ge/ay133 what effects do 1-10 m earth cores & jovian planets have on the surrounding disk? or,...
Post on 21-Dec-2015
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Ge/Ay133
What effects do 1-10 MEarth cores & Jovian planets have on the surrounding disk?
Or, … Migration & Gaps
Disks can be unstable globally:
Toomre’s criterion Q ≡ c/(Gaxisymmetric perturbations)
= epicyclic frequency
Disks can be unstable globally if Mdisk/M*≥h/r. Locally?
r-3 d/dr[(r2
n a Keplerian disk, where 2 = GM/r3 ,
= epicyclic frequency
S. Corder et al. 2005, OVRO
2"
AB AurNeed to look at Q.
Inner/outertidal torque, f≈0.2 (const.)
Torque fromthe viscous disk.
Balance torques from tides and viscous response, or…
Look at time to open a gap as compared to the viscous response time scale of the disk gas. Find:
Planet mass needed to open gap:
Local resonances can propagate globally!
Sufficiently large planets can create gaps, but gas accretion does continue. Can these structures assist in the formation of additional Jovian planets?
Inner/outertidal torque, f≈0.2 (const.)
If the inner &outer torque arenot balanced…
The is a radial force on the planet Migration.
If you do a LINEAR analysis in a LAMINAR disk, three types of migration mechanisms emerge:
Type I – “Low mass” cores w/o an induced gap.Type II – “High mass” core with an induced gap.Type III – Runaway migration in high mass disks (really needs a non-linear analysis)
Type I:
Ward, Icarus 126, 261(1997).
Ruden review:
Type II:
When a gap opens,the force balancechanges. The growingplanet is now tied tothe disk transporttimescale(s). For alaminar disk:
Ward, Icarus 126, 261(1997).
Ruden review:
Recall Type I migration has
Type II versus Type I: Type II is slower, butin a linear analysis themigration rate can stillbe very fast!
Type III: With a massive disk,“runaway migration”can occur:
Very sensitive to themass surface densityprofile (can go out!).
What can we think about that might slow down migration rates?
Idea #1: Turbulent disks & stochastic migration.
Idea #2: Do not use linearity assumptions!
Non-linearities in the gas flow around an accreting protoplanet should scale as:
Where q is the secondary to primary mass ratio and h=H/r, the disk scale height/radius. In this scenario, deviations from linearity should follow:
Masset, D’Angelo & Kley (2006, ApJ, in press)
2-D and 3-D Disk simulations reveal significant non-linearity:
This can dramatically alter the outcome of migration. With sufficiently shallow mass surface density profiles the direction of migration can even be changed. (With a sufficiently shallow profile the migration is outward.)
Linear
Tests with disk viscosity.
Comparison of migration predictions to observables?
The histogram data at right are from the extrasolar planet sample in Fischer & Valenti (2005) that is cut at 30 m/s for completeness. It also ignores the “hot Jupiter pile up.” The green line is the simple disk evolution model+migration.
The plot at left is a prediction that uses a simple disk evolutionary model with gas dissipation (more next time) and Type I+Type II migration.