title: Analysis on gaseous envelope of protoplanets based on the theory of stellar structure

authors: Kazuhiro KANAGAWA, Masayuki Y. FUJIMOTO

abstract: Protoplanetary disk is the location where planets form, and it's evolution is closely related to the formation of planets.
Especially, gas giant planets, such as Jupiter and Saturn, interact in powerful ways with the protoplanetary disk.
In order to discuss the evolution of protoplanetary disk, it is important to know the location in the disk where gas giant planets are formed.\\
The runaway accretion is the key event for the formation of gas giant planets.
It is known that the accretion of surrounding gas onto the core starts to be accelerated to form gas giant planets when the critical core mass is reached.
In particular, it is important to extend our knowledge on the critical core mass to explain various characteristics of extra-solar planets.
We analyze the structure of protoplanets based on the theory of stellar structure and by using the homology invariants, which enables to extend the former studies based on the small envelope approximation.
We attempt to understand systematically how the critical core mass is determined with the use of simple polytropic relation.
We find that all of proto-planetary envelopes take the structure of the so-called centrally condensed type solution, peculiar to the core-halo structure, such as red-giant stars.
It imposes the special relation between the core mass and the thermal condition of gas at the bottom of envelope.
In order to discuss the gaseous envelope with a realistic thermal structure, we consider the model constructed of an inner finite polytropic model and an overlying isothermal layer, and we investigate the dependence of critical core mass on the width of isothermal layer.
We discuss the mechanisms and resultant formulae for estimating the critical core mass.
In the poster, these results are presented with the discussion on the relevance to the origin of variety of extrasolar