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Formation of Planets around M & L dwarfs
D.N.C. LinUniversity of California with
AAS Washington
Jan 11th, 2006
S. Ida, H. Li, S.L.Li, E. Thommes, I. Dobbs-Dixon, S.T. Lee,P. Garaud, M. Nagasawa
Doug Lin:Doug Lin:
17 slides
Disk properties
Hillenbrand Calvet
1 Disk life time is independent of M*:similar available time2 Disk accretion rate varies as M*
2 : Less gas content3 Disk heavy element mass varies as M*
1-2?Less metals
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
Feeding zones: 10 rHill
Isolation mass:Misolation ~a3M*
-1/2
From planetesimals to embryos
Initial growth: (runaway)
Shorter growth time scale at the snow line
M* dependence
Misolation ~1.3a/1AU)3/4(M*/Mo)3/2Mearth less massive embryos
embryos ~0.033a/1AU)59/20(M*/Mo)-16/15Myr longer growth timeCan form >3Mearth embryos outside 5AU within 10Myr
Scaling disk models with M*:a)Solar system: Minimum-mass nebula b)Other stars: (a) = SN(a) hd
where hd = (M*/Msun)0,1,2
c)Embryos with Mp>Mearth are formed outside snow lineImportance of snow line:
Interior to it: growth limit due to isolationExterior to it: long growth time scale
Outside the snow line:
type-II migration
planet’s perturbation
viscous diffusion
type-I migration
disk torque imbalance
MyrAU1
05.023
23
*
g
SNg,Imig,
a
M
M
M
M
op
MM )10010( MM )11.0(
MyrAU1
10
2
12
1
*
o3
J
p
g
SNg,IImig,
a
M
M
M
M
Disk-planet tidal interactions
viscous disk accretion
Goldreich & Tremaine (1979), Ward (1986, 1997), Tanaka et al. (2002)
Lin & Papaloizou (1985),....
(Mass) growth vs (orbital) decay
Loss due to Type I migration
MyrAU1)(
)0(04.0
*
o
g
gImig,
43
a
M
M
t
Embryos’ migration time scale
511
AU1)0(
)(
g
g
Imig,
embryo
at
Outer embryos are better preserved only after significant gas depletion
Critical-mass core:Mp=5Mearth
MyrAU1)(
)0(01.0
23
21
*
g
gImig,
a
M
M
t o
Flow into the Roche potential
1
2
s-
r
C
Dt
DUEquation of motion:
Bondi radius (Rb=GMp /cs2)
Hill’s radius (Rh=(Mp/3M* )1/3 a)Disk thickness (H=csa/Vk)
Rb/ Rh =31/3(Mp /M*)2/3(a/H)2
decreases with M*
If Rb> Rh, , a large decline in (+ve r gradient) would be needed to overcome the tidal barrier.
A small at the Hill’s radius would quench the accretion flow.
Reduction in the accretion rate
Growth time scales:
Embryos’ emergence time scale: ~ 0.033a/1AU)59/20(M*/Mo)-16/15Myr
KH cooling/contraction of the envelope: ~102-4 (Mp/Mearth)-(3-4)MyrUninhibited Bondi accretion: ~(H/a)4(M*
2/MpMd k ~102-3yr(MJ/Mp)
Uninhibited accretion from the disk: ~Mp/(dM/dt)~ 103-4yr(Mp/MJ)
Reduction due to Hill’s barrier: >disk depletion
Tidal barriers suppress the emergence of gas giants around low-mass stars
Gap formation & type II migrationViscous and thermal conditions
Lower limiting mass for gas giants around low-mass stars
MyrAU1
10
2
12
1
*
o3
J
p
g
SNg,IImig,
a
M
M
M
M
Neptune-mass planets can open up gaps and migrate close to the stars
Migration-free sweeping secular resonances
Resonant secularperturbationMdisk ~Mp
(Ward, Ida, Nagasawa)Ups And
Transitional disks
Dynamical shake up (Nagasawa, Thommes)Bode’s law: dynamically porous terrestrial planetsorbits with low eccentricities with wide separation
Formation of water worlds
Jupiter-Saturn secular interaction& multiple extrasolar systems
Sweeping secular resonance may bemore intense in low-mass stars. But the absence of gas or ice giants would leave behind dynamically-hot earth-mass objects
Summary1. 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 stars3. 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.