A Generalized Kompaneets Formalism for Inelastic Neutrino-Nucleon Scattering in Supernova Simulations

Abstract

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next-higher-order in ε/mc2 correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. Our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

arXiv comment13 pages, 4 figures. Accepted on June 19 by Physical Review D

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Cited by in corpus (4)

• Neutrino transport in general relativistic neutron star merger simulations
• Impact of magnetic field on neutrino-matter interactions in core-collapse supernova
• Non-thermal neutrinos created by shock acceleration in successful and failed core-collapse supernova
• On the derivation of the Kompaneets equation