The Stability of Supermassive Stars

The studies presented in this paper constitute an extension of previous work on relaxation oscillations in supermassive stars. It is shown that a relatively small amount of rotation is sufficient to remove the general-relativistic instability which arises in such stars when rotation is absent. The post-Newtonian equations for the binding energy and for the frequency of the fundamental mode of radial oscillation are derived and the close connection between these two quantities is exhibited. The equatorial instability associated with contraction under rotation is investigated and the results used to estimate the limiting mass in which hydrogen burning can be effective as a source of energy during relaxation oscillations. This limit is found to be at least 108 Mo and perhaps as high as l0 Mo whereas, without rotation, the limit arising from general relativistic considerations is 106 Mo.