. (AU)1
Reference
HD 213845
6.09
139
Lafrenière et al. (2007)
late M
HD 220140
10.9
214
Lowrance et al. (2005)
mid M
HD 220140
963
19000
Makarov et al. (2007)
∼M
HD 221503
339
4700
Gould & Chanamé (2004)
binary M stars
HIP 117410
1.84
50
Rossiter (1955)
early M
Companion Type
1 SB indicates a spectroscopic binary
2 These stars have Hipparcos proper motion and parallax within errors, and similar values of
calcium R’HK (-4.424 and -4.451 for HD 93528 and HIP 52776, respectively).
Binarity is likely to disrupt planet formation, or at the very least change the
underlying distribution of planets between binary stars hosting planets and single stars. Bonavita & Desidera (2007) have shown that the distribution of radial
velocity planets for binary and single-star hosts is quite similar, and Holman &
Wiegert (1999) suggest that planets are stable in binary systems with a planet
semi-major axis <20%
of the binary separation. We take this into account for our
∼
consideration of power-law distributions of semi-major axis by excluding target
stars with binaries within a factor of 5 of the planetary semi-major axis being considered. In Table 5.4, we give the results of a literature search for binaries among
our target stars, including binary separation and binary type.
By adopting these power laws, and using the normalization of Fischer &
Valenti (2005) to give the total fraction of stars with planets, we can then predict
how many planets these three surveys should have detected for various power
law fits. If a large number of planets is predicted, our null result can be used to
strongly exclude that model. If we accept the power-law distribution for mass
of Cumming et al. (2008) and the normalization of Fischer & Valenti (2005), the
two remaining parameters are the semi-major axis power-law index α, and the
semi-major axis upper cut-off (that is, what maximum semi-major axis the dis-
150
Figure 5.7 Twelve models for the semi-major axis distribution of extrasolar planets, using the planet luminosity models of Baraffe et al. (2003), with power law
indices of α = -1, -0.61, and -0.25, and upper cut-offs (the limit up to which there
are planets, but beyond which planets no longer appear) of 10, 20, 40, and 80 AU.
The solid purple line gives the histogram of known radial velocity planets, the
horizontal and diagonal green lines give different values of the power law index,
and the red vertical lines mark the upper cut-offs. The vertical black dashed line
at 2.5 AU gives the approximate upper limit to which the radial velocity survey
is complete to planets. The percentages at each intersection of power law and upper cut-off show the confidence with which that model ( dN
∝ aα for a ≤ acut−of f ,
da
and
dN
da
= 0 for a > acut−of f ) can be rejected. For example, a planet population
with dN/da ∼ a−1 and an outer cutoff of 10 AU is ruled out at 5.3% confidence.
For the power law of index -0.61 (Cumming et al., 2008), at 95% confidence the
upper cut-off must be less than 65 AU, which would fall between the dashed and
dot-dashed vertical lines of this graph.
151
tribution continues to until planets are no longer present). We illustrate this in
Fig. 5.7, where we depict various models of the semi-major axis distribution, and
the confidence with which we can reject them, using the models of Baraffe et al.
(2003). For 12 different combinations of semi-major axis power law index and
upper cut-off we give the percentage we can reject each of these 12 models in this
figure. For the model of Cumming et al. (2008), with
dN
da
∝ a−0.61 , and at 95%
confidence, the upper cut-off must be less than 65 AU, and less than 30 AU with
68% confidence.
We again use the theoretical models for planet fluxes of Baraffe et al. (2003),
and consider a broader range of power-law index α and upper cut-off in Fig. 5.8.
As before, the results from the two hot start models (Burrows et al., 2003; Baraffe
et al., 2003) are generally similar, as the upper cut-offs must be less than 28 and
56 AU (68% and 95% confidence) for the Burrows et al. (2003) models. The fainter
predicted fluxes from the Fortney et al. (2008) models reduce the areas of parameter space that our null result can exclude: the 68% and 95% confidence level upper
limits for upper cut-off become 83 and 182 AU, for a -0.61 power law index.
5.3.5 The Dependence on Stellar Mass of the Frequency of Extrasolar Giant
Planets
In Sections 5.3.3 and 5.3.4, we assume the distribution and frequency of giant planets is constant across all the stars in our survey. Johnson et al. (2007)
show this assumption to be incorrect by examining the frequency of giant planets around stars in three mass bins from radial velocity surveys, and showing
that more massive stars are more likely to harbor giant planets (see their Fig. 6).
As in Nielsen et al. (2008), we divide the target stars into two samples, one containing only M stars, and the other with FGK stars (Our sample contains a single
A star, HD 172555 A, with spectral type A5, with all our stars F2 or earlier. We in-
152
Figure 5.8 Contours showing the confidence with which we can exclude models
of the semi-major axis distribution of extrasolar giant planets of the form
dN
da
∝ aα ,
with an upper cut-off beyond which there are no longer planets, using the models of Baraffe et al. (2003). The power law index of -0.61 as given by Cumming
et al. (2008) is marked with a dotted line. The jags in the contours are due to
binaries being removed as we move up in power law cut-off (binary target stars
are pulled once the considered semi-major axis cut-off reaches one-fifth the binary separation). The pronounced jag between 50 and 55 AU corresponds to the
binary M-dwarfs TWA 8A and TWA 8B (21 pc, 10 Myr) being removed from the
sample, indicating the strong effect a few M stars have on our results. For the
power law of index -0.61, the 68% and 95% confidence levels for rejection of this
model are at 30 and 65 AU. Similar plots for the Burrows et al. (2003) and Fortney
et al. (2008), for this and future plots, are available in the online version of Nielsen
& Close (2010). The 68% and 95% confidence levels are 28 and 56 AU (Burrows
et al., 2003) and 83 and 182 AU (Fortney et al., 2008).
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clude this A star with the FGK stars; however, observations of this single star are
not sufficient to make any meaningful statements about the population of planets around A stars). We then imagine a planet fraction (fp ) with one value for M
stars, and another for stars of earlier spectral types.
In Fig. 5.9 we use the Baraffe et al. (2003) models to show the upper limit that
can be placed on the planet fraction for M stars. Since only 18 of the 118 target
stars are M stars, the smaller sample size greatly reduces the constraints that can
be placed on planet fraction near the center of the contours, and the outer edge
in semi-major axis. Interestingly, the small separation edge of the contours is
virtually unchanged between Figs. 5.4 and 5.9, indicating that the power with
which these surveys can speak to the populations of short-period giant planets is
entirely due to the M stars in the surveys.
Fig. 5.10 uses the models of Baraffe et al. (2003) to give the upper limit on
planet fraction for the FGK stars in the survey. The result for long-period planets
and within the central contours is much the same as for stars of all spectral types
(Fig. 5.4), but the contours at the smallest values of semi-major axis march outward without the M stars to provide high contrasts at small angular separations.
A more satisfying way to address the issue of stellar mass dependence is to
weight the results by target star mass, so that all stars in the survey can be applied
to the result simultaneously. To do this, we construct a linear fit to the metallicitycorrected histogram from Fig. 6 of Johnson et al. (2007), to give a correction to
planet fraction as a function of stellar mass, as we show in Fig. 5.11. (Here we
assume that the relation found by Johnson et al. (2007) for short-period planets
(less than six years) applies to the entire range of semi-major axis. While this
assumption is obviously untested, in the absence of better data we believe it is
a good starting point.) In the case of setting upper limits on planet fraction, we
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Figure 5.9 Contours giving the upper limit on planet fraction around all the stars
of M spectral type in the three surveys, using the models of Baraffe et al. (2003).
Comparing to Fig. 5.4, which considered stars of all spectral types, the behavior
of the contours at small semi-major axis is roughly the same, while the outer edge
and depth of the upper limit are limited by the reduced sample size (only 18 of
the 118 target stars are M stars). For 68% confidence, fewer than 1 in 5 stars have
a planet more massive than 4 MJup between 9.0 and 207 AU. For the models of
Burrows et al. (2003) this range is 8.3 to 213 AU, and is 43 to 88 AU for the Fortney
et al. (2008) models.
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Figure 5.10 The upper limit on planet fraction, using only the FGK stars in our
survey (as well as the single A star in the survey, HD 172555 A), using the models
of Baraffe et al. (2003). The shapes of the contours and the behavior at large semimajor axes are roughly the same as in Fig. 5.4, when all stars were considered,
but without the M stars and their favorable contrasts at small separations, the
small-period planets are much less accessible. The 20% contours, at the 68% and
95% confidence levels, for planets more massive than 4 MJup , are found between
25 and 856 AU and between 38 and 469 AU, respectively. For the Burrows et al.
(2003) models, the 68% and 95% limit ranges are between 25 and 807 AU, and 40
and 440 AU; for the Fortney et al. (2008) models, the 95% confidence 20% contour
never reaches 4 MJup , but the 68% confidence range is from 59 to 497 AU.
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Figure 5.11 Our linear fit to the dependence of the likelihood a target star has
of hosting a close-in, giant extrasolar planet as a function of stellar mass. The
histogram shown is the metallicity-corrected histogram of Johnson et al. (2007)
(their Fig. 6). As noted by Johnson et al. (2007), the probability for the high-mass
bin is likely underestimated, so future work may show an even greater boost for
the value of high-mass target stars. For the target stars considered in this work,
35 are in the low-mass bin, 78 are in the medium-mass bin, and 5 are in the bin
for the highest masses.
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now allow planet fraction to become a function of stellar mass (M∗ ) in addition
to planet mass and semi-major axis (Mp and a). In that case we can specify planet
fraction for the stellar mass of a solar mass (fp,1.0(a, Mp )), and find the upper limit
as with Equation 5.2, but now including an extra term for the mass correction:
fp,1.0 (a, Mp ) ≤ PNobs
i=1
3
Pi (a, Mp )mc1.0 (M∗,i )
(5.3)
where mc1.0 (M∗,i ) is the mass correction as a function of the stellar mass of the
ith star in the sum, normalized to 1.0 M⊙ , and defined by mc1.0 (M∗ ) =
Fp (M∗ )
,
Fp (1.0M )
⊙
where Fp is the fraction of stars with a detected radial velocity planet as a func-
tion of stellar mass, using the linear fit to the Johnson et al. (2007) results. Again,
going back to our earlier example, imagine that we have 10 stars, each with
50% completeness to Jupiter-like planets. If all 10 stars are 1 solar mass, then
⊙ ) = 1, and as before the upper limit on planet fraction (for
Fp (1.0M )
⊙
the 95% confidence level, as given by the 3 in the numerator) is 60%. On the
mc1.0 (M∗ ) =
Fp (1.0M
other hand, if only four of the ten target stars had masses of 1 M⊙ , and the remaining six had masses of 2.5 M⊙ , we must weight the results to account for the
greater likelihood of stars of earlier spectral types to have planets. A 2.5 M⊙ star
is twice as likely to have a planet as a solar mass star (see Fig. 5.11), so for the
four stars of 1 M⊙ , mc1.0 (1.0M⊙ ) remains 1, as before, while for the stars of 2.5
M⊙ , this factor doubles, mc1.0 (2.5M⊙ ) = 2. In this case, Equation 5.2 becomes
fp,1.0 (a, Mp ) ≤
3
0.5+0.5+0.5+0.5+1+1+1+1+1+1
= 3/8 =37.5%. Including A stars in this
fictional example almost doubles the constraint we can place on the fraction of
stars with a giant planet. Similarly, M stars will be weighted against to account
for their decreased likelihood of having planets. As an aside, we note that while
our sample is spread across spectral type (1 A star, 8 F, 33 G, 58 K, and 18 M stars),
only 18 of our target stars are more massive than the sun. Despite the increased
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probability of finding planets around higher mass target stars, these stars are intrinsically brighter, and so moving earlier in spectral type very quickly results in
any potential planet photons being swamped by the glare of its host star (though
the recent discoveries of planets around A stars, e.g. Marois et al. (2008), show
that this difficulty can be overcome and produce exciting results).
