Issue |
A&A
Volume 433, Number 1, April I 2005
|
|
---|---|---|
Page(s) | 247 - 265 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361:20042029 | |
Published online | 14 March 2005 |
Models of accreting gas giant protoplanets in protostellar disks
Astronomy Unit, Queen Mary, University of London, Mile End Rd, London E1 4NS, UK e-mail: jcbp@maths.qmw.ac.uk
Received:
20
September
2004
Accepted:
14
December
2004
We present evolutionary models of gas giant planets forming in
protoplanetary disks. We first consider protoplanet models
that consist of solid cores surrounded by hydrostatically supported
gaseous envelopes that are in contact with the boundaries of
their Hill spheres, and
accrete gas from the surrounding disk. We neglect planetesimal accretion, and
suppose that the luminosity arises from gas accretion alone.
This generally occurs on a long time scale which may be
comparable to the protostellar disk lifetime.
We classify
these models as being of type A, and follow their quasi static evolution
until the point of rapid gas accretion is reached.
We consider a second class of protoplanet models that have not hitherto
been considered. These models have a free surface, their energy supply
is determined by gravitational contraction, and mass accretion
from the protostellar disk
that is assumed to pass through a circumplanetary disk.
An evolutionary sequence is obtained by specifying the accretion rate
that the protostellar disk is able to supply.
We refer
to these models as being of type B. An important
result is that these protoplanet models
contract quickly to a radius cm
and are able to accrete
gas from the disk at any
reasonable rate that may be supplied without any consequent expansion
(e.g. a Jupiter mass in ~few
years, or more slowly
if so constrained by the disk model).
We speculate that the early stages of gas giant
planet formation proceed along evolutionary paths described by models
of type A, but at the onset of rapid gas accretion
the protoplanet contracts interior to its Hill sphere,
making a transition to an evolutionary path
described by models of type B, receiving gas through a circumplanetary
disk that forms within its Hill sphere, which is in turn
fed by the surrounding protostellar disk.
We consider planet models with solid core masses of 5 and
,
and consider evolutionary sequences
assuming different amounts of dust opacity
in the gaseous envelope.
The initial protoplanet mass doubling time scale is very approximately
inversely proportional
to the magnitude of this opacity.
Protoplanets with
cores, and standard dust opacity
require
years to grow to a Jupiter mass,
longer than reasonable disk life-times.
A model with 1% of standard dust opacity requires
years.
Rapid gas accretion in both these cases ensues once the planet
mass exceeds
with substantial time
spent in that mass range.
Protoplanets with
cores grow to a Jupiter mass
in
years if standard dust opacity is assumed,
and in
years if 1% of standard dust opacity is adopted.
In these cases, the planet
spends substantial time with mass between 30-40
before
making the transition to rapid gas accretion. We emphasize that these growth times
apply to the gas accretion phase and not to the prior core formation phase.
According to the usual theory of protoplanet migration,
although there is some dependence on disk parameters,
migration in standard model disks
is most effective in the mass range where the transition
from type A to type B occurs. This is also
the transitional regime
between type I and type II migration. If a mechanism
prevents the type I migration of low mass protoplanets, they
could then undergo a rapid inward migration at around the transitional
mass regime. Such protoplanets would end up in the inner regions of the
disk undergoing type II migration and further accretion potentially
becoming sub Jovian close orbiting planets. Noting that more dusty
and higher mass cores spend more time at a larger transitional
mass that in general favours more rapid migration, such planets are more likely
to become close orbiters.
We find that the luminosity of the forming protoplanets
during the later stages of gas accretion is dominated by the circumplanetary
disk and protoplanet-disk boundary layer.
For final accretion times for one Jupiter mass
in the range 105-6 y, the luminosities are in the range
and the characteristic
temperatures are in the range 1000-2000 K.
However, the luminosity may reach
for shorter time periods at the faster rates of accretion
that could be delivered by the protoplanetary disk.
Key words: accretion, accretion disks / solar system: formation / stars: planetary systems
© ESO, 2005
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