Formation of Planets around M

1
Formation of Planets around M L dwarfs
Doug Lin
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, M. Nagasawa

AAS
Washington Jan
11th, 2006
17 slides
2
Disk properties
Calvet
Hillenbrand

• 1 Disk life time is independent of Msimilar
  available time
• 2 Disk accretion rate varies as M2 Less gas
  content
• 3 Disk heavy element mass varies as M1-2?Less
  metals

3
Preferred locations
Meteorites Dry, chondrules CAIs
Enhancement factor gt 4
Icy moons
4
Stellar mass dependence
T(snow line) 160K, L M2
a(snow line) (L)1/2/T2 2.7(M/Mo) AU
Vk(snow)(M/a)1/2 Const H/a Const
Similar aspect ratio and Keplerian speed! But
shorter time scales (a/Vk) for lower M
Water-rich planets form near low-mass stars
5
From planetesimals to embryos
Feeding zones D 10 rHill Isolation
mass Misolation S1.5 a3M-1/2
Initial growth (runaway)
Shorter growth time scale at the snow line
6
M dependence
Scaling disk models with M a)Solar system
Minimum-mass nebula b)Other stars S(a) SSN(a)
hd where hd (M/Msun)0,1,2 c)Embryos
with MpgtMearth 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
Misolation 1.3(a/1AU)3/4(M/Mo)3/2Mearth less
massive embryos tembryos 0.033(a/1AU)59/20(M/Mo
)-16/15Myr longer growth time Can form gt3Mearth
embryos outside 5AU within 10Myr
7
Disk-planet tidal interactions
type-I migration
type-II migration
Lin Papaloizou (1985),....
Goldreich Tremaine (1979), Ward (1986, 1997),
Tanaka et al. (2002)
planets perturbation
viscous diffusion
disk torque imbalance
viscous disk accretion
8
Low-mass embryo (10 Mearth)
Cooler and invisic disks
9
(Mass) growth vs (orbital) decay
Embryos migration time scale
Outer embryos are better preserved only after
significant gas depletion
Critical-mass coreMp5Mearth
Loss due to Type I migration
10
Flow into the Roche potential
Equation of motion
Bondi radius (RbGMp /cs2) Hills radius
(Rh(Mp/3M )1/3 a) Disk thickness
(Hcsa/Vk) Rb/ Rh 31/3(Mp /M)2/3(a/H)2 decrease
s with M
If Rbgt Rh, , a large decline in r (ve r
gradient) would be needed to overcome the tidal
barrier. A small r at the Hills radius would
quench the accretion flow.
11
Reduction in the accretion rate
Growth time scales Embryos emergence time
scale 0.033(a/1AU)59/20(M/Mo)-16
/15Myr KH cooling/contraction of the envelope
102-4 (Mp/Mearth)-(3-4)Myr Uninhibited Bondi
accretion (H/a)4(M2/MpMd
)/Wk 102-3yr(MJ/Mp) Uninhibited accretion from
the disk Mp/(dM/dt) 103-4yr(Mp/MJ)
Reduction due to Hills barrier
gttdisk 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
Neptune-mass planets can open up gaps and
migrate close to the stars
13
Hot Neptunes around low-M stars
Radial extent is determined by Vk gt Vescape
14
Migration-free sweeping secular resonances
Resonant secular perturbation Mdisk Mp (Ward,
Ida, Nagasawa) Ups And
Transitional disks
15
Dynamical shake up (Nagasawa, Thommes)
Bodes 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

• 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.
• 2. Planet-disk interaction can lead to depletion
  of first
• generation planetesimals, especially around
  low-mass stars
• Self regulation led to the stellar accretion of
  most
• heavy elements, the late emergence of
  planets, and
• perhaps the inner holes inferred from SEDs.
• 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.
• 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.