Equilibrium and stability of supermassive stars in binary systems

Abstract

We investigate the equilibrium and stability of supermassive stars of mass $M\gtrsim {10}^5{M}_{\odot }$ in binary systems. We find that corotating binaries are secularly unstable for close, circular orbits with $r\lesssim {4R(M/10}^6{M}_{\odot }{)}^{1/6}$ where r is the orbital separation and R the stellar radius. We also show that corotation cannot be achieved for distant orbits with $r\gtrsim {12R(M/10}^6{M}_{\odot }{)}^{-11/24},$ since the time scale for viscous angular momentum transfer associated with tidal torques is longer than the evolution time scale due to emission of thermal radiation. These facts suggest that the allowed mass range and orbital separation for corotating supermassive binary stars is severely restricted. In particular, for supermassive binary stars of large mass $M\gtrsim 6\times {10}^6{M}_{\odot },$ corotation cannot be achieved, as viscosity is not adequate to mediate the transfer between orbital and spin angular momentum. One possible outcome for binary supermassive stars is the onset of quasi-radial, relativistic instability which drives each star to collapse prior to merger: We discuss alternative outcomes of collapse and possible spin states of the resulting black holes. We estimate the frequency and amplitude of gravitational waves emitted during several inspiral and collapse scenarios.