Stellar critical parameters in the uniform density approximation
G. S. Bisnovatyi-Kogan, E. A. Patraman
TL;DR
The paper addresses the stability limits of massive stars by using a uniform-density approximation with general-relativistic corrections and a detailed iron-rich equation of state. It develops a variational, isentropic framework to derive the equilibrium and stability conditions and produces $M(\rho)$ curves from which critical parameters $\rho_{cr}(M)$ and $S_{cr}(M)$ are extracted. A comprehensive EoS, including radiation, plasma contributions, and high-energy processes, enables tabulated results across wide $\rho$ and $T$ ranges, and the authors compare their uniform-density results with polytropic/isentrope models, finding substantial agreement in $S_{cr}$ but larger differences in density. The findings offer a rapid, robust method to estimate critical states and provide seeds for constructing more accurate, density-profile models of supermassive, radiation-pressure-dominated stars.
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 $10^9 < T < 10^{10} K$, $10^5 < ρ< 10^{10}\,\frac{g}{cm^3}$ 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$\%$.