In Fig. 5.12, we plot the upper limit on planet fraction for stars of 1 M⊙ , using Equation 5.3. When comparing Figs. 5.9 and 5.10 with Fig. 5.4, we see that
the contours at small values of semi-major axis are set mainly by the 18 M stars
in our sample, while the behavior at large separations and the depth of the contours at intermediate values of semi-major axis are set by the 100 FGK stars in the
sample. So it is then not too surprising that Fig. 5.12 is quite similar to Fig. 5.4,
with the contours corresponding to the smallest upper limits on planet fraction
shrinking slightly, and the contour at lower semi-major axis moving to the right
in the figure, as M stars are now given less weight.
Alternatively, instead of normalizing to solar-type stars, we can instead consider what constraints are placed on stars of 0.5 M⊙ (about an M0 spectral type).
The constraints should become more powerful, as we assume a global decrease
in the planet fraction for massive planets around lower-mass stars. (Again, this
applies strictly to massive planets, >0.5MJup . The direct imaging surveys considered here are not sensitive to Neptune mass planets, which may be more common
around M-stars: Endl et al. (2008) suggest that Hot Neptunes may be ∼4 times
more prevalent orbiting M-stars than Hot Jupiters around FGK stars) In fact, the
only result of this change is to multiply a constant factor by the right-hand-side
of Equation 5.3 corresponding to the ratio of the likelihood of finding a planet
around a solar mass star to that of finding a planet around a star of 0.5 M⊙ , or
1.5 in this case. We plot these limits on planet fraction for half solar mass stars
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Figure 5.12 The upper limit on planet fraction for stars of 1 M⊙ (fp,1.0), with constraints from target stars of higher and lower mass stars weighted according to
a fit to the Johnson et al. (2007) dependence on stellar mass of the frequency of
radial velocity planets, using the models of Baraffe et al. (2003). The plot is similar to that of Fig. 5.4, which weighted all stars equally, but the contours shrink
slightly (mainly on the low separation side of the plot) as the M stars are now
effectively given less weight. The 20% confidence level for planets more massive
than 4 MJup are between 13 and 849 AU at 68% confidence, and between 30 and
466 AU for the 95% confidence level. For the Burrows et al. (2003) models, these
ranges are 13 to 805 AU, and 30 to 440 AU, while for the models of Fortney et al.
(2008) the limits are between 41 and 504 AU, and 123 and 218 AU.
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Figure 5.13 The upper limit on planet fraction, this time normalizing to stars of
a half solar mass (fp,0.5 ), or about M0, using the models of Baraffe et al. (2003).
The constraints become stronger, as expected, as our assumption going into this
calculation is that lower mass stars are less likely to have planets overall. With
this set of assumptions, the dearth of giant, large-separation planets around M
stars is made quite clear. The possibility of lower mass, inner planets around M
stars (and indeed, planets like those in our own solar system) remains, however.
Fewer than 20% of M stars can have planets more massive than 4 MJup between
9.0 and 1070 AU at 68% confidence, and 23-605 AU at the 95% confidence level.
These limits are 8.3 to 1016 AU and from 22 to 573 AU for the Burrows et al. (2003)
models, as well as 26 to 656 AU and 71 to 341 AU for the Fortney et al. (2008).
161
in Fig. 5.13, with the models of Baraffe et al. (2003). As expected, the contours
move outward, setting strong constraints on the frequency of giant planets in
long-period orbits around M stars.
We also reconsider the implications of stellar mass on the constraints put on
the power-law model for the semi-major axis distribution of extrasolar planets,
as discussed in Section 5.3.4. Again, by using the linear fit to the results of Johnson et al. (2007), we boost the predicted number of planets for higher mass target
stars, and suppress that number for lower mass stars. In Fig. 5.14 we show the
same combination of three power law indices and four values of the upper cut-off
as before, and the models of Baraffe et al. (2003), but now with the additional correction for the dependence of planet frequency on the stellar mass of each target
star. The confidence level at which we can exclude each model drops compared
to Fig. 5.7, as M stars are effectively given less weight. While the upper limit on
planet fraction as a function of planet mass and semi-major axis is specific to a
given stellar mass, Fig. 5.14 (and the next one, Fig. 5.15) need not be normalized
to a specific spectral type. The Johnson et al. (2007) mass correction and the Fischer & Valenti (2005) planet fraction sets the absolute likelihood a given target
star has a giant planet, which is used to calculate the predicted number of planets detected from our entire survey. Given our null result, this expectation value
is used to set a confidence level with which the entire model (giant planet selfluminosity, giant planet fraction, dependence of planet fraction on stellar mass,
and planet mass, semi-major axis, and orbital eccentricity distributions) can be
rejected.
For the full range of power law index and upper cut-off, again with the Baraffe
et al. (2003) models, we plot contours for the confidence level of rejection in
Fig. 5.15. This figure is again generally similar to Fig. 5.8, but with the constraints
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Figure 5.14 As with Fig. 5.7, power-law models for the semi-major axis distribution of extrasolar planets, and the confidence with which we can rule out these
models, using the results of our survey and the models of Baraffe et al. (2003).
This time, we utilize the results of Johnson et al. (2007) to appropriately give additional weight to high mass stars, which are more likely to harbor giant planets.
163
Figure 5.15 Contours showing the confidence with which we can exclude a model
for the distribution of semi-major axis of extrasolar giant planets given by
dN
da
∝
aα up to some upper cut-off. This figure shows the results for the models of
Baraffe et al. (2003), with the stellar mass correction of Johnson et al. (2007) to
account for the dependence of likelihood of finding giant planets upon the mass
of the parent star. The upper cut-off for the Cumming et al. (2008) power law of
index -0.61 (as marked by the dotted line) is 37 AU at the 68% confidence level,
and 82 at 95% confidence. For the Burrows et al. (2003) models, the 68% and 95%
confidence limits are at 36 and 82 AU, and at 104 and 234 AU for the Fortney et al.
(2008) models.
164
slightly looser as M stars in the sample receive less weight. With the Johnson
et al. (2007) mass correction, the 68% and 95% confidence level upper limits on
the semi-major axis distribution cut-off are 37 and 82 AU for the Baraffe et al.
(2003) models, respectively (without the mass correction, these were 30 and 65
AU). For the Fortney et al. (2008) models these move from 83 and 182 AU to 104
and 234 AU.
5.3.6 Ida & Lin (2004) Core Accretion Formation Models
As in Nielsen et al. (2008), we turn to the giant planet formation and dynamical
evolution models of Ida & Lin (2004), which predict the final state of giant planets,
mass and semi-major axis, following the core accretion scenario. We extract 200300 planets from their Fig. 12, and use these masses and semi-major axes in our
Monte Carlo simulations. We plot the predicted number of planets detected from
these models in Fig. 5.16, with target stars divided by binarity. Even with our 118
target stars, without removing close binaries, not accounting for stellar mass (the
Ida & Lin (2004) models were run with a 1 M⊙ primary star), and using the planet
luminosities of the Baraffe et al. (2003) models, the Monte Carlo simulations show
that for each of the three cases of Ida & Lin (2004), we would expect to detect
about 1 planet for each. In Nielsen et al. (2008), we could only exclude the cases of
Ida & Lin (2004) A, B, and C at 45%, 49%, and 50% confidence, respectively, with
the expanded target star sample here these rejection levels only become 45%, 59%,
and 63% (using the Burrows et al. (2003) models to be consistent with Nielsen
et al. (2008)). When using the models of Baraffe et al. (2003), the limits for the
sample of this Chapter are 38%, 58%, and 62%. The models of Ida & Lin (2004)
predict very few giant planets in long-period orbits: fewer than 20% of the giant
planets predicted by these models are beyond 10 AU, while our 68% confidence
limit on the upper limit of the Cumming et al. (2008) power-law, 23 AU, gives
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Figure 5.16 The number of planets we’d expect to detect, as a function of the
number of stars in our survey. Target stars are divided into bins: one for single
stars, and binaries divided by separation; within each bin the best targets are
placed to the left of the graph, so they’re “observed first” in this manner. Using
the models of Baraffe et al. (2003), and not accounting for stellar mass effects or
removing binaries, the core accretion models of Ida & Lin (2004) predict detecting
between 0.5 and 1 planets with the combination of the Masciadri et al. (2005),
Biller et al. (2007), and Lafrenière et al. (2007) surveys. The Ida & Lin (2004)
models A, B, and C (green curves) can only be excluded with 38%, 58%, and 62%
confidence, respectively.
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30% of giant planets in orbits beyond 10 AU. However, our current limits can
neither confirm nor rule out the Ida & Lin (2004) populations.
5.4 Discussion
Overall, the conclusions from this work are largely similar to those of Nielsen
et al. (2008), that extrasolar giant planets are rare at large separations around
Sun-like or less massive stars. Even for the models which predict the faintest
planet NIR flux densities (Fortney et al., 2008), and weighting against the M stars
(which provide the most favorable contrasts for finding planets), we find that
at 95% confidence, fewer than 20% of solar-mass stars can have a planet more
massive than 4 MJup in an orbit between 123 and 218 AU. Also, a power-law
model for the semi-major axis distribution of giant planets following the results
of Cumming et al. (2008) must have a cut-off of 104 AU at 68% confidence, and
234 AU at 95% confidence, again using the Fortney et al. (2008) models and the
Johnson et al. (2007) mass correction.
