Planetary interiors: What they can(not) tell us about formation Methods and constraints Jérémy Leconte
Timeline Formation ( 1-10 Myr) Mass Radius Orbital Parameters Stellar Parameters... Evolution ( 1-10 Gyr) Observation ( 1-10 yr)
Planetary interiors: What they can(not) tell us about formation I. How can we link observations and internal physical properties: Structure and evolution models II. Constraints on the composition and enrichment. III. Can we «rewind» and directly constrain formation processes?
Mass-Radius Diagram Bouchy et al. (A&A 2004)
Mass-Radius Diagram M M 1 10 100 1000 10 000 100 000 R RJ 10.0 5.0 2.0 1.0 0.5 100 50 20 10 5 R R 0.2 2 0.1 1 0.01 0.1 1 10 100 1000 M M J
(Sub)stellar evolution equations r m = 1 4πr 2 ρ P m = Gm(r) 4πr 4 Heavy elements: Iron/Rock/H2O EOS (ANEOS, SESAME; See Baraffe et al. (A&A 2008) H/He (Z=0.02): SCvH EOS l m = T S t ln T ln P = T Consistent Irradiated Atmosphere models (Barman et al. 2001)
(Sub)stellar evolution equations EOS Heavy elements, H, He mixing? r m = 1 4πr 2 ρ Presence of a 1 st order Plasma Phase Transition? P No calibration experiments at high pressure & temperatures m = Gm(r) 4πr 4 Boundary conditions Chemical composition? Heavy elements: Iron/Rock/H2O EOS (ANEOS, Opacities? SESAME; See Baraffe et al. (A&A 2008) Day/Night redistribution? H/He (Z=0.02): SCvH EOS Consistent Irradiated Atmosphere models (Barman et al. 2001) l m = T S t Showman et al. 2009 global average ln T isotropic approximation ln P = T Fortney et al. 2005 HD 209458 b global average κ v * /10 Iro et al. 2005 Guillot (A&A 2010) Barman et al. 2005
Mass-Radius Diagram: the good news! M M 1 10 100 1000 10 000 100 000 R RJ 10.0 5.0 2.0 1.0 0.5 0.2 0.1 Mc 10100M Irradiated Water Rock Iron 0.01 0.1 1 10 100 1000 M M J HHeZ 10 8 yr 5.10 9 yr 100 50 20 10 5 2 1 R R Chabrier et al. (A&A 1997) Fortney et al. (ApJ 2007) Baraffe et al. (A&A 2008) Leconte et al. (2009, 2010d)
How can we link observations & internal physical properties? Can we constrain the composition?
Super-Earths Even for a perfectly defined mass and radius: Degeneracy of Composition Can hint at H2O/Fe dominated planets in favorable cases Can reject some extreme compositions Still uncertainties on the EOS in the high pressure range!!! Uncertainties on the differentiation of the solid core. Valencia et al. (ApJ 2007)
When gas comes into play: a new degeneracy Entropy (radius) is dominated by the gas Depends on temperature and Composition of the gaseous envelope a few % of gas can double the radius!!!: prevents the determination of the precise composition of the core Valencia et al. (A&A 2010)
Super Earth or Mini Neptunes? Transmission spectra of GJ1214b. H+He dominated atmosphere + 30-50 x Solar abundances δ = 2αH pr p R 2 H p = k BT µg H2O - CO2 dominated atmospheres Miller Ricci & Fortney (ApJ 2010)
Mass-Radius Diagram M M 1 10 100 1000 10 000 100 000 R RJ 10.0 5.0 2.0 1.0 0.5 0.2 0.1 Mc 10100M Irradiated Water Rock Iron 0.01 0.1 1 10 100 1000 M M J HHeZ 10 8 yr 5.10 9 yr 100 50 20 10 5 2 1 R R Chabrier et al. (A&A 1997) Fortney et al. (ApJ 2007) Baraffe et al. (A&A 2008) Leconte et al. (2009, 2010d)
Pattern in Atmospheric boundary conditions Robust pattern Irradiation forces a radiative zone For the same internal adiabat: Teff decreases Barman et al. (ApJ 2001) Baraffe et al. (A&A 2003)
Gas Giants: Diagnostic for enrichment. 0.8 R R irrad R irrad 0.6 0.4 0.2 0.0 0.2 TrES-4b WASP-12b WASP-17b XO-3b CoRoT-3b HAT-P-20b CoRoT-15b WASP-30b 0.4 0.5 1.0 5.0 10.0 50.0 M M Jup Leconte et al. (A&A 2010a)
