Threshold Mass of the General-relativistic Instability for Supermassive Star Cores

The dependence of the final fate of supermassive star (SMS) cores on their mass and angular momentum is studied with simple modeling. SMS cores in the hydrogen-burning phase encounter the general-relativistic instability during stellar evolution if the mass is larger than ∼3 × 10 M . Spherical SMS cores in the helium-burning phase encounter the general-relativistic instability prior to the onset of the electron-positron pair instability if the mass is larger than ∼1 × 10 M . For rapidly rotating SMS cores, these values for the threshold mass are enhanced by up to a factor of ∼5, and thus, for SMSs with mass smaller than ∼10 M , the collapse is triggered by the pair instability, irrespective of the rotation. After the onset of the general-relativistic instability, SMS cores in the hydrogen-burning phase with reasonable metallicity are likely to collapse to a black hole irrespective of the degree of rotation, whereas SMS cores in the helium-burning phase could explode via nuclear burning with no black hole formation, as previous works demonstrate.