It is worth noting that there are additional models of giant planet distributions beyond what we consider here. Cumming et al. (2008) found a good fit to
distributions of close-in giant planets from radial velocity work using a single
power-law for the distribution of semi-major axis. It is also possible, however,
that while this is a good fit for giant planets within ∼5 AU, it may not hold for
planets at larger separations; perhaps a broken power law or some other distribution governs the population of giant planets in long period orbits. If all giant
planets are formed beyond the snow line, perhaps the final distribution differs
for planets that migrate inwards and those that remain beyond the snow line. Alternatively, there may be multiple methods of planet formation, such as the core
accretion scenario and the disk instability model (e.g. Ida & Lin (2004) vs. Boss
167
(2007)), and the frequency with which each occurs is a function of distance from
the star. Another possibility is that mass and semi-major axis are not independent
distributions, which should become testable as the number of known exoplanets
increases. Additionally, moving across spectral type may not only change the
frequency of giant planets, but also their distributions of mass and semi-major
axis. The analysis of Cumming et al. (2008) relied exclusively on solar-type (FGK)
planet hosts, with the number of planets orbiting M stars being too small to draw
any conclusions about a possible dependence of planet distributions on spectral
type. These issues cannot be well addressed with further null results; they require a large number of detected planets at intermediate (∼5-20 AU) and large
(>20 AU) separations to make statistically significant statements on long-period
giant planet populations.
Since this Chapter was first prepared, the discovery of several planet candidates, via direct imaging, was announced; planets were detected around the three
stars, all of A spectral type, HR 8799 (Marois et al., 2008), Fomalhaut (Kalas et al.,
2008), and β Pic (Lagrange et al., 2009). These exciting discoveries are consistent with the predictions of Johnson et al. (2007), as even though planets within
100 AU (like the three found around HR 8799) should be easier to detect around
lower-mass stars (where the self-luminosity of the star is smaller), similar planets
have not been found around stars of solar mass or smaller. However, each one
of these planetary systems is different from the other. Moreover, all are around
more massive stars than were analyzed here. Since the full survey papers for
each of these discoveries have not yet been published, it is difficult to incorporate
these results into our analysis of Sun-like (and less massive) stars.
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5.5 Conclusions
We have used Monte Carlo simulations to examine the null result from three
direct imaging surveys (Masciadri et al., 2005; Biller et al., 2007; Lafrenière et al.,
2007) to set constraints on the population of extrasolar giant planets. We use three
commonly cited sets of planet models (Burrows et al., 2003; Baraffe et al., 2003;
Fortney et al., 2008) in order to reach conclusions as broad as possible. Doubling
the sample size, as expected, increased the strength of our null results. However,
including better modeling for giant planets–using the stellar mass dependence
of giant planet frequency of Johnson et al. (2007), and the core-accretion based
luminosity models of Fortney et al. (2008)–have actually loosened the constraints
reported in Nielsen et al. (2008). There is still some uncertainty, however, in which
if any of these models of planet luminosity is correct; likely the truth may fall in
between that of the optimistic “hot start” models and the somewhat pessimistic
“core accretion” model.
With the COND models of Baraffe et al. (2003), a planet more massive than 4
MJup is found around 20% or less of FGKM stars in orbits between 8.1 and 911
AU, at 68% confidence. These limits become 7.4 to 863 AU for Burrows et al.
(2003), and 25 to 557 AU for the models of Fortney et al. (2008). At 95% confidence, 4 MJup (and larger) planets are found around fewer than 20% of stars
between 22 and 507 AU, 21 and 479 AU, and 82 and 276 AU for the models of
Baraffe et al. (2003), Burrows et al. (2003), and Fortney et al. (2008), respectively.
Using the power law distribution of Cumming et al. (2008), with index -0.61,
the upper cut-off for the distribution of giant planets is found at 30 and 65 AU,
at the 68% and 95% confidence levels, respectively, using the models of Baraffe
et al. (2003). With the models of Burrows et al. (2003) these limits become 28 and
56 AU, and with the Fortney et al. (2008) models they are 83 and 182 AU.
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When we apply the Johnson et al. (2007) dependency of planet fraction on stellar mass, the M stars in our sample (where we achieve the greatest sensitivity to
planets), are weighted down to account for their decreased likelihood of hosting
a giant planet. As a result, the improved null results cited above retreat to levels
similar to those cited in Nielsen et al. (2008) and Lafrenière et al. (2007). Given
our results, fewer than 20% of solar-type stars have a >4 MJup planet between
13 and 849 AU at 68% confidence with the Baraffe et al. (2003) models (also 13
and 805 AU for the models of Burrows et al. (2003), and 41 and 504 AU for the
Fortney et al. (2008) models). At 95% confidence, for the models of Baraffe et al.
(2003), Burrows et al. (2003), and Fortney et al. (2008), fewer than 20% of 1 M⊙
stars have 4 MJup planets between 30 and 466 AU, 30 and 440 AU, and 123 and
218 AU, respectively.
Applying the Johnson et al. (2007) results to the Cumming et al. (2008) model
for semi-major axis distribution, giant planets cannot exist beyond 37 and 82 AU
for the Baraffe et al. (2003) models at 68% and 95% confidence. The 68% and 95%
confidence figures become 36 and 82 AU for the Baraffe et al. (2003) models and
104 and 234 AU for the models of Fortney et al. (2008). In general, the Johnson
et al. (2007) dependence of planet fraction on stellar mass makes direct imaging
planet searches more difficult, as the stars most likely to harbor giant planets are
also the most luminous, giving extreme contrast ratios between star and planet
that impede planet detection.
We note that while the constraints on giant planet populations from this and
other work have, for the first time, reached the equivalent of extrasolar “Kuiper
Belts,” there is still a gap (∼5 - ∼30 AU) between these results for FGKM stars
and those of radial velocity surveys, which focus more on the inner solar system.
Delving into this unprobed region from the direct imaging side can be achieved
170
two ways: increasing sensitivity to planets at small separations (achievable with
dedicated planet finders using “extreme” adaptive optics, e.g. GPI (Graham et al.,
2007) and VLT-SPHERE (Boccaletti et al., 2008)), or with large-scale surveys to increase the sample size of target stars, such as the 500 hour Near-Infrared Coronagraphic Imager (NICI) survey at Gemini South (Chun et al. 2008). Our technique
can be applied to the results from any direct imaging survey for giant exoplanets,
requiring only the target list and achieved contrast curves. By building up the
statistics of null results, it will be possible to more directly focus direct imaging
efforts on where planets are most likely to exist, and create a fuller picture of
the distribution of extrasolar giant planets. Additionally, such an analysis helps
to put the survey into context with respect to previous work, by determining
what area of parameter space (in terms of both planetary and stellar parameters)
the survey is probing, and so allows it to be compared directly to other surveys.
There is also no limitation based on observation wavelength, even when target
stars are observed by multiple surveys, since simulated planets are advanced in
their orbits and compared to each contrast curve. As such, it will be interesting in future work to consider the results from L and M band surveys currently
being conducted (e.g. Kasper et al. (2007)). Baraffe et al. (2003) and Burrows
et al. (2003) predict planets with significantly lower contrasts to their parent stars
at these longer wavelengths, and so the inclusion of results from such surveys
could strengthen our null results, especially at large separations.
5.6 Online Figure Sets: Completeness Plots for Each Target Star
In the online version of Nielsen & Close (2010), we provide versions of Figures 5.8, 5.9, 5.10, 5.12, 5.13,and 5.15 for the planet flux models of Burrows et al.
(2003) and Fortney et al. (2008), to complement the current versions of these plots
171
using the Baraffe et al. (2003) models. Additionally, we have produced onlineonly figure sets that give the completeness plots for each target star considered in
this Chapter.
Each plot gives the completeness to planets from observations of a given target star by the three surveys considered in this article (Masciadri et al., 2005; Biller
et al., 2007; Lafrenière et al., 2007), as a function of semi-major axis and planet
mass. Stars that have been observed at multiple epochs by different surveys are
handled by the method discussed in Section 5.3. Fig. 5.17 gives an example for
the target star 2E 759, using the Baraffe et al. (2003) models of planet fluxes. This
plot shows that for the Lafrenière et al. (2007) observation of this star, for planets
whose orbital radius and mass place them within the inner contour, there was
an 80% chance of detecting such a planet around this star, given the measured
contrast curve for this observation. Fig. 5.18 and 5.19 give completeness plots for
this same star, but with the planet flux models of Burrows et al. (2003) and Fortney et al. (2008), respectively. Similar plots for the remaining 117 target stars we
consider here may be found in the online version of Nielsen & Close (2010)
5.7 Acknowledgments
We are grateful to the anonymous referee for providing many helpful comments
that improved the quality of this Chapter. We thank Beth Biller for the publication and compilation of the SDI contrast curves, as well as a large amount of
useful input in preparing these simulations. We also thank Elena Masciadri for
providing published contrast curves, and the authors of Lafrenière et al. (2007)
for the careful preparation and publication of their achieved contrasts and observational techniques. We thank Eric Mamajek for a great deal of assistance in
determining the ages of our target stars, as well as Michael Liu for providing the
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broadband-to-narrowband colors of low-mass objects. We thank Remi Soummer
for the idea of presenting sensitivity to planets as a grid of mass and semi-major
axis points, and we thank Daniel Apai for presenting the idea of constructing a
grid of semi-major axis power law indices and cut-offs. We also thank Rainer
Lenzen, Thomas Henning, and Wolfgang Brandner for their important work in
the original data gathering, and helpful comments over the course of the project.
This work makes use of data from the European Southern Observatory, under
Program 70.C - 0777D, 70.C - 0777E, 71.C-0029A, 74.C-0548, 74.C-0549, and 76.C0094. Observations reported here were obtained at the MMT Observatory, a joint
facility of the University of Arizona and the Smithsonian Institution. Based on
observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative
agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council
(United Kingdom), the National Research Council (Canada), CONICYT (Chile),
the Australian Research Council (Australia), Ministério da Ciência e Tecnologia
(Brazil) and SECYT (Argentina) This Chapter makes use of data products from
the Two Micron All-Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute
of Technology, funded by the National Aeronautics and Space Administration
and the National Science Foundation. This research has made use of the SIMBAD
database, operated at CDS, Strasburg, France. ELN is supported by a Michelson
Fellowship, without which this work would not have been possible. LMC was
supported by an NSF CAREER award and by NASA’s Origin of Solar Systems
program.
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Figure 5.17 The completeness to planets for this target star, 2E 759, as a function
of orbital semi-major axis and planet mass, based on all observations of this star
from this work, using the models of Baraffe et al. (2003). A given contour is only
plotted if observations of the star have reached that level of completeness; if no
contours are plotted, then for no set of planet parameters are the observations 5%
complete to planets. The contours plotted (from outside to inside) are 5% (solid
line), 10% (dotted line), 20% (short dashed line), 40% (short dashed-dotted line),
60% (short dashed-dotted-dotted-dotted line), and 80% (long dashed line). Plots
for the other 117 target stars are available in the online version of Nielsen & Close
(2010).
