Issue |
A&A
Volume 440, Number 3, September IV 2005
|
|
---|---|---|
Page(s) | 1183 - 1194 | |
Section | Planets and planetary systems | |
DOI | https://doi.org/10.1051/0004-6361:200500005 | |
Published online | 05 September 2005 |
Giant planet formation
A first classification of isothermal protoplanetary equilibria
1
Max-Planck-Institut für extraterrestrishe Physik, Postfach 1312, 85748 Garching, Germany
2
Astrophysikalisches Institut und Universitäts- Sternwarte, Schillergächen 2-3, 07745 Jena, Germany e-mail: bonnie@astro.uni-jena.de
Received:
7
May
2003
Accepted:
16
December
2004
We present a model for the equilibrium of solid planetary cores embedded in a gaseous nebula.
From this model we are able to extract an idealized roadmap of all hydrostatic states of the isothermal
protoplanets. The complete classification of the isothermal protoplanetary equilibria should improve the
understanding of the general problem of giant planet formation, within the framework of the nucleated instability
hypothesis. We approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in
equilibrium, around a rigid body of given mass and density, with
the gaseous envelope required to fill the Hill-sphere. Starting
only with a core of given mass and an envelope gas density at the
core surface, the equilibria are calculated without prescribing
the total protoplanetary mass or nebula density. In this way, a
variety of hydrostatic core-envelope equilibria has been obtained.
Two types of envelope equilibria can be distinguished:
uniform equilibrium, were the density of the envelope gas
drops approximately an order of magnitude as the radial distance
increases to the outer boundary, and compact equilibrium,
having a small but very dense gas layer wrapped around the core
and very low, exponentially decreasing gas density further out.
The effect of the envelope mass on the planetary gravitational
potential further discriminates the models into the
self-gravitating and the non-self gravitating ones. The static
critical core masses of the protoplanets for the typical orbits of 1, 5.2, and 30 AU, around a parent star of 1 solar mass
() are found to be 0.1524, 0.0948, and 0.0335 Earth
masses (
), respectively, for standard nebula
conditions (Kusaka et al. 1970). These values are much
lower than currently admitted ones primarily because our model is
isothermal and the envelope is in thermal equilibrium with the
nebula. Our solutions show a wide range of possible envelopes. For
a given core, multiple solutions (at least two) are found to fit
into the same nebula. Some of those solutions posses equal
envelope mass. This variety is a consequence of the envelope's
self-gravity. We extend the concept of the static critical core
mass to the local and global critical core mass.
Above the global critical mass, only compact solutions
exist. We conclude that the “global static critical core
mass” marks the meeting point of all four qualitatively different
envelope regions.
Key words: planets and satellites: general / solar system: general
© ESO, 2005
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