Motivation
Inferring M and Si from L and age
Conclusion
Constraining the initial entropy of directly-detected exoplanets
Gabriel-Dominique Marleau1,2
1
MPIA (Heidelberg)
Skemer et al. (2012)
2
Andrew Cumming2
McGill University (Canada)
Currie et al. (2011)
Motivation
Inferring M and Si from L and age
Conclusion
Overview
1
Motivation
Direct detection surveys
Uncertainty in post-formation conditions
2
Inferring M and Si from L and age
Cooling models
Applications
3
Conclusion
Constraining the initial entropy of directly-detected exoplanets
1 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Overview
1
Motivation
Direct detection surveys
Uncertainty in post-formation conditions
2
Inferring M and Si from L and age
Cooling models
Applications
3
Conclusion
Constraining the initial entropy of directly-detected exoplanets
2 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Direct detection surveys
Direct imaging
Bias towards young, massive, and hot planets
Many surveys on now or soon: SPHERE, GPI, VLT, HiCIAO, JWST, etc.
→ Dramatic increase in number and detection of core-accretion candidates
Luminosity (LSun)
10-2
10-3
10-4
10-5
10-6
10-7
106
108
Age (yr)
109
1010
Neuhäuser & Schmidt (2012)
Dominik (2011), modif.
Constraining the initial entropy of directly-detected exoplanets
107
3 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Direct detection surveys
Direct imaging
Bias towards young, massive, and hot planets
Many surveys on now or soon: SPHERE, GPI, VLT, HiCIAO, JWST, etc.
→ Dramatic increase in number and detection of core-accretion candidates
Luminosity (LSun)
10-2
10-3
10-4
10-5
10-6
10-7
106
108
Age (yr)
109
1010
Neuhäuser & Schmidt (2012)
Dominik (2011), modif.
Constraining the initial entropy of directly-detected exoplanets
107
3 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Hot start or cold start?
Core accretion: closer-in, less massive, colder (lower S)
Gravitational instability: tens of AU, heavier, hotter
? Actually, uncertain initial conditions →
Marley et al. (2007)
Constraining the initial entropy of directly-detected exoplanets
4 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Hot start or cold start?
Core accretion: closer-in, less massive, colder (lower S)
Gravitational instability: tens of AU, heavier, hotter
? Actually, uncertain initial conditions → need to consider arbitrary Si
Marley et al. (2007)
Constraining the initial entropy of directly-detected exoplanets
4 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Hot start or cold start?
Core accretion: closer-in, less massive, colder (lower S)
Gravitational instability: tens of AU, heavier, hotter
? Actually, uncertain initial conditions → need to consider arbitrary Si
Marley et al. (2007)
Spiegel & Burrows (2012)
Constraining the initial entropy of directly-detected exoplanets
4 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Consequences
Hot-start models used for planning → overpredict yields
Masses assigned from hot starts → wrong statistics
Conversely: use detections to inform formation scenarios
Constraining the initial entropy of directly-detected exoplanets
5 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Consequences
Hot-start models used for planning → overpredict yields
Masses assigned from hot starts → wrong statistics
Conversely: use detections to inform formation scenarios
Constraining the mass and initial entropy of directly-detected planets
Make planet models with arbitrary entropy → L(M, S(t))
Given L and age, find which (M, Si ) correspond to this
Constraining the initial entropy of directly-detected exoplanets
5 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Consequences
Hot-start models used for planning → overpredict yields
Masses assigned from hot starts → wrong statistics
Conversely: use detections to inform formation scenarios
Constraining the mass and initial entropy of directly-detected planets
Make planet models with arbitrary entropy → L(M, S(t))
Given L and age, find which (M, Si ) correspond to this
? Independent of formation model!
Constraining the initial entropy of directly-detected exoplanets
5 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Uncertainty in post-formation conditions
Consequences
Hot-start models used for planning → overpredict yields
Masses assigned from hot starts → wrong statistics
Conversely: use detections to inform formation scenarios
Constraining the mass and initial entropy of directly-detected planets
Make planet models with arbitrary entropy → L(M, S(t))
Given L and age, find which (M, Si ) correspond to this
? Independent of formation model!