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Figure 5.18 The completeness to planets for this target star, 2E 759, as a function
of orbital semi-major axis and planet mass, based on all observations of this star
from this work, using the models of Burrows et al. (2003). A given contour is only
plotted if observations of the star have reached that level of completeness; if no
contours are plotted, then for no set of planet parameters are the observations 5%
complete to planets. The contours plotted (from outside to inside) are 5% (solid
line), 10% (dotted line), 20% (short dashed line), 40% (short dashed-dotted line),
60% (short dashed-dotted-dotted-dotted line), and 80% (long dashed line). Plots
for the other 117 target stars are available in the online version of Nielsen & Close
(2010).
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Figure 5.19 The completeness to planets for this target star, 2E 759, as a function
of orbital semi-major axis and planet mass, based on all observations of this star
from this work, using the models of Fortney et al. (2008). A given contour is only
plotted if observations of the star have reached that level of completeness; if no
contours are plotted, then for no set of planet parameters are the observations 5%
complete to planets. The contours plotted (from outside to inside) are 5% (solid
line), 10% (dotted line), 20% (short dashed line), 40% (short dashed-dotted line),
60% (short dashed-dotted-dotted-dotted line), and 80% (long dashed line). Plots
for the other 117 target stars are available in the online version of Nielsen & Close
(2010).
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C HAPTER 6
CHOOSING THE TARGET LIST AND OBSERVING STRATEGY FOR THE
GEMINI NICI PLANET-FINDING CAMPAIGN
We describe the method by which we constructed the final Gemini NICI PlanetFinding Campaign target list. By combining numerous lists and catalogs, we
construct an input list of 1352 nearby, young stars accessible from Gemini South.
The results of Monte Carlo simulation show that the survey design and final target list are highly dependent on the assumptions and models that are input into
the simulations. The final choice of target list is made to balance these competing directions, and to have a final result from the survey that addresses as many
possibilities for planet populations and luminosity models as possible.
6.1 The Near Infrared Coronagraphic Imager (NICI)
The Near Infrared Coronagraphic Imager, or NICI, is a specialized instrument
designed specifically for the purpose of directly imaging giant extrasolar planets.
The instrument makes use of four techniques for achieving high contrast imaging
at small separations: a high-order adaptive optics system, a Lyot coronagraph,
a beam splitter with dual science cameras to perform Simultaneous Differential
Imaging, and the ability to operate with the derotator off to utilize Angular Differential Imaging. The 85-element curvature wavefront sensor routinely returns
∼40% Strehl in the H-band, for good observing conditions (better than median
seeing for Gemini South, ∼0.5”) and a bright (V<10) guide star (as NICI uses a
visible wavefront sensor, the V magnitude of the star is key). The partially transmissive coronagraphic mask greatly attenuates the starlight while allowing for
photometric and astrometric measurements using the residual starlight that is
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transmitted through the mask (Chun et al., 2008). A 50/50 beamsplitter sends
light to two science cameras (Holmes and Watson), and in SDI mode the two
beams are passed through medium band (4%) filters on either side of the 1.6 µm
methane bandhead. Fig. 6.1 shows NICI data with a simulated methane-rich
companion placed in the data: the companion is heavily attenuated in the onmethane filter, while the residual stellar halo and speckles are identical between
the two images. Finally, by allowing the image plane to rotate throughout the
observation (ADI), speckles (especially at larger separations, where there’s more
sky rotation) are further reduced in amplitude. The final contrasts achieved by
the NICI instrument are 15 magnitudes at 1” separation, deeper than any other
instrument operating to date (Liu et al., 2010). Mounted at the 8.1m Gemini South
telescope in Chile, the camera was commissioned in 2008, and is currently conducting science operations.
6.1.1 The Gemini NICI Planet-Finding Campaign
In order to make the optimal use of this instrument, Gemini has allocated 500
hours of guaranteed observing time to the Gemini NICI Planet-Finding Campaign. Led by PI Michael Liu, the Campaign seeks to answer fundamental questions about the nature and distribution of extrasolar planets by leveraging the superior capabilities of the instrument and the tremendous opportunity provided
by the large amount of observing time. The Campaign time is allocated in “semiclassical” mode, with a block of time (typically ∼1 week per month) assigned to
the NICI Campaign, with Campaign observers monitoring the telescope observations in Chile via video link. When the seeing drops below 0.6”, Campaign
observations begin, thus saving the Campaign observing time for only the best
seeing conditions. The Campaign has already discovered two previously unknown brown dwarf companions to target stars, and has published analyses of
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Figure 6.1 NICI data showing the SDI mode in action; the left image goes through
the medium band “off-methane” filter, and so the artificial companion (upper
left) is seen at normal brightness. The right image is the “on-methane” filter,
which would attenuate a methane-rich object, as this artificial companion is assumed to be. Since the stellar halo and speckles are identical in the two filters, the
two images may be subtracted from each other, leaving the companion’s signal
behind. Figure from Liu et al. (2010).
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these objects (Biller et al., 2010; Wahhaj et al., 2011).
6.2 Defining the Input Target List
With 500 hours of telescope time on a new instrument granted to the Campaign,
our goal was to determine the most efficient way to utilize that time to answer the
science questions of the Campaign. Our first step was to assemble in input target
list broad enough to encompass as many nearby, young stars as possible. The
final target list could then be drawn from this input list, based on our analysis of
the individual stars. We used our planet population simulation code to determine
the completeness of NICI to detecting planets around each of these stars, using a
variety of assumptions about planet populations and observing strategies.
6.2.1 VLT Adaptive Optics H and Ks Band Imaging, SDI, GDPS Targets
There are 132 unique target stars observed at the VLT (with broadband H and Ks
imaging (Masciadri et al., 2005)), at the MMT and VLT using Simultaneous Differential Imaging (Biller et al., 2007), and at Gemini North using Angular Differential Imaging (Lafrenière et al., 2007). These stars are all within ∼50 pc, and either
belong to established moving groups, or have ages determined by calcium H&K
emission or lithium absorption. Since we have the individual contrast curves for
each of these stars from the actual observations, the simulated planets are first
run against those contrast curves before being compared to the NICI curve, so
that only simulated planets that could be detected by NICI but were below the
5σ detection limit of all previous observations are considered detectable. (The
simulated planets are advanced in their orbits from the times of the initial observers, e.g. ∼2005 for VLT H and Ks band imaging, to an epoch of 2009.0 for a
potential NICI observation. This is a relatively minor effect, as we’re most sensitive to planets in very long period orbits). 95 of these stars have declinations
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south of +30, and these are included in the list.
6.2.2 A Stars
A stars have been shown more likely to harbor close-in (periods less than 4 years)
giant (greater than 2 MJup ) planets by Johnson et al. (2007), when compared to
solar-type stars, though their greater intrinsic brightness makes detecting these
planets challenging. To build up a sample of A stars, we’ve taken all stars in the
Hipparcos catalog (Perryman et al., 1997) that are within 100 pc, have a spectral
type of A or B, and luminosity class V or IV, and are below +30 in declination,
yielding an additional 297 stars. Since there isn’t a robust method to determine
ages of these stars, we assume the stars have a uniform probability of being between 5 Myr and the main sequence lifetime of the star (depends on spectral
type, going from 400 Myr for A0 to 1.8 Gyr for A9). we use “statistical ages” to
determine the final probability of NICI detecting a planet around these stars, by
simulating planets at ten ages (uniformly spaced in log space). Then, this curve
(probability versus age) is interpolated into linear space, and the average probability is returned for each star.
6.2.3 Hipparcos R’HK Stars
Calcium R’HK is a good tracer of age for stars of spectral type ∼F to ∼K5. We
compiled stars from three large spectroscopic surveys of Calcium R’HK emission
(Gray et al., 2003b, 2006b; Wright et al., 2004), and used the age conversion of
Mamajek & Hillenbrand (2008), keeping all stars younger than 1 Gyr, and crossreferenced with the Hipparcos catalog (Perryman et al., 1997), to limit this sample
to stars within 50 pc and south of +30◦ , giving 402 stars.
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6.2.4 Additional Moving Group Stars
There are ∼150-200 stars in well-known young, nearby moving groups, not all of
which were observed by the surveys described in 6.2.1. Using the membership
lists of Zuckerman & Song (2004) and López-Santiago et al. (2006), removing binaries within 3” and stars north of +30◦ , we add 183 stars to our target list. In
general, these stars have more robust age determinations than stars from other
samples, since the large number of stars per moving group (20-60) means that
random noise in the age metrics can be averaged out and a more consistent age
can be assigned to all members of the group.
6.2.5 Young Nearby M Stars
Neill Reid and collaborators have compiled a sample of young, nearby M stars
based on activity and X-ray emission, with distances from photometric parallax.
The ages of these stars are estimated to be less than 300 Myr (Allen & Reid, 2008).
These were observed at Gemini with Altair, and the contrast curve of Daemgen
et al. (2007) is applied for those objects observed at Gemini to exclude simulated
planets that could have already been detected. As with the A stars, we allow a
uniform distribution of ages, this time between 5 and 300 Myr. We again screen
for binaries within 3” and stars above +30. In addition to these publicly available
stars, we also use a private compilation of additional M stars based on additional
work by these authors (Liu, 2008), for a total of 78 additional target stars.
6.2.6 Debris Disk Host Stars
Stars that are known to host debris disks may be more likely to harbor planets,
and so we also include stars with known debris disks from Moór et al. (2006),
Rhee et al. (2007), and Hillenbrand et al. (2008). Since the only criteria for inclusion in this catalog is the presence of a debris disk (as determined by imaging or
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an infrared excess), these stars tend to be older on average than stars from other
sources. There are 105 of these stars in the input target list. It is important to note
that the presence of (bright) debris disks may lower our constrasts to planets; we
do not consider that effect quantitatively in our analysis here, though we caution
that the final reduced data (and subsequent contrast curves) may be less sensitive
than the estimates used in the simulations.
6.2.7 Additional Sources
We also include 104 stars from the Spitzer legacy program “The Formation and
Evolution of Planetary Systems” (FEPS), as given by Carpenter et al. (2009). We
add to this 81 stars from Su et al. (2006), a MIPS study of nearby A stars. And
finally, we include 7 stars from the HST NICMOS survey conducted by Lowrance
et al. (2005). We use stars that have declination below +30, and adopt the ages
given by these individual papers. In total, the input target list consists of 1352
unique stars.
6.3 Simulation Parameters
With this input target list, we proceed to run Monte Carlo simulations on each
target star, and determine the probability of detecting a planet around every star,
given the simulations’ assumptions of planet populations and survey construction.
