Spirals and whirls
The worlds came into being as follows: many bodies of all sorts and
shapes move from the infinite into a gread void; they come together there
and produce a single whirl,
in which, colliding with one another and revolving in all manner of
ways, they begin to separate like to like.
Leucippus (480BC-420BC)
Simulating Planet formation and migration
A simulation of two protoplanets embedded in a disk.
A zoomed-in region of the above disk, showing the planet wakes more
clearly.
Two planets in resonance in a tidally truncated disk cavity.
Theory of planet migration
Planets are thought to form in protoplanetary accretion disks.
These are the leftover bits that remain after the star has contracted out
from the the protostellar nebula. The disk is primarily composed of
gas, but also contains solid dust and ice. The dust and ice particles
merge by a process of inelastic binary collisions to form first
planetessimals, which then merge further to form solid protoplanetary
cores. If these cores are massive enough, they will accrete the gas
from the disk, and become a giant gas giant planet (like jupiter or
saturn). If they aren't massive, then the gas accretion doesn't occur and
a terrestrial planet is formed. At some point some process (maybe the
solar wind) clears the disk and only the planets are left, orbiting around
the central star. Obviously this disk clearing must occur only after gas
has accreted onto the gas giants, hence there must be a time where we have
giant protoplanets embedded inside the disk.
In order for the planets to have formed, the velocity dispersion
inside the disk must be low, which implies a cold disk. This in turn means
the disk is very thin, and also means the gas flow around the star is
highly supersonic. The forming protoplanets will interact with the disk
via gravity, but the effect only becomes significant when the planets are
massive.
The planetary gravitational potential orbiting around the star
causes perturbations in the disk. These perturbations are strongest when
the natural epicyclic frequency of the disk is an exact multiple of the
forcing frequency, and the points at which this occurs are called
lindblad resonances. Launched from these resonance points are
spiral density waves, which propagate both outwards and inwards,
away from the perturbing planet. Outwards travelling waves carry angular
momentum outwards, and inwards waves carry negative angular momentum
inwards. These waves are damped by viscous or nonlinear effects, and where
they are damped they deposit the angular momentum in the disk. This
tidal interaction has the effect of pushing material away from the the
orbit of the planet, and is opposed by viscous torques. If the planet is
massive enough, the tidal torques dominate and a large annular gap
in the disk opens up around the planet, and the disk becomes highly
non-linear at that location.
The back reaction of the tidal torques causes protoplanetary
migration. The angular momentum deposited in the disk by the spiral
waves is lost from the planet, and the orbital radius varies as a result
of a loss of angular momemntum. Becasue of an asymmetry in the outer and
inner torques, the protoplanets are thought to migrate inwards and
this might explain the positions of the giant extrasolar planets found
very close to their parent stars. However this also creates a problem as
theory predicts the planets will migrate all the way and become swallowed
by the star in a very short time. Some mechanism needs to halt the
migration and prevent the planets being eaten in this way. One possible
mechanism is the resonance interaction of two planets, which can be
shown in some circumstances to reverse the direction of
migration.
Ph.D. Thesis
Migration, Resonance and Turbulence in
Protoplanet-Disk Interactions (M.D. Snellgrove 2003)
(Note: Download is 8MB)
Papers
Reversing type II migration: Resonance
trapping of a lighter giant protoplanet (F. Masset and
M. Snellgrove 2001) MNRAS 320 L55
On disc driven inward migration of
resonantly coupled planets with application to the system around
GJ876 (M.D. Snellgrove, J.C.B. Papaloizou and R.P. Nelson
2001) A&A 374 1092
The interaction of planets with a
disc with MHD turbulence III: Flow morphology and conditions for gap
formation in local and global simulations (R.P. Nelson,
J.C.B. Papaloizou and M.D. Snellgrove 2003) (submitted to
MNRAS) (Note: Download is 10MB)
Conference proceedings
Reversing type II migration: Resonance
trapping of a lighter giant protoplanet (F. Masset and
M. Snellgrove 2000) Proceedings of the IAU Symposium 202, Manchester,
August 2000
Conference abstracts
Migration Driven Protoplanetary Resonance Trapping (M.D. Snellgrove 2001)
Astronomische Gesellschaft Abstract Series, Vol. 18, abstract #P43.
Orbital Relaxation and Extrasolar Planets (J.C.B Papaloizou, R.P Nelson,
M.D. Snellgrove, C. Terquem 2001)
Astronomische Gesellschaft Abstract Series, Vol. 18, abstract #MS 04 09.
Other planet pages
Extrasolar planets
encyclopaedia
Lynette cook's
planet artwork
Contact details
Last updated 10 December 2003.
This page is maintained by Mark Snellgrove