Close-in Planets: From Hot Jupiters to Super-Mercuries E. Chiang (UC Berkeley)
From exo-jupiters to exo-mars
n number of planets per star 2 n R α P β (say) ln R ln P Youdin 11 Planet Counts per Star 10 2 10 3 10 4 slow = 1.93 fast = 1.44 1 10 Planet Radius [R Earth ] Planet Counts per Star 10 2 10 3 10 4 fast = 2.23 slow = 0.63 1 10 Period [day] divide into fast and slow populations and fit separately P < 7 days 2 n ln R ln P R 1.4 P 2.2 P > 7 days 2 n ln R ln P R 1.9 P 0.6 n (R > 2 R, P < 50 days) ~ 0.2 planet per star Trust detection efficiency down to 1R, and extrapolate to 365 days : n (R > 1 R, P < 365 days) ~ 2 planets per star
10 5 Minimum-Mass Kepler-11 system (turns out Toomre Q ~ 2)
In situ formation of rocky planets Mass accretion rate v Ṁ ρvr 2 F grav R ρ b ρ σ h v Ω Ṁ σ Ω R 2 F grav t form Ṁ M ρ br σ Ω 1 F grav 10 4 yr for Kepler-11
In situ formation of hot Jupiters? Core accretion ρ, T M core M atm M atm (M core, ρ, T, κ, M planetesimal ) if M atm M core instability (runaway envelope accretion)
In situ hot Jupiter R B = GM/c 2 s (v esc c s ) ρ, c s M atm 4πρR 3 B M core instability M core,crit c 3 s 4πG3 ρ Rafikov 2006
Formation of hot Jupiters by disk-driven migration Lubow et al. 99 What is the source of disk viscosity? MRI activity in surface layers only FUV X-ray
Ṁ [M /yr] 10 6 10 7 10 8 10 9 10 10 10 11 Perez-Becker & EC 11ab Bai & Stone 11, Bai 11 Conventional Disk Observed Rates max β plasma < 1 FUV X-ray 1 10 100 a [AU] Ṁ 2 3πΣ ν 6πΣ α kt µω MRI accretion rates too low FUV-ionized layer too thin X-ray-ionized layer weakened by PAHs and ambipolar diffusion
Spin-orbit alignment of hot Jupiters λ = stellar obliquity (sky projected) λ Ω ~50% are misaligned, including retrograde
Measuring spin-orbit angles by Rossiter-McLaughlin 0 HAT-P-14 Winn+ 11 Gaudi & Winn 08
Migration by eccentricity excitation and tidal decay Planet forms far from star Eccentricity is excited (somehow) When planet comes close enough to star, strong tides are raised on planet, circularizing its orbit Y. Lithwick
Start with 3 widely spaced, mildly eccentric & inclined planets: Secular Chaos a(au) ecc. inc. (deg) mass (Mj) 1 0.066 4.5 0.5 6 0.188 19.9 1.0 16 0.334 7.9 1.5 no close encounters or strong resonances Wu & Lithwick 11
Secular Chaos and Migration Wu & Lithwick 11
Hot Jupiters are inflated Rp (RJ) Age (Gyr) Transit radii > Theoretical radii Burrows et al. 2007
jθ B r Wind Power and Ohmic Heating v Surface current thermal (Saha) ionization ~0.01 S/m ~1 km/s j σ v c B ~1 G Ohmic power at RC boundary P j2 σ R 2 z RC RC Batygin & Stevenson 10
Ohmic inflation (or suspension) Wu & Lithwick 12 only works if hot Jupiter is parked early (cf. secular migration which parks late)
hot Jupiter v esc 40 km/s Thermally driven mass loss (Parker winds) T 10 4 K UV heating PdV work vs. radiative loss (e.g., Ly- cooling) transition from subsonic to supersonic occurs at sonic point R s = GM 2c 2 s Von Braun / Saturn V de Laval nozzle R. Murray-Clay