For all planet simulations, we assume a power-law distribution that matches
observations of known radial velocity planets (Cumming et al., 2008): a powerlaw of index -0.61 that continues to some outer cut-off, beyond which planets
are no longer found. Mass follows a power-law distribution of index -1.2, also
from the Cumming et al. (2008) analysis. Orbital eccentricity is given by a fit to
radial velocity planets, which are nicely modeled by simple linear fits, one for Hot
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Jupiters (periods less than 21 days) and another for all other planets. Geometric
distributions are used to model the viewing angles and orbital phases, and finally
we solve for the separation between star and planet on the plane of the sky, which
we convert to arcseconds given the distance to the star.
We compute the fluxes of the simulated planets given the age of the target
star and the mass of the simulated planets, using the two classic models of giant
planets, Burrows et al. (2003) and Baraffe et al. (2003), and the new core-accretion
models from Fortney et al. (2008). To determine the probability a given target star
has a planet, we use the Fischer & Valenti (2005) volume-limited sample, which
gives ∼5% of stars having a planet within 2.5 AU above 1.6 MJup , which we then
scale given the power-law distributions for mass and semi-major axis. Then, the
sum of the probability of finding a giant planet for each target star, evaluated
across all target stars, gives the predicted number of planets from the end of the
survey.
We run the simulations with our current NICI contrast curve (Fig. 6.2), with
three different parameters being toggled on and off. 1) We insert a population of
GQ Lup-like objects (giant planets at large separations, Neuhäuser et al. (2005)),
which consist of the same mass and eccentricity distributions, but with semimajor axis now a constant probability distribution between 60 and 500 AU, and
a star having a 2% probability of hosting such a planet. 2) Switching between the
20% and median Gemini South seeing values, which set the Strehl as a function of
guide star V magnitude. The strehl scales the contrast curve, as well as the faint
limit for detecting a planet, regardless of separation. 3) Finally, we either allow
all stars to have an equal likelihood of hosting planets, or use the Johnson et al.
(2007) results to make a linear fit to the likelihood of harboring a giant planet as
a function of stellar mass, and correct the expected number of detected planets
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Figure 6.2 The contrast curve used to simulate the performance of NICI during
the survey. Within an arcsecond, the curve is generated by Zahed Wahhaj in July
2008, for a single NICI target star observed during commissioning. Beyond 1”, we
use the NICI Request for Proposal (RFP) curve. We note that this is the contrast
curve only, which can in theory reach arbitrarily faint planets, especially for faint
target stars. For the simulations themselves, we use the more physical constraint
that no planet fainter than mH =23 can be detected from a NICI observation.
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for this factor. This results in 8 sets of simulations, with the most optimistic being
one with GQ Lup-like objects, 20% seeing, and no Johnson et al. (2007) scaling
of planet fraction for stellar mass, and the worst having no GQ Lup-like objects,
median seeing, and the Johnson et al. (2007) stellar mass scaling.
Finally, we do each of these simulations at four exposure times, 30 minutes,
one hour, two hours, and four hours, scaling the contrast curve and minimum
detectable planet flux by the square root of the exposure time.
6.4 Constructing a Survey
If we have 420 hours for the full NICI survey (the remaining 80 hours are reserved
for follow-up of interesting objects), we need to find a good balance between the
number of stars we want to observe and the exposure time for each target star.
We’re allowing 15 minutes of overhead per star for slewing and locking onto the
star, as well as a 30% overhead on the total on-star integration time. Using these
constraints, Fig. 6.3 gives the possible survey size as a function of integration
time.
In Fig. 6.4, we give the range of expectation values for predicted number of
planets across the eight sets of simulation parameters. Each pair of connected
data-points go from the model which predicts the most detected planets (20th
percentile seeing, a population of GQ Lup-like objects at large separations, and no
scaling for the likelihood of having a giant planet with stellar mass), to the more
pessimistic set (median seeing, no large-separation massive objects like GQ Lup,
and weighting against M stars by scaling the planet fraction by stellar mass, as
given by Johnson et al. (2007)). We denote four survey designs by the ID numbers
1, 2, 3, and 4, with exposure times of 30 minutes, 1 hour, 2 hours, and 4 hours,
respectively, which allow for survey sizes of 556, 323, 175, and 92 stars. The
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Figure 6.3 The number of stars we could include in our survey, assuming we
have 420 hours of telescope time. The calculation assumes a 15 minute per star
overhead, and a 30% overhead on the total integration time. Exposure times of
30 minutes, one hour, two hours, and four hours are marked.
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Figure 6.4 The predicted number of planets from our survey using two sets of
models for planet fluxes (Burrows et al., 2003; Fortney et al., 2008), and with four
basic survey designs: from a large survey with short integration times (467 stars
at half an hour each) to a deep survey with much fewer stars (4 hours per star
on 77 stars), and two other designs between the two extremes. The blue numbers (left) give, while using the Burrows et al. (2003) models, how many stars in
each survey design come from the five target star sources, previously observed
stars at the VLT, MMT, and Gemini North for SDI/GDPS, the A star sample, Hipparcos stars selected by calcium R’HK emission, unobserved moving group stars
(Z&S, denoting that most of these stars are from Zuckerman & Song (2004)), and
the young, nearby M stars of Allen & Reid (2008). The red numbers (right) give
the same target breakdown, only for the Fortney et al. (2008) models. The two
connected data points at each survey type denote the most optimistic set of simulation parameters (20% seeing, GQ Lup-like objects, and no scaling for stellar
mass), and the most pessimistic combination (median seeing, no GQ Lup-like
objects, and using the Johnson et al. (2007) mass scaling). The top set of numbers
correspond to the optimistic models (uppermost set of blue diamonds and red
crosses), and the lower numbers are for the pessimistic case.
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two sets of connected points correspond to the models of planet luminosities of
Burrows et al. (2003) and Fortney et al. (2008), denoted by blue circles and red
crosses, respectively.
For each survey design, the stars with the largest likelihood of planet detection are placed into the survey. The numbers in the center of the figure give what
number of stars were drawn from each of the five sets of target stars. The top
set of numbers is for the optimistic case, represented by the upper datapoints
for both sets of luminosity models, and the bottom numbers for the pessimistic
case. Frustratingly, the best survey design for the Burrows et al. (2003) models is
#2, with 323 stars at 1 hour integration times, with the predicted yield of planets
dropping significantly at larger exposure times and fewer targets. The Fortney
et al. (2008) models, on the other hand, suggest the best survey design is to increase exposure time to two hours, and cut the number of stars by a half.
We note that this and subsequent plots were made when the input target list
was only partially complete. As a result, these plots only show 467 stars, instead
of having the full 1352 target stars that comprises the final input target list. However, since these were the plots used to determine the design of the NICI survey,
we include them here.
6.4.1 Scaling the Upper Cut-Off with Spectral Type
Another likely model of planet populations would not only have M stars with
fewer overall planets, but have M-star planets at closer star-planet separations.
To account for this, we’ve also run a set of simulations with the semi-major axis
cut-off scaled by the location of the snow line in the disk (this scales as the square
root of the star’s total luminosity), using 60 AU as the cut-off for solar-mass stars,
and scaling it up or down based on spectral type of the target star. The GQ Luplike objects in the optimistic cases are not scaled, and still reside between 60 and
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Figure 6.5 The same as Fig. 6.4, except with the outer semi-major axis limit is
allowed to vary as a function of luminosity of the target star (to track the snow
line). As we’d expect, M stars become less viable targets, while the A stars become very popular, accounting for most of the detectable simulated planets. The
optimal survey design ranges from 1 to 4 hours, depending on the choice of models used for planet fluxes, and the input planet population models.
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Figure 6.6 The same as Fig. 6.5, except with the outer semi-major axis limit now
30 AU.
500 AU for stars of all spectral types, in 2% of cases. Fig. 6.5 gives the results
with this scaled outer semi-major axis limit. The “sweet spot” for both models in
terms of survey design is about the same as it was with Fig. 6.4. This rewarding
of A stars gives us many more predicted planets, mostly from the earlier spectral
type target stars.
We must also consider the default of 60 AU for the outer cut-off: it is somewhat optimistic. When we consider the null result from the VLT H and Ks, SDI,
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and GDPS surveys, using the stellar mass dependence of stellar mass from Johnson et al. (2007) (but with no GQ Lup-like objects, and no scaling of the outer
cut-off of semi-major axis with stellar mass), we can exclude 60 AU or larger as
the upper limit on semi-major axis at 92% confidence, for the models of Burrows
et al. (2003). With the more pessimistic Fortney et al. (2008) models this limit
drops to 68%, or about 1σ. In order to consider other possible descriptions of
planet populations, we change this outer limit in to see what it does to our predictions. So we also consider these results for an outer limit of 50, 40, and 30 AU
(excluded to 88%, 81%, and 70% confidence for the Burrows et al. (2003) models,
and 55%, 40%, and 25% confidence for the models of Fortney et al. (2008)).
It is important to remember that these numbers are only for the case with
a fixed outer limit, which is constant across all spectral types, which is not the
model we’re simulating here. The VLT broadband, SDI, and GDPS surveys combined contained only a single A star, so a model of planet populations that makes
planet detection more likely would not be significantly constrained by previous
null results.
We plot the results of the smallest outer cut-off, 30 AU, in Fig. 6.6. The main effect, as expected, is we expect to detected fewer planets overall (note the values of
the Y-axis). As we move to smaller upper limits for semi-major axis, the Fortney
et al. (2008) models maintain the same general shape, with the longest exposure
times producing the most planets. This makes sense: given the faintness of these
models, we need the longest exposure times to reach planets. The Burrows et al.
(2003) models actually switch from advocating a 1 hour exposure time to 2 hours,
but not by a large amount, and this changes whether we use the optimistic or
pessimistic simulation parameters. Across the range of outer cut-off, the overall
composition of the survey doesn’t vary to a large extent.
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Figure 6.7 The same as Fig. 6.4, except with the outer semi-major axis limit now
30 AU.
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In Fig. 6.7 we plot the same details on the survey as in Fig. 6.4, keeping the
extent of the semi-major axis distribution fixed, but setting the outer edge at 30
AU. Again, moving to smaller outer limits on the semi-major axis distribution
reduces the expected planet yield from the survey, and keeping the extent of the
distribution fixed makes A stars less promising targets, while positively weighting M stars.
6.4.2 Parameters of the Target Stars
Next, we consider what types of stars make it into these different survey designs.
For each of the hypothetical surveys of Fig. 6.5, we extract the target stars that
make up those surveys, and plot their parameters in Fig 6.8 and Fig. 6.9. The
surveys consist mainly of stars more massive than the sun, as expected from the
fact that we scale the outer semi-major axis limit with stellar mass.
