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 o rbits at the Kepler period, is reduced by similar to 36% below the usual Ed dington luminosity from a corresponding nonrotating star. A supermassive st ar is believed to evolve in a quasi-stationary manner along such a maximall y rotating "mass-shedding" sequence before reaching the point of dynamical instability; hence this reduced luminosity determines the evolutionary time scale. Our result therefore implies that the lifetime of a supermassive sta r prior to dynamical collapse is similar to 36% longer than the value typic ally estimated by employing the usual Eddington luminosity.