Lecture II: Gas Giant Planets 1.The Mass-Radius diagram - interiors 2.Equations of State and Phase transitions 3.Phase separation 4.Hot Jupiters

The Giant Planets

HD b: a Hot Jupiter

HD b: highly eccentric one

Some of the Hot Jupiters do not match well models based on Jupiter & Saturn: More diversity than expected ?... Charbonneau et al (2006) w Bodenheimer et al.(2003), Laughlin et al. (2005) models; and Burrows et al. (2003 & 2006)

Mass-Radius Diagram

Properties of planets & small stars Models: Baraffe et al. four different ages: 0.5, 1, 3, & 5 Gyr Red: Pont et al. (2005) OGLE-TR-122

Stellar Mass and Age: Stellar evolution track for 3 metallicities and Helium content: Stars evolve from bottom zero-age main sequence HD Our Sun Lines of constant stellar radii Cody & Sasselov (2002) Age = 7 Gyrs

HAT-P-1b: the ‘lightest’ planet yet RA = 22 h 58 m Dec = +38 o 40’ I = 9.6 mag G0 V M s = 1.12 M O P orb = 4.46 days M p = 0.53 M jup

HAT-P-1 = ADS 16402B: Bakos et al. (2006) The HR diagram and evolutionary tracks fits:

 Our own Solar System: Jupiter & Saturn  Constraints: M, R, age, J 2, J 4, J 6  EOS is complicated:  mixtures of molecules, atoms, and ions;  partially degenerate & partially coupled.  EOS Lab Experiments (on deuterium):  Laser induced - LLNL-NOVA  Gas gun (up to 0.8 Mbar only)  Pulsed currents - Sandia Z-machine  Converging explosively-driven - Russia (up to 1.07 Mbar) Interiors of Giant Planets

The giant planets - interiors

Phase diagram (hydrogen): Guillot (2005)

 New hydrogen EOS Experiment:  Russian Converging explosively-driven system (CS)  Boriskov et al. (2005):  matches Gas gun & Pulsed current (Z-machine) results  deuterium is monatomic above 0.5 Mbar - no phase transition  consistent with Density Functional Theory calculation (Desjarlais) Interiors of Giant Planets

Jupiter’s core mass and mass of heavy elements : Interiors of Giant Planets Saumon & Guillot (2004) For M Z - the heavy elements are mixed in the H/He envelope

Saturn’s core mass and mass of heavy elements : Interiors of Giant Planets Saumon & Guillot (2004)

 Core vs. No-Core:  How well is a core defined?  Saturn: metallic region can mimic ‘core’ in J 2 fit (Guillot 1999);  Core dredge-up - 20 M Earth in Jupiter, but MLT convection… ?  Overall Z enrichment:  Jupiter ~ 6x solar  Saturn ~ 5x solar  a high C/O ratio from Cassini ?? (HD b? Seager et al ‘05) Interiors of Giant Planets

Hot Jupiters could capture high-Z planetesimals if parked so close early… Interiors of Hot Jupiters DS (2003) w updates OGLE-TR-56b has: V orb = 202 km/sec, V esc = 38 km/sec.

 Tidal heating  small ones require cores & enrichments larger than those of Jupiter and Saturn (Burrows et al. 2006);  large ones - their low densities are still difficult to explain:  additional sources of heat  high-opacity atmospheres Hot Jupiters: Internal heating

 Core vs. No-Core:  Core - leads to faster contraction at any age;  the case of OGLE-TR-132b > high-Z and large core needed ?  the star OGLE-TR-132 seems super-metal-rich… (Moutou et al.)  Cores: nature vs. nurture ? - capturing planetesimals.  Evaporation ? - before planet interior becomes degenerate enough - implications for Very Hot Jupiters;  the case of HD b (Vidal-Madjar et al. 2003) ?  Overall Z enrichment:  After the initial ~1 Gyr leads to more contraction. Interiors of Hot Jupiters

Summary: Hot Jupiters  Our gas giants - Jupiter & Saturn:  have small cores  are enriched in elements heavier than H (and He)  The Hot Jupters we know:  most need cores & enrichment  six or so need tidal heating or a similar heating source…  Is the core-accretion model in trouble ?  not yet, but we should understand Jupiter and Saturn better.

Its current luminosity is ~50% greater than predicted by models that work for Jupiter: A Problem with Saturn ?... Fortney & Hubbard (2004) Saturn reaches its current T eff (luminosity) in only 2 Gyr !

 One idea for resolving the discrepancy - phase separation of neutral He from liquid metallic H (Stevenson & Salpeter 1977): for a saturation number fraction of the solute (He), phase separation will occur when the temperature drops below T : x = exp (B - A/kT) where x=0.085 (solar comp., Y=0.27), B=const.(~0), A~1-2 eV (pressure- dependent const.), therefore T = 5, ,000 K A Problem with Saturn ?…

Phase diagram for H & He: A Problem with Saturn ?... Fortney & Hubbard (2004) Model results: Stevenson (‘75) vs. Pfaffenzeller et al. (‘95) - different sign for dA/dP !

New models: A Problem with Saturn ?... Fortney & Hubbard (2004) Model results: The modified Pfaffenzeller et al. (‘95) phase diagram resolves the discrepancy. Good match to observed helium depletions in the atmospheres of Jupiter (Y=0.234) & Saturn (Y~0.2).

Cooling curves: Evolution Models of Exo-planets: Fortney & Hubbard (2004) Models: All planets have 10 M E cores & no irradiation. The models with He separation have ~2 x higher luminosities.

Could the very low-density “puffy” planets be heated by phase separation ? Evolution Models of Exo-planets: Phase separation of other elements Ne, O

Issues:  Sizes of extrasolar planets are already precise  but beware of biases & systematic errors!  Models are based on Jupiter & Saturn  Perhaps, Hot & Very Hot Jupiters are more Z enriched:  because of history - excessive migration through disk, or  because of orbit - manage to capture more planetesimals ?  Implications for the core-accretion model:  it requires at least ~6 M E for M core of Jupiter & Saturn  invoke Jupiter core erosion (e.g. Guillot 2005) ?

Conclusions  Sizes of extrasolar planets are already precise  beware of biases & systematic errors  Models are based on Jupiter & Saturn  Perhaps, Hot & Very Hot Jupiters are more Z enriched:  because of history - excessive migration through disk, or  because of orbit - manage to capture more planetesimals ?  Implications for the core-accretion model:  it requires at least ~6 M E for M core of Jupiter & Saturn  invoke Jupiter core erosion (e.g. Guillot 2005),  use the He settling for Saturn (Fortney & Hubbard 2003)