We reproduce these plots of target star parameters for the case of planets forming out 30 AU, regardless of the spectral type of the target star (fixed rather than
scaled), in Fig. 6.10,6.11. A stars become less common in the surveys, as lowermass stars can now have planets at much larger separations. These plots represent the major difficulty in designing the NICI Campaign: both the design of the
basic survey parameters and the composition of the target list cannot be simultaneously optimized for all possible models of planet populations.
6.4.3 The Curve of Growth
In order to determine the relative worth of the different targets stars, we’ve also
made plots that show how many planets we detect as we conduct the survey,
showing which target stars are most likely to contain detectable planets, and
which are less productive. In Fig. 6.12 and 6.13, we show two such curve-ofgrowth plots, giving the number of planets we’d expect to detect as a function of
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Figure 6.8 The target stars in the hypthetical surveys of Fig. 6.5, for the models
of Burrows et al. (2003), using the optimistic planet parameters. The semi-major
axis distribution continues out to 60 AU before being truncated, and this limit
is scaled with the spectral type of the star. In all cases, stellar mass is estimated
from the spectral type of the target star.
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Figure 6.9 The same as Fig. 6.8, only with the optimistic paramters for the planet
populations, and using the Fortney et al. (2008) models for planet brightness.
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Figure 6.10 The target stars in the hypothetical surveys of Fig. 6.7, for the models
of Burrows et al. (2003), using the optimistic planet parameters. The semi-major
axis distribution continues out to 30 AU before being truncated, which is constant
across all spectral types of target stars. In all cases, stellar mass is estimated from
the spectral type of the target star.
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Figure 6.11 The same as Fig. 6.10, only with the optimistic paramters for the
planet populations, and using the Fortney et al. (2008) models for planet brightness.
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the number of stars in the survey. For the most part, we’re adding a significant
number of planets across the survey, except for the largest, most shallow survey.
Which is unsurprising, as it would be unlikely there to be 500 equally good target
stars for direct imaging planet searches.
For each set of four plots, the left two panels contain the pessimistic case of
planet populations, the right two the optimistic case. The top two panels show
the curves of growth for different exposure times, and the bottom two panels
break up the 1 hour survey into the different input target list samples. Since
each survey is limited to 420 hours of total telescope time, the smaller exposure
time surveys encompass more stars than the deeper surveys. The Fortney models
show a common characteristic, that there are a limited number of target stars
where NICI can go deep enough to detect Fortney planets. So while planets are
initially detected at a reassuring rate, the curve quickly levels off, so that adding
additional target stars is not expected to yield additional planets.
This effect is even more stark in the 30 AU Fixed case (Fig. 6.13). With most
planets close to their parent star (and so in a part of the contrast curve where it is
more difficult to detect faint planets), there is a relatively small number of target
stars that are predicted to make good targets with the Fortney models, especially
at 1 hour integration times.
6.4.4 Implications for Spectral Type Composition of the Campaign Target List
We consider the properties of the target stars, and its influence on the probability
of detecting planets, given different input models. In Fig. 6.14, we plot the mass
of the target star as a function of its expected number of detected planets, for
the 60 AU scaled planet populations and the optimistic case. Each star is plotted
twice, once as the red point for the Fortney models, once as the blue point for the
Burrows models. The most favorable stars are the highest mass stars, especially
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Figure 6.12 The expected planet yield as a function of survey size (at each point
along the x-axis, if a survey is conducted of the best 30 stars, say, in the survey,
the y-axis gives the expected number of planets). The two left-hand plots give the
results for the pessimistic set of planet parameters, no GQ Lup objects, Johnson
et al. (2007) mass scaling, and median seeing, and the optimistic case is given
on the right. The top two plots contain stars from all sources for the four survey
designs, and the bottom plots break up the sample by target source. In these plots,
the outer limit of semi-major axis is at 60 AU for solar mass stars, and allowed to
scale with spectral type.
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Figure 6.13 The same as Fig. 6.12, except with the outer limit on semi-major axis
fixed at 30 AU for all stars.
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Figure 6.14 The probability of finding a planet around each target star in the four
types of surveys, using the optimistic planet parameters and the scaled 60 AU
upper limit on semi-major axis, as a function of the mass of the target star, as
estimated from spectral type.
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for the 1-hour exposure time plot. Some lower mass stars achieve high probabilities, but overall the best stars are the A stars (M > 2 M⊙). The Fortney models
show the same general trends, expect the predicted planet yields are systematically lower than those for the Burrows models.
Figure 6.15 shows this spectral type distribution again, only now for the 30
AU Fixed case (though again for the optimistic model). The trend has almost exactly reversed, with the lowest mass stars now reaching the highest probabilities.
Since planets extend out to 30 AU for stars of all spectral types, the high contrasts
required for the A stars make them much less favorable targets. For longer exposure times, stars more massive than the sun have almost disappeared, making
the preferred sample almost exclusively one of low-mass stars.
Making a similar plot for distance to the target star, as in Fig. 6.16, the results
are as we would expect. The closest stars achieve the highest planet yields, as
smaller-period planets become accessible to NICI. Looking at age, as in Fig. 6.17,
again the youngest stars are the most favored. The spike at 150 Myr represents
the young M-star sample (their probabilities are computed in a statistical manner, for ages between 0 and 300 Myr, but for plotting purposes they’re shown
at their average age of 150 Myr here). For this model of planet populations, the
youngest, closest, lowest mass stars are favored for the NICI Campaign. However, as the model is altered to allow the outer radius to scale with spectral type,
the recommendations for survey design and composition change dramatically.
6.4.5 Properties of the Detected Planets
Finally, we examine the parameters of the simulated planets we’d detect with
NICI. In Fig. 6.18, we plot histograms of “detectable” simulated planets, broken
up by target star source, with the area under each histogram showing the expected number of planets detected. These plots use the 60 AU scaled model, and
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Figure 6.15 The probability of finding a planet around each target star in the four
types of surveys, using the optimistic planet parameters and the fixed 30 AU
upper limit on semi-major axis, as a function of the mass of the target star, as
estimated from spectral type.
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Figure 6.16 The probability of finding a planet around each target star in the four
types of surveys, using the optimistic planet parameters and the fixed 30 AU
upper limit on semi-major axis, as a function of the distance to the target star.
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Figure 6.17 The probability of finding a planet around each target star in the four
types of surveys, using the optimistic planet parameters and the fixed 30 AU
upper limit on semi-major axis, as a function of the age of the target star.
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the optimistic set of planet parameters. With the Burrows et al. (2003) models,
most of the planets around M stars that we’re seeing are within an arcsecond,
and mostly between 5 and 20 AU. For A stars, most planets are well beyond an
arcsecond, outside of 100 AU. The other three surveys (which contain ranges of
spectral types) have planets spread across many separations. The bulk of the
planets are 10-15 magnitudes fainter than the primary, and have an apparent H
from 14 to 18.
For the Fortney et al. (2008) models, which predict systematically fainter planets, we find overall fewer planets, and in very different places (see Fig. 6.19). Most
of the detectable planets (except for those around M stars) are outside of 2”, and
closer to 100 AU (we’re really depending on those GQ Lup objects). As expected,
we need a more extreme delta-H (14-18) to reach planets, which are at apparent
magnitudes of 18-20 for those that we do find.
In Fig. 6.20, we again plot the properties of the detectable planets, using the
Burrows models, but now for the 30 AU Fixed case. The semi-major axis plot
shows a clear bifurcation, with the inner planets following distributions consistent with radial velocity planets (<30 AU), and the other objects following the
GQ Lup distribution (>60 AU). The most planets now come from the youngest
target stars, especially from the Zuckerman & Song (2004) young moving group
objects. The A stars, on the other hand, do the worst of the various input samples.
For the Fortney models, in Fig 6.21, the same general trends hold, only with
a decrease in the overall expected number of planets detected. Finally, we plot
all the detectable planets in term of the observable quantities, delta-magnitude
and separation, in Fig. 6.22 and 6.23. As we would expect, the detectable planets
trace out the input contrast curve. For the Burrows models, the planets pile up at
the inner edge of the NICI coronagraphic mask; with the 30 AU fixed cases, most
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Figure 6.18 Histograms giving mass, semi-major axis, on-sky separation (both
in arcseconds and AU), delta H magnitude, and apparent H magnitude for the
simulated planets NICI could detect, using the models of Burrows et al. (2003).
These planets are again from the optimistic scenario, with GQ Lup-like objects,
20th percentile seeing, and no scaling of the likelihood of finding a planet with
stellar mass. The outer limit for semi-major axis, however, is scaled by stellar
mass, with a value of 60 AU at a solar mass. The area under each histogram
represents the number of planets we’d expect to detect from the given set of target
stars.
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Figure 6.19 Histograms giving mass, semi-major axis, on-sky separation (both
in arcseconds and AU), delta H magnitude, and apparent H magnitude for the
simulated planets NICI could detect, using the models of Fortney et al. (2008).
These planets are again from the optimistic scenario, with GQ Lup-like objects,
20th percentile seeing, and no scaling of the likelihood of finding a planet with
stellar mass. The outer limit for semi-major axis, however, is scaled by stellar
mass. The area under each histogram represents the number of planets we’d
expect to detect from the given set of target stars.
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Figure 6.20 Histograms giving mass, semi-major axis, on-sky separation (both
in arcseconds and AU), delta H magnitude, and apparent H magnitude for the
simulated planets NICI could detect, using the models of Burrows et al. (2003).
These planets are again from the optimistic scenario, with GQ Lup-like objects,
20th percentile seeing, and no scaling of the likelihood of finding a planet with
stellar mass. The area under each histogram represents the number of planets
we’d expect to detect from the given set of target stars.
210
Figure 6.21 Histograms giving mass, semi-major axis, on-sky separation (both
in arcseconds and AU), delta H magnitude, and apparent H magnitude for the
simulated planets NICI could detect, using the models of Fortney et al. (2008).
These planets are again from the optimistic scenario, with GQ Lup-like objects,
20th percentile seeing, and no scaling of the likelihood of finding a planet with
stellar mass. The outer limit for semi-major is fixed at 30 AU. The area under each
histogram represents the number of planets we’d expect to detect from the given
set of target stars.
211
planets are close to their star, so most detections are at the inner working angle
of the system. For Fortney planets, the key is the overall faintness of the planets, so most detectable planets are beyond 1”, where the contrast curve becomes
sensitive enough to reach Fortney planets.