Constraining the initial entropy of directly-detected exoplanets
5 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Overview
1
Motivation
Direct detection surveys
Uncertainty in post-formation conditions
2
Inferring M and Si from L and age
Cooling models
Applications
3
Conclusion
Constraining the initial entropy of directly-detected exoplanets
6 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets
Standard opacities and composition
Usual constant-S structure equations
Given M and S → Lbol and tcool
105
Temperature (K)
(Found Lbol (M, S)) explanable)
Si
Si-∆S
104
time
10
3
100
102
104
106
Pressure (bar)
108
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
7 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets
L, LD (LSun)
10-2
Standard opacities and composition
10-4
15 MJ
at t=0
10 MJ
at t=0
10-8
7
Given M and S → Lbol and tcool
8
9
10
11
12
Entropy (kB/baryon)
105
Temperature (K)
→ Grid of models specified by M and S
20 MJ
at t=0
10-6
Usual constant-S structure equations
(Found Lbol (M, S)) explanable)
20 MJ
15 MJ
10 MJ
3 MJ
1 MJ
13
14
Si
Si-∆S
104
time
10
3
100
102
104
106
Pressure (bar)
108
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
7 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets
L, LD (LSun)
10-2
Standard opacities and composition
10-4
15 MJ
at t=0
10 MJ
at t=0
10-8
7
Given M and S → Lbol and tcool
8
9
10
11
12
Entropy (kB/baryon)
105
Temperature (K)
→ Grid of models specified by M and S
20 MJ
at t=0
10-6
Usual constant-S structure equations
(Found Lbol (M, S)) explanable)
20 MJ
15 MJ
10 MJ
3 MJ
1 MJ
13
14
Si
Si-∆S
104
time
10
3
100
102
104
106
Pressure (bar)
108
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
7 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets (cont’d)
Cooling curves:
! Low S means long tcool
t < tcool : ≈ remember i.c.
t > tcool : ≈ power law
Luminosity (LSun)
10-2
10 MJ
3 MJ
1 MJ
10-3
10-4
Si = 12
10-5
10-6
Si = 9
10-7
Si = 8
10-8
106
107
108
Age (yr)
109
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
8 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets (cont’d)
Cooling curves:
! Low S means long tcool
t < tcool : ≈ remember i.c.
t > tcool : ≈ power law
Luminosity (LSun)
10-2
10 MJ
3 MJ
1 MJ
10-3
10-4
Si = 12
10-5
10-6
Si = 9
10-7
Si = 8
10-8
106
107
108
Age (yr)
109
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
8 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets (cont’d)
Cooling curves:
! Low S means long tcool
t < tcool : ≈ remember i.c.
t > tcool : ≈ power law
Luminosity (LSun)
10-2
10-3
10 MJ
3 MJ
1 MJ
Si = 12
10-4
10-5
10-6
10-7
Si = 9
Si = 8
10-8
106
107
108
Age (yr)
109
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
8 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Cooling models
Thermal evolution of gas giant planets (cont’d)
Cooling curves:
! Low S means long tcool
t < tcool : ≈ remember i.c.
t > tcool : ≈ power law
Luminosity (LSun)
10-2
10 MJ
3 MJ
1 MJ
10-3
10-4
10-5
10-6
10-7
10-8
106
107
108
Age (yr)
109
Marleau & Cumming 2012 (in prep.)
Neuhäuser & Schmidt (2012)
Constraining the initial entropy of directly-detected exoplanets
8 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
HR 8799 b
Luminosity (LSun)
10-2
10-3
10-4
10-5
10-6
10-7
106
107
108
Age (yr)
109
Marois et al., Zuckerman (2010)
Hot-start masses
Constraining the initial entropy of directly-detected exoplanets
9 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
HR 8799 b
Luminosity (LSun)
10-2
8.1 MJ, high Si
10-3
10-4
10-5
10-6
10-7
106
Marois et al., Zuckerman (2010)
0
12
Hot-start masses
Initial entropy
11
2
107
108
Age (yr)
4
6
109
8
10
8
10
30 Myr
60 Myr
10
9
8
7
0
Constraining the initial entropy of directly-detected exoplanets
9 / 13
2
4
6
Mass (MJ)
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
HR 8799 b
Luminosity (LSun)
10-2
8.1 MJ, high Si
10-3
10-4
10-5
10.5 MJ, Si = 9.3
10-6
10-7
106
Marois et al., Zuckerman (2010)
0
12
Hot-start masses
→ Lower bound on Si
11
Initial entropy
Multiple system → dynamical info
2
107
108
Age (yr)
4
6
109
8
10
8
10
30 Myr
60 Myr
10
9
8
7
0
Constraining the initial entropy of directly-detected exoplanets
9 / 13
2
4
6
Mass (MJ)
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
HR 8799 b
Luminosity (LSun)
10-2
8.1 MJ, high Si
10-3
10-4
10-5
10.5 MJ, Si = 9.3
10-6
10-7
106
Marois et al., Zuckerman (2010)
0
12
Hot-start masses
→ Lower bound on Si
CA too cold by ∆S = 0.5 but ok
11
Initial entropy
Multiple system → dynamical info
2
4
6
109
8
10
8
10
30 Myr
60 Myr
10
9
8
7
0
Constraining the initial entropy of directly-detected exoplanets
107
108
Age (yr)
9 / 13
2
4
6
Mass (MJ)
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
HR 8799 b
Luminosity (LSun)
10-2
8.1 MJ, high Si
10-3
10-4
10-5
10.5 MJ, Si = 9.3
10-6
10-7
106
Marois et al., Zuckerman (2010)
0
12
Hot-start masses
→ Lower bound on Si
CA too cold by ∆S = 0.5 but ok
11
Initial entropy
Multiple system → dynamical info
2
4
6
109
8
10
8
10
30 Myr
60 Myr
10
9
8
7
0
Constraining the initial entropy of directly-detected exoplanets
107
108
Age (yr)
9 / 13
2
4
6
Mass (MJ)
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
β Pic
12
4 Myr
20 Myr
Initial entropy
11
Lagrange et al. (2011)
Upper mass from RV → minimum Si
10
9
8
7
0
5
10
Mass (MJ)
15
20
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
10 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
β Pic
12
4 Myr
20 Myr
Initial entropy
11
Lagrange et al. (2011)
Upper mass from RV → minimum Si
10
Excluded
by RV
9
8
7
0
5
10
Mass (MJ)
15
20
Traditional CA too cold by ∆S = 1.5
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
10 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
β Pic
12
4 Myr
20 Myr
Initial entropy
11
Lagrange et al. (2011)
Upper mass from RV → minimum Si
10
Excluded
by RV
9
8
7
0
5
10
Mass (MJ)
15
20
Traditional CA too cold by ∆S = 1.5
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
10 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
β Pic
12
4 Myr
20 Myr
Initial entropy
11
Lagrange et al. (2011)
Upper mass from RV → minimum Si
10
Excluded
by RV
9
8
7
0
Traditional CA too cold by ∆S = 1.5
(but more realistic shock → ok?)