Hydrodynamic planetary wind Pressure balance with stellar wind Roche lobe radius 6 R p P ~ 10 picobar 4.5 R p Sonic point 2-4 R p T wind 3000-10000 K H, H + Photoionization base ( UV = 1) 1.1 R p P ~ nanobar 1 bar surface of planet H 2 R p ~ 10 10 cm T eff 1300K
Atmospheric escape from HD 209458b FUV = 450 erg/cm 2 /s Mp = 0.7 MJ Rp = 1.4 RJ hν0 = 20 ev ρbase = 4x10-13 g Tbase = 1000 K fbase = 10-5 τsp = 0.0046 Murray-Clay, EC, & Murray 09
Mass-Loss Rates GMṀ R At low UV flux, wind is energylimited εf UV πr 2 Ṁ F UV main sequence T Tauri At high UV flux, wind is recombinationlimited n 2 +α rec F UV hν σ bfn 0 Ṁ F 1/2 UV Planet loses ~1% of mass over lifetime Murray-Clay, EC, & Murray 09
HST Ly-α absorption and charge exchange -100 km/s 100 km/s Holmstrom+ 08 Ekstrom+ 10 H + hot H 0 cold H 0 cold + H + hot H 0 hot + H + cold Log density (cm -3 ) Tremblin & EC, in prep. Vidal-Madjar+ 03
Kepler Input Catalog (KIC) 12557548 eclipse depth varies from orbit to orbit K-type star Companion M = 0.7 M R = 0.7 R T = 4400 K Porb = 15.685 hr a = 0.013 AU (4 R ) Teff = 2100 K Rappaport, Levine, EC+ 12
folded about 15.685 hr folded, binned, averaged pre-ingress bump variable eclipse depth 0.2-1.3% fast ingress slow egress Orbital Phase Orbital Phase out-of-eclipse variation < 5e-5 M < 3 MJ (no ellipsoidal light variation)
What it could be A disintegrating super-mercury R ~ 0.5 R M ~ 0.1 M R occulting size Ro 0.1 R 15 R Teff ~ 2100 K cs ~ 0.7 km/s vesc a few km/s (sub-earth) R Ro Rappaport, Levine, EC+ 12
Mass loss rate optical depth Grain and Planet Lifetimes Ṁ d ρ d v o R 2 o τ ρ d R o κ d ρ dr o }ρbs s 2 /(ρ b s 3 ) ~Ro R Ro eclipse depth f τro/r 2 2 pyroxene grain Ṁd fsv o ρ b R /R 2 ( o sublimation )( ) f s 0.5 M Gyr 1 lifetime ~ 10 4 s 0.01 0.1 µm ~ travel time across Ro planet lifetime M Ṁ = M Ṁ d + Ṁg 0.1 Gyr Ṁ TBD M
10 2 Olivine, T=2100 K 10 1 10 0 M [M /Gyr] 10 1 10 2 10 3 10 4 10 5 10 2 10 1 10 0 M p /M
Coriolis force + stellar radiation pressure on grains creates trailing tail Tail causes prolonged egress Scattered light off head of comet causes pre-ingress bump Predictions: (i) infrared eclipses shallower (ii) deeper eclipses in gas absorption lines
Disk properties / Planet-disk interaction (Herschel, ALMA) Highly eccentric hot Jupiters (RV, Kepler) Hot Jupiter magnetospheres (LOFAR, SKA) Evaporating atmospheres (HST, JWST)
What it is not: gas giant (dynamically unstable) background blend with RR Lyrae variable star (background blends will be further checked with deep imaging) RR Lyrae star with Kepler What it is probably not: hierarchical triple containing accretion disk (no out-of-eclipse variability) Porb = 15.7 hr K
How much extra power and where? Spiegel+ 09 Where : convective interior Radiativeconvective (RC) boundary Convective zone Isothermal radiative layer L 4πa 2 σt 4 eq How much : F rad RC σt 4 eq τ RC P L 4πa 2 πr2 τ 1 RC