A MODEL OF AN EXPLODING, RADIATING STAR IN GENERAL-RELATIVITY

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describ ing the evolution of a spherically symmetric, radiating star were solv ed analytically The evolution of the star was determined by the applic ation of boundary conditions at the center and at the edge. Due to lim itations in the presupernova model, only the very slow inward motion o f an unstable, degenerate core could be considered. The solution was a lso limited by the need to exclude a ''runaway'' term, one that increa sed exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative. This paper presents a completely analytic solution t o the equations of General Relativity describing the evolution of a Ty pe II supernova. Professor S.E. Woosley kindly gave us data on the phy sical variables of a 12 M(0) presupernova star. In our model the core collapses within 1 s, leaving a 1.3 M(0) remnant. Shortly afterward 10 .6 M(0) is ejected to infinity, and 0.17 M(0) is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity dec reases proportionally to the inverse four-thirds power. Although the r unaway solution was modified by the exploding rather than a static env elope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to p hysically non-sensical results such as negative luminosity. The inclus ion of a term describing motion of the mantle due to neutrino interact ions provides the additional degree of freedom necessary for physicall y reasonable results.