The Migration and Growth of Protoplanets in Protostellar Discs
Richard P. Nelson, John C.B. Papaloizou, Frederic Masset, & Willy Kley
MNRAS, 318, 18
Abstract:
We investigate the gravitational interaction of a Jovian mass protoplanet
with a gaseous disc with aspect ratio and kinematic
viscosity expected for the protoplanetary disc from which it formed.
Different disc surface density distributions have been investigated.
We focus on the tidal interaction with the disc
with the consequent gap formation and orbital migration of the protoplanet.
Nonlinear hydrodynamic simulations are employed using three
independent numerical codes.
A principal result is that the direction
of the orbital migration is always inwards and such that the
protoplanet reaches the central star in a near circular orbit
after a characteristic viscous time scale of $\sim 10^4$
initial orbital periods.
This was found to be independent
of whether the protoplanet was allowed to accrete mass or not.
Inward migration is helped through
the disappearance of the inner disc,
and therefore the positive torque it would exert,
because of accretion onto the central star.
Maximally accreting protoplanets reached about four
Jovian masses
on reaching the neighbourhood of the central star.
Our results indicate that a realistic upper limit for the masses of closely
orbiting giant
planets is $\sim 5$ Jupiter masses, because of the reduced accretion rates
obtained for planets of increasing mass.
Assuming some process such as termination of the inner disc
through a magnetospheric cavity stops the migration,
the range of masses estimated for a number of close orbiting
giant planets (Marcy, Cochran, \& Mayor 1999; Marcy \& Butler 1998)
as well as their inward orbital migration can be
accounted for by consideration of disc--protoplanet interactions
during the late
stages of giant planet formation.
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