Gas Giants: constraining the bulk property For many «standard» systems, the radius is consistent with models with irradiated atmosphere. The mass of heavy elements can be constrained. Model with Irradiated atmosphere - solar composition Irradiated atmosphere + MZ=10M water (Z=5%) Model with Non-Irradiated atmosphere - solar composition CoRoT 4b; Leconte et al. (A&A 2009)
Fig. 8. Position of CoRoT-13b (square) among the other transitgasinggiants: constraining the bulk property planets in a mass-radius diagram. 9 Fig. 9. Age (in Ga=10 versus transit CoRoTCoRot 13b (1.3Mjupyears) ); Cabrera et al.radius (A&Aof2009) Fig. 1 a fun redis Agol =0 gray The b
Correlation with Stellar Metallicity (Guillot et al. 2006)
Gas Giants: Missing mechanism!!! 0.8 R R irrad R irrad 0.6 0.4 0.2 0.0 0.2 TrES-4b WASP-12b WASP-17b XO-3b CoRoT-3b HAT-P-20b CoRoT-15b WASP-30b 0.4 0.5 1.0 5.0 10.0 50.0 M M Jup Leconte et al. (A&A 2010a) The inferred MZ is still a lower limit!
Gas Giants: Differentiating Planets / Brown Dwarfs in their overlapping domain 1.6 HATP20 b, M p 7.246M J Model with Irradiated atmosphere - solar composition Irradiated atmosphere + 340M water core R RJ 1.4 1.2 1.0 M Z η Z (f M ) η 30% (Alibert, Mordasini et al) 0.8 0.01 0.1 1 10 Age Gyr M c 340 M HAT-P-20b; Leconte et al. (2009, 2010c)
1 st take home message Planets do form by core accretion up to «at least» 8 Mjup ( and close...) Formation processes must explain very large heavy element content: > 300-400 M Even for not so massive planets
Can we rewind and directly constrain formation? Role and limitations of internal evolution models
0.023 AU Is mass and composition conserved? The mass of Hot Jupiters could be affected Only element in the outer envelope are affected => enhanced enrichment 0.023 AU 0.046 AU 0.023 AU 0.046 AU no evaporation 0.023 AU 0.046 AU But: Yelle (2004) Tian et al. (2005) Garcia Munoz (2007) Yelle et al. (2008) Murray-Clay et al. (2009) 0.046 AU no evaporation no evaporation Baraffe et al. (A&A 2004) Lower evaporation rates: 1% of mass for HD209458
254 191 1 5 9 1 2 7 Is mass and composition conserved? 318 a) in situ For highly irradiated low mass planets, this can be very important: the case of CoRoT-7b Migration history will also play a role 100 10 100 95 191 95 222 rocky cores 286 15.9 3 7.9 222 14. 9.5 254 15.9 3 7.9 H-He planets 14. 9.5 12.7 H-He planets 12.7 11. 1 11. 1 286 vapor planets 1 0.01 0.1 1 10 10 318 b) inward migration vapor planets rocky cores 1 0.01 0.1 1 10 Valencia et al. (A&A 2010)
Internal Energy: Hot Start - Cold Start How much energy is left into the planet after the end of the accretion? Is there an accretion shock? (probably yes) Is this accretion shock sub or supercritical? τ KH = GM 2 RL τ KH = 10 7 10 8 yr Marley et al. (ApJ 2007)
Hot Start - Cold Start Up to now, direct detection community uses mass-luminosity relationship to infer the mass Need to constrain young objects If mass are constrained by the dynamics, young objects imaging can constrain the evolution and the formation models
2 st take home message Evolution does not stop when disk is gone and system «stable» We cannot go back but we can move forward: Evolve your population synthesis Tidal migration (heating), Mass Loss... B...
Conclusion For low mass planets, precise composition retrieval is impeded by degeneracies in the model In all cases, a lower limit on the heavy element content can be evaluated For giant planets this composition might might not change much during evolution Some strong constraints: Heavy element content vs Stellar metallicity Correlation Planet must form in a disk up to 8 Mjup and with large cores (->1Mjup) Cannot rewind, but we can move forward: Do not stop population synthesis after a few Myrs Should evolve your populations (Tidal effects, Mass loss...) Mardling, Schlaufman...