Protoplanetary Formation
efficiency and time scale
D.N.C. Lin
University of California, Santa Cruz,
KIAA, Peking University, China
with
K. Kretke, S. Watanabe, Shulin Li, I. Dobbs-Dixon, P.Garaud,
Jilin Zhou, M. Nagasawa, H. Klahr, N. Turner, G. Ogilvie, H. Li,
C. Agnor, ZX Shen, T. Takeuchi, G. Bryden, C. Beichman, E. Thommes
Astronomy Department
University of Florida
Apr 14th, 2007
23 slides
Mass-period distribution
A continuous logarithmic period distribution
A pile-up near 3 days and another pile up near 2-3 years
Does the mass function depend on the period?
Is there a frequency enhancement near the snow line?
Is there an edge to the planetary systems?
Does the mass function depend on the stellar mass or [Fe/H]?
2/23
Dependence on
the stellar [Fe/H]
Santos, Fischer & Valenti
Frequency of Jovian-mass planets increases rapidly with [Fe/H].
But, the ESP’s mass and period distribution are insensitive to [Fe/H]!
Is there a correlation between [Fe/H] & hot Jupiters ?
3/23
Do multiple systems tend to associated with stars with high [Fe/H]?
Disk evolution
Protostellar disks:
Gas/dust = 100
Dabris disks:
Gas/dust = 0.01
Transitional Disks
(CG, Garaud)
only external disk
but accreting star
4/23
surface ripples and self shaddows
5/23
Watanabe, Kretke, Klahr
Retention of condensable grains
Preferred site: snow line
Gas-solid transition
Local enrichment: abundances
fractionation (Stevenson,Takeuchi)
Kretke
Kyoto minimum mass nebula model
Cuzzi
6/23
The lively dead zone
z
Horizontally-Averaged Magnetic Stress
Versus Height and Time
Ideal MHD
100
+4
Resistive MHD with Ionization Chemistry
0
-4
0
50
v 2Az
1

Lundquist number unity
indicates marginal
linear stability.
Turner et al 07
100
time
150
years
mxy / dyn cm -2
1
 
104 104


1

7/23
Surface density distribution & ice grain retention
Kretke
8/23
Disk-planet tidal interactions
type-II migration
type-I migration
Goldreich & Tremaine (1979),
Ward (1986, 1997), Tanaka et al. (2002)
M  (0.1  1) M 
M  (10  100) M 
planet’s perturbation
viscous diffusion
disk torque imbalance
3
2 
3
2
 mig, I
  g,SN   M   M *
a



 0.05

 Myr





  g   M p  M o   1AU 
 mig, II
  g,SN   M p   10



   M  
 g  J 
3
 M o 


 M * 
Lin & Papaloizou (1985),....
1
2
viscous disk accretion
1
2
 a 

 Myr
 1AU 
9/23
Competition: M growth & a decay
10 Myr
1 Myr
0.1 Myr
Shen
Hyper-solar nebula
x30
Limiting isolation
Mass (Ida)
Metal enhancement does not always help! need to slow down migration
10/23
Embryos’ type I migration (10 Mearth)
Cooler and invisic disks
Warmer disks
11/23
Giant impacts
1)
2)
3)
4)
Diversity in core mass
Spin orientation
Survival of satellites
Retention of atmosphere
Late bombardment of planetesimals (Zhou, Li, Agnor)
12/23
20/43
Flow into the Roche lobe
H/a=0.07
Bondi radius (Rb=GMp /cs2)
Hill’s radius (Rh=(Mp/3M* )1/3 a)
Disk thickness (H=csa/Vk)
H/a=0.04
Rb/ Rh =31/3(Mp /M*)2/3(a/H)2 Dobbs-Dixon, Li
decreases with M*
13/23
The period distribution:
Type II migration
14/23
Disk depletion versus migration
Mean motion
resonance capture
Migration of gas giants can lead
To the formation of hot earth
Implication for COROT
Zhou
Impact enlargement
Rejuvenation of gas
Giant. HD 209458b
(Guillot)
15/23
Detection probability of hot Earth Narayan, Cumming
Tidal decay out of
mean motion
resonance
(Novak & Lai)
Effect of type I & II migration
Habitable
planets
M/s accuracy
16/23
Stellar mass-metallicity
More data needed for high
and low-mass stars 17/23
Dependence on M*
1) J increases with M*
2) Mp and ap increase with M*
Do eccentricity and multiplicity depend on M*?
18/23
Migration-free sweeping secular resonances
Resonant
secular
perturbation
Mdisk ~Mp
(Ward, Ida,
Nagasawa)
Transitional disks
19/23
Outer edge of planetary systems
Bryden, Beichman
20/23
Migration, Collisions, & damping
1. Clearing of the asteroid belt
2. Earlier formation of Mars
3. Sun ward planetesimals
A. Late formation (10-50 Myr)
B. Giant-embryo impacts
C. Low eccentricities, stable orbits
Nagasawa, Thommes
21/23
Sequential accretion scenario summary
1) Damping & high  leads to rapid growth & large
isolation masses at the snow line. Jupiter formed prior to the
final assemblage of terrestrial planets within a few Myrs.
2) Emergence of the first gas giants after the disk mass was
reduced to that of the minimum nebula model.
3) Planetary mobility promotes formation & destruction.
Snow line is a good place to halt migration.
4) The first gas giants induce formation of other siblings.
5) Shakeup led to the dynamically
porous configuration
of the inner solar system &
the formation of the Moon.
6) Earths are common and
detectable within a few yrs!
22/23
Outstanding issues:
1) Frequency of planets for different stellar masses
2) Completeness of the mass-period distribution
3) Signs of dynamical evolution
4) Mass distribution of close-in planets: efficiency of migration
5) Halting mechanisms for close-in planets
6) Origin of planetary eccentricity
7) Formation and dynamical interaction of multiple planetary systems
8) Internal and atmospheric structure and dynamics of gas giants
9) Satellite formation
10) Low-mass terrestrial planets
23/23