Giant planet formation. Core accretion = core nucleation = core instability = bottom-up. M total M rocky core M gas envelope

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1 Giant planet formation M total M rocky core M gas envelope Core accretion = core nucleation = core instability = bottom-up Runaway gas accretion when M envelope ~ M core Miguel & Brunini 08

2 Critical core masses for various accretion rates Rafikov 2006

3 Core or No Core? M, R, J 2, J 4, J 6,... + P(ρ) + hydrostatic equilibrium (w/rotation) ρ(r)

4 J2 core J4 x 100 J6 x 100 r/r Relative contribution to gravitational harmonics in Saturn ( ( a r ) Φ= GM r 1 ) 2n J2n P 2n (cos θ) n=1

5 Giant planet formation by gravitational fragmentation = gravitational instability = top-down Kratter et al. 10 Requirements: Q ~ 1 and tcool < Ω -1 Could be met at large distance > 70 AU Uncertainties include disk temperature mass infall rate from surrounding natal envelope final planet masses More easily fragments into brown dwarfs than planets

6 Degeneracy pressure R ( 0.1 RJ ) bound electrons unbound electrons log M/M

7 M dwarf L dwarf T dwarf Jupiter 75 M J 65 M J 30 M J 1M J The new spectral classes O B A F G K M L T

8 Cooling curves (standard hot start )

9 Early evolution uncertain cold start (core accretion) hot start

10 Hot Jupiters are inflated Transit radii > Theoretical radii Burrows et al. 2007

11 How much = How long ago Radiative cooling: L = σte 4 4πR 2 = Nk dt c ( dt Not completely degenerate: R R J 1+ kt c ɛ F ) T c R T e Isentrope: 3 equations in 3 unknowns T e,t c,r using more accurate analytic formulae from Burrows & Liebert 93 s e (T e,p e g/κ e )=s c (T c,p c GM 2 /R 4 ) R T c t L L t 24/17 T c t 7/17 to increase R by 30%, t yr L erg/s vs. numerical L erg/s Burrows et al. 07 Log Luminosity (solar units) Cooling tracks Log t (Gyr)

12 Compare required L 6 x erg/s to Incident L L 4πa 2 πr2 pa erg/s Easy problem Even easier : When planet is irradiated, actual required L ~ 4 x erg/s

13 jθ B r v

14 Induced Current Ohmic Power F = q c v B ε emf = W/q = Fl/q I = ε emf /R = ε emf σa l Ohmic P = Iε emf = v2 B 2 σla c 2

15 P = I 2 R j 2 P = σ dv copper 6e7 S/m drinking water to 0.05 S/m j = σf = σ ( v c B + E ) Planetary conductivity Batygin & Stevenson 10, Spiegel et al. 09

16 j = σf = σ ( v c B + E ) delta ~ 2.3e8 cm (R ~ 1.05e10) θ δ v m 1 km/s δ = 0.02 R φ 0 v(r, θ) =v m sin θ ˆφ r f L 4πa 2 πr2 1 2 ρv2 4πR 2 h R/v v 3 L /a 2

17 Differential rotation may only be skin deep If winds extend too deep, Ohmic power > internal luminosity δ < 0.03R for Jupiter (maybe) Also Taylor-Proudman theorem, plus observed stability of B field, enforces near solid-body rotation in convective interior (maybe) [ P( ) v constant on cylinders ] Liu, Goldreich, & Stevenson 08 see also critique by Glatzmaier 08

18 Br 3 ( v ) j = σf = σ c B + E Elsasser Number = Assume B(R) = 10 G [cf. Jupiter B(R) = 4.2 G] O(j B)/c O(2ρΩ v) σb2 ρω Elsasser Number 1 B 2 ρω/σ To reproduce assumed B, assume surface dynamo different from Jupiter Energy flux scaling : B 2 ρ 1/3 q 2/3 Internal flux q for Hot Jupiter 10 2 q for Jupiter Christensen, Holzwarth, & Reiners 2009

19 Atmospheric Power j = σf = σ ( v c B + E ) σ v c B P = j 2 σ dv σv2 B 2 c 2 4πR 2 δ erg/s

20 Power at Radiative-Convective (RC) Boundary δ δrc j δ j P RC = P j 2 j2 σ dv σ RC 2πR δδ RC σ δ RC σ RC R erg/s δrc δ

21 How much extra power and where? RC boundary on Jupiter bar Where : convective interior Radiativeconvective (RC) boundary Specific entropy s = s RC s core R(s, M) Spiegel, Silverio, and Burrows 2009