Existence and uniqueness of stellar equilibrium models |
| |
| Authors: | J Perdang |
| |
| Institution: | (1) Institut d'Astrophysique, Cointe-Ougrée, Belgium |
| |
| Abstract: | The stellar equilibrium equations for given surface pressureP
* and temperatureT
*, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP
M
is selected, which restricts the allowed pressure and temperature range |P(r)–P
*|+E|T(r)–T
* P
M
(E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R
E
. This solution isunique forR<R
c
.R
E
andR
c
are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
