Luminosity versus rotation in a supermassive star

We determine the effect of rotation on the luminosity of supermassive stars. We apply the Roche model to calculate analytically the emitted radiation from a uniformly rotating, radiation-dominated supermassive configuration. We find that the luminosity at maximum rotation, when mass at the equator orbits at the Kepler period, is reduced by similar to 36% below the usual Eddington luminosity from a corresponding nonrotating star. A supermassive star is believed to evolve in a quasi-stationary manner along such a maximally rotating "mass-shedding" sequence before reaching the point of dynamical instability; hence this reduced luminosity determines the evolutionary timescale. Our result therefore implies that the lifetime of a supermassive star prior to dynamical collapse is similar to 36% longer than the value typically estimated by employing the usual Eddington luminosity.