Stellar critical parameters in the uniform density approximation

TL;DR

This paper calculates stellar stability limits using a uniform density model, accounting for general relativity, and finds that the critical parameters differ by no more than 12% from more complex models.

Contribution

It introduces a simplified uniform density approximation for stellar models to determine stability boundaries, incorporating relativistic effects.

Findings

Critical parameters differ by up to 12% from more accurate models.

The variational method effectively determines stability boundaries.

Relativistic effects are significant in high-mass stellar models.

Abstract

Stellar models are calculated in the approximation of a uniform density distribution. Variational method was used for determination of the boundary of a stability loss, for stellar masses in the range from 2 up to $10^5$ $M_{\odot}$. The effects of the general relativity had been taken into account. The equation of state in the temperature and density ranges $10^9 < T < 10^{10} K$, $10^5 < \rho < 10^{10}\,\frac{g}{cm^3}$ had been taken from the work of Imshennik and Nadyozhin (1965). The critical parameters for the values of entropy and stellar masses differ from more accurate values, obtained using a more complicated variant of accepted density distribution, not more than 12$\%$.