5
10
Mass (MJ)
15
20
Marleau & Cumming 2012 (in prep.)
Assume dN/dM → posterior on Si
Constraining the initial entropy of directly-detected exoplanets
10 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
β Pic
12
4 Myr
20 Myr
Initial entropy
11
Lagrange et al. (2011)
Upper mass from RV → minimum Si
10
Excluded
by RV
9
8
7
0
Traditional CA too cold by ∆S = 1.5
(but more realistic shock → ok?)
With different
N(M) priors
5
10
Mass (MJ)
15
20
Marleau & Cumming 2012 (in prep.)
Assume dN/dM → posterior on Si
Constraining the initial entropy of directly-detected exoplanets
10 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
Complication: Deuterium burning
Add deuterium burning (M & 13 MJ ):
Z
dS
Lbol = −
T dm + LD
dt
Si = 14
16 MJ
10-3
L (LSun)
Cooling slowed down
10-2
10-4
10-5
Gives late-time D flashes
10-6
Can realistically be formed?
10-7
Si = 7.5
106
107
108
Time (yr)
109
1010
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
11 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
Complication: Deuterium burning
Add deuterium burning (M & 13 MJ ):
Z
dS
Lbol = −
T dm + LD
dt
16 MJ
10-4
10-5
Gives late-time D flashes
10-6
Can realistically be formed?
10-7
→ Observational consequences
Si = 14
10-3
L (LSun)
Cooling slowed down
10-2
Si = 7.5
106
107
108
Time (yr)
109
1010
Detectable by D in spectrum?
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
11 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Applications
Complication: Deuterium burning
Add deuterium burning (M & 13 MJ ):
Z
dS
Lbol = −
T dm + LD
dt
16 MJ
10-4
10-5
Gives late-time D flashes
10-6
Can realistically be formed?
10-7
→ Observational consequences
Si = 14
10-3
L (LSun)
Cooling slowed down
10-2
Si = 7.5
106
107
108
Time (yr)
109
1010
Detectable by D in spectrum?
Marleau & Cumming 2012 (in prep.)
Constraining the initial entropy of directly-detected exoplanets
11 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Overview
1
Motivation
Direct detection surveys
Uncertainty in post-formation conditions
2
Inferring M and Si from L and age
Cooling models
Applications
3
Conclusion
Constraining the initial entropy of directly-detected exoplanets
12 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Application to HR 8799 system and β Pic: their Si > 9.5
→ Need to tweak core accretion to explain β Pic
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Application to HR 8799 system and β Pic: their Si > 9.5
→ Need to tweak core accretion to explain β Pic
Exciting future as close-in planets start being detected
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Application to HR 8799 system and β Pic: their Si > 9.5
→ Need to tweak core accretion to explain β Pic
Exciting future as close-in planets start being detected
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Application to HR 8799 system and β Pic: their Si > 9.5
→ Need to tweak core accretion to explain β Pic
Exciting future as close-in planets start being detected
Marleau & Cumming (2012) soon on arXiv!
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming
Motivation
Inferring M and Si from L and age
Conclusion
Summary and outlook
? Thank you for your attention!
?
Proper interpretation of direct detections → M possibly M hot start
Key point
Given L at t, can calculate curve of allowed M–Si
Other M information → constrain hot-/coldness of start
→ Statistically compare with formation models (population synthesis)
Application to HR 8799 system and β Pic: their Si > 9.5
→ Need to tweak core accretion to explain β Pic
Exciting future as close-in planets start being detected
Marleau & Cumming (2012) soon on arXiv!
Constraining the initial entropy of directly-detected exoplanets
13 / 13
Marleau & Cumming