Low-mass quark stars as Maclaurin spheroids

We show that in the limit of low masses (M<0.1M solar), the orbital and rotational frequencies in exact relativistic numerical models of rotating, axially symmetric, quark stars coincide with those for Maclaurin spheroids. In particular, when the eccentricity of the 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. The orbital frequency in the marginally stable orbit, and all other orbits, around Maclaurin spheroids goes to zero in the limit e=1. Maximum orbital frequencies in accreting Galactic X-ray sources may be a poor indication of the source mass.