6.5 Final Survey Design
The analyses we have considered so far lead to a disturbing bifurcation: a NICI
Campaign conducted under the assumption that the 60 AU scaled model of planet
populations is correct would draw from a target list composed mostly of earlytype stars, while the 30 AU Fixed model suggests a Campaign observing mainly
late-type stars. There’s a secondary split, where the Burrows models favors short
exposure times and a large number of target stars, while the Fortney models point
to long exposure times, and observations of only the best stars. In a sense, it’s becoming necessary to pick a distribution of extrasolar planet populations before
conducting the survey that is meant to measure that very distribution. There is
an additional observing mode consideration: SDI observations are able to effectively attenuate the speckle noise within 1”, but at the cost of throughput (light
is first reduced by 50% at the beamsplitter, then cut down by the 4% methane filter). Analysis of the contrasts achieved with NICI show that we are speckle noise
limited within 1”, and shot noise limited outside of 1”. So Fig. 6.22 and 6.23 give
different answers for this as well: the Fortney planets are detectable beyond 1”,
so SDI would hinder the detections, while Burrows planets are expected to be in
the inner arcsecond, where they would greatly benefit from SDI.
For the final survey design, we choose a path of compromise between these
competing interests. Each star is observed with a “hybrid” mode, 60 minutes of
ADI (no beamsplitter, all the light passes through the broadband H filter and is
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Figure 6.22 All detectable planets, the ones that were in the previous histograms,
with contrast plotted against separation. As expected, they trace out the input
contrast curve quite nicely. This plot uses the models of Burrows et al. (2003).
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Figure 6.23 All detectable planets, the ones that were in the previous histograms,
with contrast plotted against separation. This plot uses the models of Fortney
et al. (2008).
214
observed with only one science camera), and 30 minutes of combined ADI and
SDI. This exposure time also represents a halfway point between the deep survey
preferred by the Fortney models, and the shallow survey for the Burrows models.
Finally, we choose the highest-ranked target stars from both the 60 AU scaled and
30 AU Fixed lists. We also set up a quota system where we require a minimum
number of stars in various mass bins (otherwise our survey would become half A
stars and half M stars), to allow us to use the results to examine planet population
data as a function of spectral type.
There are certainly compelling arguments against such a solution, namely the
idea that we should commit to a model and place all our resources into testing that model. For example, we might simply begin by assuming the 30 AU
Fixed Burrows model is the correct representation of reality, and draw our target
stars so that we maximize the number of planets predicted by this model. Then,
should we have a null result, we can reject this model with high statistical confidence, and embrace an alternate model. But this is not a compelling argument
to me, since it assumes there are a limited number of planet population models (for example, the two we have considered here), and it is simply a matter of
testing each of them in sequence. There are a number of free parameters in our
power-law fits, and that’s not even allowing for more complicated distributions
of planet parameters beyond simple power laws.
A null result has limited ability to direct us to the proper model of reality, it
can only rule out certain models. It is only by detecting planets in these surveys
that we can make solid progress toward coming up with a unified distribution
of exoplanet populations. A null result from the completed NICI Campaign will
still be valuable, it would rule out the 60 AU scaled and 30 AU fixed models
for the Burrows models of planet fluxes, and place strong constraints on the 60
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AU scaled Fortney model. By balancing our priorities, we have chosen a final
Campaign target list of 300 stars, which will allow us to place strong constraints
on the population of extrasolar giant planets.
6.6 Current NICI Planet-Finding Campaign Status
As of May 2011, the NICI Planet-Finding Campaign is entering its final year. Over
200 stars have been imaged for at least one epoch, with first epoch observations,
and second-epoch confirmations, being conducted on a regular basis. Two discovery papers have been published thus far, announcing brown dwarf companions to NICI target stars (Biller et al., 2010; Wahhaj et al., 2011). We have a number
of candidates that, given their age and brightness, are consistent with planetmass companions. Most of the similar objects analyzed to date with secondepoch astrometry have proven to be background stars, but we continue to sort
through the list of candidates to determine which, if any, are physical co-moving
companions (Liu et al., 2010).
The contrasts achieved have been consistent with predictions made before
the start of the Campaign, and the instrument has performed well throughout
the Campaign. A preliminary analysis of the stars without detected companions
(a null result for this subset of the final NICI observing list) places constraints
on extrasolar planet populations that are significantly stronger than presented in
Nielsen & Close (2010). With or without detected planets from the NICI stars
that remain to be observed (or re-observed for second epoch follow-up), the final
results from the NICI Campaign will greatly shape our knowledge of exoplanet
populations.
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C HAPTER 7
CONCLUSIONS AND FUTURE DIRECTIONS
In this thesis, I have put forward my experience in designing direct imaging surveys, and using null results from existing surveys to place constraints on the populations of extrasolar planets. In this concluding section, I look ahead to future
direct imaging surveys, with existing and future instruments, and what important scientific questions should be addressed by these new endeavors.
7.1 A Unified Distribution of Extrasolar Planet Populations
As radial velocity surveys became more efficient at finding planets over the last
16 years, we have learned a lot about the populations of extrasolar giant planets.
The very existence of Hot Jupiters was a surprise, and as the number of planets
continued to grow, more could be said about planet distributions. Some of the
relations measured to date include the correlation between planet frequency and
metallicity (Fischer & Valenti, 2005), power-law fits to orbital period and planet
mass (Cumming et al., 2008), and a correlation between planet frequency and
stellar host mass (Johnson et al., 2007). A robust quantitative description of planet
parameters, and how their distribution depends on properties of the host stars,
will be a strong constraint on theories of planet formation and evolution, and will
shape our understanding of extrasolar planets.
In essence, the function that planet searches (using any method) are attempting to define is:
dN
da dMp de dM∗ dτ∗ d[F e/H]∗
(7.1)
that is, the frequency of planets as a function of orbital semi-major axis, planet
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mass, eccentricity, stellar mass, stellar age, and stellar metallicity. (In fact, it may
be even more complicated than this, as binarity among planet host stars should
have a strong effect on the formation and evolution of planets.) Such an expression would greatly inform planet formation theories, and the time dependence
will set the constraints on models of how planetary systems evolve with time.
To define this function, it will be necessary to discover planets throughout this
six-dimensional parameter space. Radial velocity and transit surveys have made
extraordinary progress in finding planets at small separations (semi-major axis <
∼
5 AU), and have been pushing down to smaller and smaller masses. The Kepler
mission is likely to fill out much of this parameter space within 1 AU, for masses
down to almost an Earth mass. Yet direct imaging serves an important role, as it
will be the only planet search technique sensitive to planets at larger separations.
It is also complementary to radial velocity techniques in terms of stellar age, in
that RV surveys prefer older, less active stars for precise radial velocity measurements, while direct imaging campaigns are focused on the youngest stars, where
the planets are the most self-luminous. It will be by combining the statistics from
planet discoveries across every search technique that we can truly build a unified
distribution of planet populations.
It is again important to note that while null results are a powerful tool for
setting constraints on particular models of planet populations (as I have done in
Chapters 4 and 5), null results alone will not allow us to determine which of many
competing models of planet distributions best fits reality. In the case of the model
that follows the RV-derived power law distributions of Cumming et al. (2008)
with no correction for mass of the host star, for example, planets must be found
only within 23 AU at 68% confidence. However, other limits can be found by
scaling the planet frequency with host mass (the Johnson et al. (2007) correction),
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or scaling the outer semi-major axis cut-off with host star mass (as in Chapter 6).
And similarly for toggling between the Baraffe et al. (2003) models and Fortney
et al. (2008) models. We can construct a model of planet populations with a given
semi-major axis distribution, upper cut-off, mass distribution, planet frequency,
and using the Baraffe et al. (2003) models, and determine that such a model, given
the sensitivity of our survey, was expected to return 3 planets, for example. We
can then conclude with 95% confidence that that model is incorrect. However,
the model is a convolution of multiple assumptions, and the null result by itself
does not guide us to which assumption (or assumptions) must be revised. Many
different constraints can come from many different potential planet population
models using null results, but actual planets are required to choose between the
different models.
7.2 Other Model Possibilities
It is also worth noting that there are other possible models of planet populations
beyond those that I have considered previously. As I have noted, multiple planet
detections will be necessary to evaluate if these models conform with observed
results. But when choosing observing strategies and target lists, it is prudent to
consider as many plausible models as possible, in order to maximize the likelihood of success for the survey.
7.2.1 Correlated Distributions
In many cases, when determining a subset of the distribution of Eqn. 7.1, the
assumption is typically that the distribution of each parameter is independent of
all others, so that
219
dN
= f (a) g(Mp ) h(e) i(M∗ ) j(τ∗ ) k([F e/H]∗ )
da dMp de dM∗ dτ∗ d[F e/H]∗
(7.2)
For example, Cumming et al. (2008) assume that mass and orbital period are described by independent power laws. Similarly, Johnson et al. (2010) find an equation for planet frequency as a function of stellar host mass and metallicity, but
the two are assumed independent. In fact, all of my own simulations assume
that each parameter is drawn from an independent distribution. (with two minor exceptions: 1) I assume orbital eccentricity has two distributions, divided at
an orbital period of 21 days. In practice, since no Hot Jupiter is detectable by direct imaging, my results depend entirely on the eccentricity distribution for outer
planets. 2) For the Ida & Lin (2004) models, planets are drawn from outputs to
their simulations, so mass and semi-major axis are correlated. However, these
models do not figure strongly into my results, due to the low number of expected
planets.)
In practice, however, it is reasonable to expect that many of these distributions
are highly correlated. It’s well-known that eccentricity of radial velocity planets follows two distributions, one for Hot Jupiters and another for longer-period
planets, as I show in Fig. 4.2. While Johnson et al. (2007) have shown that the frequency of planets correlates strongly with stellar host mass, it would not be unexpected for other planet properties to also correlate with host mass. Perhaps the
power law governing planet mass distribution also changes with spectral type,
so lower-mass stars have lower-mass planets. As we assume in Chapter 6, it is
also likely that the outer limit to which planets are found also scales with spectral
type (as may the power law index for semi-major axis).
Determining these interdependencies is quite involved, as it requires a large
enough number of detected planets across a many-dimensional parameter space
220
(and a full understanding of the completeness to each detected planet and to
regions of non-detections) to determine the mathematical description of planet
properties. Properties as a function of age will be most difficult, as evolution
of a planetary system is likely most rapid in the first ∼100 Myr after formation,
and nearby stars younger than that age are limited, and quantized in groups
of fixed ages, rather than in a well-sampled continuous distribution. In fact, it
may be the case that parameterized (or partially parameterized) prescriptions for
these variables may be all that’s possible for the foreseeable future. Nevertheless,
it is an effect that those studying planets should keep in mind, and we should
continually check out data for correlations, as it is these correlations that are likely
to tell us much about the physics behind the formation and evolution of planets.
7.2.2 Alternatives to Single Power Law Fits
In astronomy, it is unavoidable to attempt to fit most distributions with a power
law, in no small part because power laws are typically the best description of most
distributions. Distributions of planet mass and semi-major axis for RV planets
are best fit by power law distributions, as shown by Cumming et al. (2008). Yet
it is worth considering the possibility that more complicated distributions may
do a better job describing some of the parameters of extrasolar planets. For example, while a smooth power law nicely fits giant planets at small separations,
it’s entirely possible that there are breaks in this distribution representing different types of planets and formation mechanisms. Neptune-mass planets likely
form differently from Jupiter-mass planets, so a break in the mass distribution
will likely become apparent as the number of detected Neptune-mass planets increase. If there are two formation mechanisms for giant planets operating at different orbital distances, the semi-major axis distribution is likely to show a break
as well.
