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

Preferred locations

Meteorites:Dry, chondrules& CAI’s

Icy moons

Enhancement factor > 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

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

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J

p

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SNg,IImig,

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M

M

M

M

Disk-planet tidal interactions

viscous disk accretion

Goldreich & Tremaine (1979), Ward (1986, 1997), Tanaka et al. (2002)

Lin & Papaloizou (1985),....

Low-mass embryo (10 Mearth)

Cooler and invisic disks

(Mass) growth vs (orbital) decay

Loss due to Type I migration

MyrAU1)(

)0(04.0

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o

g

gImig,

43

a

M

M

t

Embryos’ migration time scale

511

AU1)0(

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Imig,

embryo

at

Outer embryos are better preserved only after significant gas depletion

Critical-mass core:Mp=5Mearth

MyrAU1)(

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21

*

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gImig,

a

M

M

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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

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SNg,IImig,

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Neptune-mass planets can open up gaps and migrate close to the stars

Hot Neptunes around low-M* stars

Radial extent is determined by Vk > Vescape

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.