Marginally stable orbits around Maclaurin spheroids and low-mass quark stars

Abstract

When the eccentricity of a Maclaurin spheroid exceeds a critical value (e > 0.83458318), circular orbits in the equatorial plane are unstable for a range of orbital radii outside the stellar surface - this is a purely Newtonian effect related to the oblateness of the star. The orbital frequency in the marginally stable orbit, and all other orbits, around Maclaurin spheroids goes to zero in the limit e = 1. The orbital and rotational frequencies in exact relativistic numerical models of rotating, axially symmetric, quark stars of very low mass (M ≤ 0.1 M≤) coincide with those for Maclaurin spheroids. It is impossible to determine the mass of a rapidly rotating quark star by measuring the maximum orbital frequency alone.