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The only obvious way to measure such a break is to have adequate statistics
of planet populations on both sides of the break; for the semi-major axis distribution, this will mean planets at larger separations than those being found by the
radial velocity technique. While it is technically possible to set limits on a multiple component function with a null result (in addition to the known power law
index for semi-major axis at small separations, we would also need the index at
large separation, the location of the break, and the upper cut-off, one dimension
more than the analysis that goes into Fig. 5.8), detected planets would provide
much more solid constraints, in addition to showing whether this broken power
law model is correct or not.
7.3 Upcoming Surveys with Dedicated High-Contrast Planet Finders
The NICI Planet-Finding Campaign represents a massive leap forward in direct imaging planet searches, with a more sensitive instrument, and an unprecedented 500 hours of observing time dedicated to the planet-finding mission. Yet
within the next year, new instruments dedicated to imaging exoplanets will come
online that achieve even higher contrasts, and are likely to push to even larger
time commitments, opening up the field of exoplanet detection to an extraordinary extent.
GPI, the Gemini Planet Imager (Graham et al., 2007), and SPHERE, the SpectroPolarimetric High-contrast Exoplanet Research instrument (Boccaletti et al., 2008),
are both set to come online in 2012, and achieve contrasts between 106 and 107
within 1” of the target star. This increased sensitivity, especially right at the inner
working angle of the instrument, will reach planets that have been hidden from
previous surveys. Fig. 7.1 shows the expected contrast of the GPI instrument,
as a function of separation and target star magnitude. For the brightest stars,
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Figure 7.1 The predicted 5σ contrast from the Gemini Planet Imager (GPI).
As a reminder, the NICI instrument is achieving contrast ratios of 15 magnitudes (10−6 ) at 1” around the brightest stars. For the brighter target stars,
GPI will reach planets up to and beyond a factor of 10 fainter, at separations
down to 3 times smaller, than NICI’s current performance. However, for all
planets past ≈1.5” GPI has no sensitivity, nor is GPI any more sensitive than
NICI for stars with I <
∼ 8 mag.
Figure from Gemini GPI instrument page,
http://www.gemini.edu/node/11552
223
GPI should reach contrasts up to a factor of 10 higher at 1”, and up to a factor
of 100 higher at 0.5”, than NICI. With SPHERE promising similarly impressive
contrasts, and both instruments likely to be available for a combined exposure
time of several thousand hours over the first 2-3 years, for the purpose of directly
imaging exoplanets, the number of directly imaged planets should increase dramatically by 2014. Other instruments already online and being completed, such
as HiCIAO at Subaru, MagAO at the Magellan telescope, and the LBT Interferometer, will provide even further opportunities for planet discoveries and characterization (Hodapp et al., 2008; Close et al., 2010; Hinz, 2009).
This amazing opportunity will be coupled with the responsibility to make the
most out of these incredible contrasts and time allocations. It will be essential
to keep in mind previous null results (and detected planets) from less sensitive
instruments when designing both the observing strategy and target list. Such an
eye to the past not only informs a survey design that maximizes the number of
expected planets, but also focuses the survey to probe areas of parameter space
that have not been reachable with previous efforts.
Additionally, there is much to be gained from pushing both radial velocity and
direct imaging to their limits, and image a radial velocity planet (or take radial
velocity data on the host star of a directly imaged planet, as the case may be). As
I have discussed in Chapter 2, there is great value in providing constraints to the
masses given by models of extrasolar planet fluxes, and independent planet mass
measurements will provide strong bounds to these models.
In the long term, extremely large telescopes such as the Giant Magellan Telescope (GMT) will push to fainter, closer-in planets than can currently be reached.
I show an example of planet simulations (as described in Chapter 4.3) in Figures
7.2 and 7.3. Contrasts offered by these giant telescopes will push to planets at
224
lower masses closer to their stars, accessing areas of parameter space not previously probed.
7.4 Direct Detection of Extrasolar Planets from Space
Beyond GPI and SPHERE, the next frontier of directly imaging extrasolar planets
will be dedicated planet-imaging spacecraft, specifically built to achieve higher
contrasts and raw sensitivity than can be obtained from ground-based observations. In the medium-term, a mission such as EXCEDE (Greene et al., 2007), designed to study planets and disks with a high contrast visible light coronagraph,
will enable the study of planets (in reflected light) at separations more commonly
associated with the radial velocity technique. This overlap of techniques is key,
as planets that can be detected by both radial velocity and imaging allow for the
testing and calibration of models of planet atmospheres. Models of planet atmospheres will have to fit both the near infrared emission spectrum measured by
instruments such as GPI and SPHERE, and the visible light reflection spectrum
from a spacecraft like EXCEDE. Having to reproduce such a wide range of wavelengths will strongly constrain models, and deepen our physical understanding
of the nature of these objects.
At the even longer term is TPF, the Terrestrial Planet Finder. Though the proposed instrument has many designs and configurations (and none are currently
fully funded by NASA), it is likely that there will be, within a few decades, a
spacecraft that meets the basic design requirements of TPF: to detect and characterize the atmosphere of an Earth analog orbiting a star within 10 pc. The potential here for the main science driver is both obvious and immense: to characterize
Earth-like planets around nearby stars will be to truly place our own planet into
context, and see if there are other planets that are suitable for animal life like
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Figure 7.2 The predicted ability of the Giant Magellan Telescope to detect planets around a 100 Myr A star at 30 pc, observing in the L’ band. In this case,
almost 40% of the simulated planets could be detected, as the contrast curve easily reaches into the equivalent of the giant planet region of our own solar system
(though at high planet masses). This simulation assumes a distribution of planets
consistent with known radial velocity planets, that continues out to a maximum
semi-major axis of 20 AU (consistent with current direct imaging null results),
and uses the Baraffe et al. (2003) models of planet brightnesses. GMT 5σ contrast
provided by Philip Hinz.
226
Figure 7.3 As in Figure 7.2, the simulated ability of the GMT to detect planets at
L’, this time for a solar-mass star slightly younger than our own Sun. A third of
the simulated planets are detected, and again the separations of giant planets in
our own solar system are probed, if only at the 2 MJup and above level. GMT
contrast curve provided by Philip Hinz.
227
us. But such an instrument will not be able to help itself, while searching for the
signal of Earth-analogs, to detect the “noise” of exo-Neptunes and Jupiters in intermediate orbits. Again, the hope will be that techniques overlap, that Jupiters
and Neptunes (and the Earths!) around nearby stars are detected with both imaging and radial velocity, and so complete, consistent models can be refined to fully
reproduce all observable quantities, including mass. This census of planets (over
many decades in mass) will greatly inform the picture of planet populations, and
from there our understanding of how planetary systems form and evolve. Terrestrial Planet Finder is designed (and named) to find Earth-like planets, but it will
be an invaluable tool to discover and characterize extrasolar planetary systems,
placing not just our own planet, but our own Solar System into context, as we
shed light on the mechanisms by which these systems are born and change over
time.
7.5 Final Thoughts
The field of directly imaging extrasolar planets looks bright indeed, with exciting prospects for the near, medium, and far term likely to revolutionize our
understanding of extrasolar planets, their structure, their formation, and their
evolution. One ongoing flaw in the field, however, has been the disparate nature of surveys and analyses conducted to date. It is natural for surveys to be
conducted with a particular (sometimes narrow) science goal in mind, especially
when observing time is at a premium. However, typically the results from these
individual surveys are isolated limits set by that survey alone, with multiple surveys of similar depths placing similar constraints on populations of extrasolar
planets. Much greater conclusions can be reached, however, by combining the
results from these various survey into a larger analysis, with a greater sample of
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target stars. Even duplicating target stars is of value, as single stars that have
been observed at multiple epochs (allowing greater orbital coverage), and multiple wavelengths, can allow for greater completeness to planets than a single
observation (Biller et al., 2010). More effort should be placed into combining the
almost decade-long backlog of direct imaging surveys, both with and without
null results, into a unified constraint on planet populations at large separations.
There is also the issue of overlap in surveys: young, nearby stars make the
best targets for direct imaging surveys. This is well known, as is the fact that
there are a limited number of young, nearby stars in the sky. Both SPHERE and
GPI will have similar capabilities, will observer at similar wavelengths, and will
observe at similar epochs (2012-2014). In a sense, this is natural in science, and
has positive benefits: the fierce competition will lead to both sides streamlining
their surveys, frontloading their best targets, and publishing results as quickly as
possible. It will also place pressure on the data reduction and analysis, so that no
detectable planets are missed, lest the competitors pick up an overlooked planet
that one’s own team could have discovered. Yet at the same time, there is a sense
of waste, that should the two teams coordinate, a larger total target list could be
constructed, and the statistical constraints placed on planet populations by the
combination of the results from the two instruments could define the distributions of giant exoplanets to an unprecedented degree.
If one is to put the names of the stars in the Beta Pic moving group, for example, into the Gemini and VLT archives, one finds observations of these objects
going back several years, often more than once per year, each with a proposal
title that includes some variant of the phrase “search for giant planets.” Some of
these observations represent complimentary search techniques, some represent
gains in contrast from previous attempts, but many are simple duplications of
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other observations. Yet it is this strong competition that leads to quick publications, and frenetic activity to confirm, follow up, and analyze objects like Beta Pic
b and the HR 8799 planets. I don’t have a clear solution to this question, about
which path is preferred from the point of view of getting the maximal science
from extrasolar planet observations. But in a way, the question is likely to be answered for us, for the odds of forming the political alliance necessary for the two
competing instrument teams to cooperate on target list selection is so vanishingly
small, that outright competition is the only plausible possibility.
Nevertheless, I am hopeful that out of the fires of that competition will still
rise a grand statistical sample from which we can gain a better understanding of
the populations of giant extrasolar planets. And while the first 100 target stars on
a direct imaging survey are quite obvious, it’s the next few hundred where different assumptions and search priorities come into play. So while the Beta Pic, AB
Dor, and Tuc/Hor moving groups will be on each target list, there should still be
a large number of stars that are observed by only one instrument, increasing the
total target sample. (In fact, this is another benefit of competition, that in order
to out-perform the opposing team, each group will be highly motivated to be as
clever and innovative as possible in their target selection.) And after each team
publishes its survey analysis papers, possibly with not-quite overlapping conclusions on planet populations, these two results can be combined (and combined
with previous results, as well), and we as a community can move toward a truly
unified picture of extrasolar planet populations.
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