Hot, Dense Matter Accretion onto a Black Hole

The accretion of hot, dense matter which consists of heavy nuclei, free nucleons, degenerated electrons, photons and neutrinos is studied. The composition of free nucleons and their chemical potentials are provided through the equation of state for hot, dense matter proposed by Lattimer and Swesty(1991). When the mass of a central black hole and the accretion rate are selected as $M_{BH} \approx 3{\rm M}_\odot$ and $\dot{M} \approx 0.1{\rm M}_\odot$sec$^{-1}$, which provide the typical luminosity of gamma ray bursts(GRBs), the fraction of free protons in the accreting matter becomes very small, $Y_p \approx 10^{-4}$, while that of free neutrons is closer to unity, $Y_n \approx 0.7$. Then the antielectron neutrinos $\bar{\nu}_e$ can freely escape through the disk but the electron neutrinos $\nu_e$ are almost absorbed in the disk. Thus the frequent collisions of $\bar{\nu}_e$ with $\nu_e$ over the disk couldn't be occurred. The accretion disk is cooled mainly by $\bar{\nu}_e$, which suppresses the increase of temperature and increases the density in the accreting matter such as $T \approx 3\times 10^{10}$K and $\rho \approx 3\times 10^{13}$g/cm$^3$ at the inner side of the disk. The scattering optical depths of $\bar{\nu}_e$ and $\nu_e$ then reach to be very large, $\tau_s(\bar{\nu}_e) \approx \tau_s({\nu}_e) \approx 10^2$. Thus the accretion disk could be thermally unstable within the duration of diffusion time of neutrinos, $t_{diff} \approx 10$(ms).