2012/12/17 by Eirik Endeve, Christian Y. Cardall, Endeve, Eirik +3
Physics and Astronomy · #FOS: Physical sciences #Solar and Stellar Astrophysics (astro-ph.SR) #astro-ph.SR
paper · pdf · doi:10.48550/arxiv.1212.4064
Submitted to the Astrophysical Journal
arxiv created 2012/12/17 · arxiv updated 2012/12/18
We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations. After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits. Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature. The third limit is a weak-field, `pseudo-Newtonian' approach \citepkimetal2009,kimetal2012 in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity v are retained. Our primary interest here is in the fourth limit: `O(v)' moment equations for use in conjunction with Newtonian self-gravitating hydrodynamics. We show that the concept of `O(v)' transport requires care when dealing with both conservative four-momentum and conservative lepton number transport, and present two self-consistent options: `O(v)-plus' transport, in which an O(v2) energy equation combines with an O(v) momentum equation to give an O(v2) number equation; and `O(v)-minus' transport, in which an O(v) energy equation combines with an O(1) momentum equation to give an O(v) number equation.