Formation of Planets around M & L dwarfs

Transcription

1 Formation of Planets around & L dwarfs D.N.C. Lin University of California with S. Ida, H. Li, S.L.Li, E. Thommes, I. Dobbs-Dixon, S.T. Lee,P. Garaud,. Nagasawa AAS Washington Jan 11th, slides

2 Disk properties Hillenbrand Calvet 1 Disk life time is independent of * :similar available time Disk accretion rate varies as * : Less gas content 3 Disk heavy element mass varies as * 1-?Less metals

3 Preferred locations eteorites: Dry, chondrules & CAI s Enhancement factor > 4 Icy moons

4 Stellar mass dependence T(snow line) ~160K, L ~ a(snow line) ~ (L) 1/ /T ~.7( * / o ) AU V k (snow)~(/a) 1/ ~Const ; H/a ~Const Similar aspect ratio and Keplerian speed! But shorter time scales (a/v k ) for lower * Water-rich planets form near low-mass stars

5 From planetesimals to embryos Feeding zones: 10 r Hill Isolation mass: isolation ~Σ 1.5 a 3-1/ * Initial growth: (runaway) Shorter growth time scale at the snow line

6 * dependence Scaling disk models with * : a)solar system: inimum-mass nebula b)other stars: Σ(a) = Σ SN (a) h d where h d = ( * / sun ) 0,1, c)embryos with p > earth are formed outside snow line Importance of snow line: Interior to it: growth limit due to isolation Exterior to it: long growth time scale Outside the snow line: isolation ~1.3(a/1AU) 3/4 ( * / o ) 3/ earth less massive embryos τ embryos ~0.033(a/1AU) 59/0 ( * / o ) -16/15 yr longer growth time Can form >3 earth embryos outside 5AU within 10yr

7 Disk-planet tidal interactions type-i migration Goldreich & Tremaine (1979), Ward (1986, 1997), Tanaka et al. (00) > (0.1 1) type-ii migration Lin & Papaloizou (1985),... > (10 100) planet s perturbation τ mig, I disk torque imbalance Σ g,sn * 0.05 a Σg p o 1AU 3 3 yr viscous diffusion viscous disk accretion τ mig, II Σ Σ g,sn g p J 3 10 o a yr α * 1AU 1 1

8 Low-mass embryo (10 earth) Cooler and invisic disks

9 (ass) growth vs (orbital) decay Loss due to Type I migration yr 1AU ) ( (0).04 0 * o g g mig,i 4 3 Σ Σ a t τ Embryos migration time scale AU (0) ) ( g g mig,i embryo Σ Σ a t τ τ Outer embryos are better preserved only after significant gas depletion Critical-mass core: p =5 earth yr 1AU ) ( (0) * g g I mig, Σ Σ a t o τ

10 Flow into the Roche potential Equation of motion: Bondi radius (R b =G p /c s ) Hill s radius (R h =( p /3 * ) 1/3 a) Disk thickness (H=c s a/v k ) R b / R h =3 1/3 ( p / * ) /3 (a/h) decreases with * DU Dt C s ρ ρ -1 + ϕ r If R b > R h,, a large decline in ρ (+ve r gradient) would be needed to overcome the tidal barrier. A small ρ at the Hill s radius would quench the accretion flow.

11 Reduction in the accretion rate Growth time scales: Embryos emergence time scale: ~ 0.033(a/1AU) 59/0 ( * / o ) -16/15 yr KH cooling/contraction of the envelope: ~10-4 ( p / earth ) -(3-4) yr Uninhibited Bondi accretion: ~(H/a) 4 ( * / p d )/Ω k ~10-3 yr( J / p ) Uninhibited accretion from the disk: ~ p /(d/dt)~ yr( p / J ) Reduction due to Hill s barrier: >τ disk depletion Tidal barriers suppress the emergence of gas giants around low-mass stars

12 Gap formation & type II migration Viscous and thermal conditions Lower limiting mass for gas giants around low-mass stars yr 1AU * o 3 J p g g,sn II mig, Σ Σ a α τ Neptune-mass planets can open up gaps and migrate close to the stars

13 Hot Neptunes around low- * stars Radial extent is determined by V k > V escape

14 igration-free sweeping secular resonances Resonant secular perturbation disk ~ p (Ward, Ida, Nagasawa) Ups And Transitional disks

15 Dynamical shake up (Nagasawa, Thommes) Bode s law: dynamically porous terrestrial planets orbits with low eccentricities with wide separation

16 Formation of water worlds Jupiter-Saturn secular interaction & multiple extrasolar systems Sweeping secular resonance may be more intense in low-mass stars. But the absence of gas or ice giants would leave behind dynamically-hot earth-mass objects

17 Summary 1. Snow line is important for the retention of heavy. Around low-mass stars, planets with mass greater than that of the earth are formed outside the snow line.. Planet-disk interaction can lead to depletion of first generation planetesimals, especially around low-mass stars 3. Self regulation led to the stellar accretion of most heavy elements, the late emergence of planets, and perhaps the inner holes inferred from SED s. 4. Around low-mass stars, gas accretion rate onto proto gas giants is also suppressed by a tidal barrier. 5. Neptune-mass embryos can open up gaps and migrate to the stellar proximity. 6. Residual planetesimals may have modest eccentricities. 7 There will be a desert of gas giants and an oasis of terrestrial planets, including short-period water worlds around dwarfs.