PlanetMigration:
InwardorOutward?
Eduardo J. Delgado-Donate
Pawel Artymowicz
Stockholm Observatory
PlanetMigration:InwardorOutward?
I. Why Migration?
- As of 10/09/2004, 128 planets in 112 planetary systems
- Significant fraction are Jupiter sized at close distances:
≈ 67/128 closer than 1 AU
- Current theories ➠ gas giants forming at
5 AU
↓
Planets must move (migrate) inward &
best candidate for pushing ➠ circumstellar gas disc
[Lin & Papaloizou 1979]
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
II. Type I Migration
- Applies to small planets 100 Mŷ
- At Lindblad resonances (LR) planet launches tidal waves
propagating outward from corotation.
[ Goldreich & Tremaine 1979, 1980; Artymowicz 1992, 1993]
- Outer disc receives angular momentum, inner
disc loses angular momentum.
- Net result is that outer disc dominates.
↓
Planet drifts inward (in e.g. 10⁵ years)
[ Ward 1986, 1997]
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
III. Type II Migration
- Gas giants (M
M♃) have Roche lobe ≳ disc
scale height
↓
open gap
- Gas flows uneasily through gap and planet becomes
effectively locked to disc kinematics
↓
planet drift inward in viscous timescale (e.g. 10⁶ yr)
[Ward 1977]
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
IV. Type III Migration: Corotation Resonances (CR) win
- LRs win in standard 1st order perturbation theory
[e.g.Tanaka,Takeuchi & Ward 2000]
- However, change in fluid trajectories in CR region are
not infinitesimal [Masset & Papaloizou 2003; Artymowicz 2003]
- Toy model : exchange of momentum in Hill’s equations:
x” - 2y’ = [ 3 - (m₂/m₁) R/R⁴] x
y” + 2x’ = - (m₂/m₁) (yR/R⁴)
with some modifications...[Artymowicz 2003]
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
V. CR Torques
Solution to
modified Hill’s eqns:
In a symmetric
situation there is no
net torque BUT...
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
- If there is initial asymmetry in density distr. → torques
will make planet move
- If density gradient is positive outward locally (e.g. inner
edge) → planet will migrate outward
- As planet moves, underdense region appears
material moves in and planet out
dense
- Migration engine runs on vacuum
- It’s fast as CR region is closer to planet than LR sites
(e.g. 10⁴ yr ?)
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
VI. Numerical Simulations
Corotation torques
need to be studied
with numerical
simulations, e.g:
Miguel de Val-Borro
poster 4.13 ➪
+ more
sophisticated
analytical models
http://www.astro.su.se/English/groups/planets/systems.html
Delgado & Artymowicz, JENAM 2004, Granada
PlanetMigration:InwardorOutward?
Conclusions
- Corotation torques may have an effect on planet
migration after all.
- Given the appropriate initial conditions, a planet can
migrate outward
- This type III migration is fast!
- We need much better theory for it: numerical calculations
+ analytical models → how fast? how large is CR region?
dependence on planet mass?
Delgado & Artymowicz, JENAM 2004, Granada