Gravo-thermal catastrophe in gravitational collapse and energy progenitor of Gamma-Ray Bursts

We study the homologous collapse of stellar nuclear core, the virial theorem for hadron collisional relaxations, and photon productions from hadron collisions. We thus show the gravo-thermal dynamical process that transforms gravitational energy to photon energy. The process is energetically and entropically favourable. The total baryon number conservation, Euler equation for energy-momentum conservation and Poisson's equation for gravitational potential are adopted to describe homologous core collapses. The virial theorem determines the hadron collision energy gain from gravitational potential. The hadronic photon production rate determines the photon energy density. The time scales of macroscopic and microscopic processes are studied to verify approximations. As a result, we show the formation of opaque photon-pair spheres, whose total energy, size, temperature and number density, accounting for the main energetic features of Gamma-Ray Burst progenitors. We obtain the intrinsic correlations of these quantities. They depend only on the averaged thermal index of the stellar core. We discuss the possibility to confront them with observational data.