Maximum mass of a barotropic spherical star

TL;DR

This paper refines the upper bound on the mass-to-radius ratio of spherical perfect fluid stars by incorporating the subluminal sound speed condition, using numerical solutions of the TOV equations.

Contribution

It introduces a tighter upper bound on the mass-radius ratio by adding the subluminal sound speed condition to previous assumptions, improving the Buchdahl limit.

Findings

Upper bound on M/R is approximately 0.364.

Numerical solutions of TOV equations support the new bound.

Adding sound speed constraints further restricts star compactness.

Abstract

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl's bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.