Relativistic supermassive stars

A plausible scenario for the formation of a stable supermassive star in the relativistic regime has been discussed. The onset of the negativity of the `distribution function' in the stable sequences of the star clusters [the stability of star clusters is assured by using the variational method (Chandrasekhar, 1964a,b) for equivalent gas spheres] described by Tolman's type VII solution with vanishing surface density has been regarded as an indication of the conversion of the cluster structure into a supermassive star. For the critical values of the `adiabatic index', (4/3) < γcrit ≤ (5/3) (forwhich a supermassive star represent neutrally stable system), the mass, and the size of this object comes out to be 6.87 × 107 M⊙ ≤M ≤ 1.7 × 109M⊙, and 2.74× 1014 cm ≤ a≤ 1.43× 1015cm respectively, for the central temperature,T0 = 6× 107°K, which is sufficient for the release ofnuclear energy. The total energy released during their evolution rangesfrom 2.46× 1060 - 3.18× 1062 erg, which is sufficient to power these objects at least for a period of ∼ 106 - 107years. These figures agrees quite well with those cited for Quasi Stellar Objects (QSOs) in the literature.