A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime

Abstract

We present an implicit finite difference representation for general\nrelativistic radiation hydrodynamics in spherical symmetry. Our code,\nAgile-Boltztran, solves the Boltzmann transport equation for the angular and\nspectral neutrino distribution functions in self-consistent simulations of\nstellar core collapse and postbounce evolution. It implements a dynamically\nadaptive grid in comoving coordinates. Most macroscopically interesting\nphysical quantities are defined by expectation values of the distribution\nfunction. We optimize the finite differencing of the microscopic transport\nequation for a consistent evolution of important expectation values. We test\nour code in simulations launched from progenitor stars with 13 solar masses and\n40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron star\nin the latter case reaches its maximum mass and collapses further to form a\nblack hole. When the hydrostatic gravitational contraction sets in, we find a\ntransient increase in electron flavor neutrino luminosities due to a change in\nthe accretion rate. The muon- and tauon-neutrino luminosities and rms energies,\nhowever, continue to rise because previously shock-heated material with a\nnon-degenerate electron gas starts to replace the cool degenerate material at\ntheir production site. We demonstrate this by supplementing the concept of\nneutrinospheres with a more detailed statistical description of the origin of\nescaping neutrinos. We compare the evolution of the 13 solar mass progenitor\nstar to simulations with the MGFLD approximation, based on a recently developed\nflux limiter. We find similar results in the postbounce phase and validate this\nMGFLD approach for the spherically symmetric case with standard input physics.\n