Analytic closures for M1 neutrino transport

Abstract

Carefully accounting for neutrino transport is an essential component of many astrophysical studies. Solving the full transport equation is too expensive for most realistic applications, especially those involving multiple spatial dimensions. For such cases, resorting to approximations is often the only viable option for obtaining solutions. One such approximation, which recently became popular, is the M1 method. It utilizes the system of the lowest two moments of the transport equation and closes the system with an ad hoc closure relation. The accuracy of the M1 solution depends on the quality of the closure. Several closures have been proposed in the literature and have been used in various studies. We carry out an extensive study of these closures by comparing the results of M1 calculations with precise Monte Carlo calculations of the radiation field around spherically-symmetric protoneutron star models. We find that no closure performs consistently better or worse than others in all cases. The level of accuracy a given closure yields depends on the matter configuration, neutrino type, and neutrino energy. Given this limitation, the maximum entropy closure by Minerbo (1978) on average yields relatively accurate results in the broadest set of cases considered in this work.

Realizability-preserving DG-IMEX method for the two-moment model of fermion transport

“…(19) with the low occupancy Eddington factor in Eq (14) results in the algebraic maximum entropy closure attributed to Minerbo [19], which is currently in use in simulation of neutrino (fermion) transport in the aforementioned nuclear astrophysics applications. In a recent comparison of algebraic (or analytic) closures for the two-moment model applied to neutrino transport around proto-neutron stars, Murchikova et al [56] obtained nearly identical results when using the closures of CB and Minerbo. For these reasons, we include the Minerbo closure in the subsequent discussion and in the numerical tests in Section 9.…”

“…Examples include simulation of neutrino transport in core-collapse supernovae [50] and compact binary mergers [51]. Algebraic moment closures in the context of these aforementioned applications have also been discussed elsewhere (e.g., [52,53,54,55,56]). Here we focus on properties of the algebraic closures that are critical to the development of numerical methods for the two-moment model of fermion transport.…”

Fast neutrino flavor instability in the neutron-star convection layer of three-dimensional supernova models

“…The system of moment equations of the transport solver is closed by an algebraic relation for non-evolved moments (i.e., for the "ij" components of the tensor with i ≥ 1 and j ≥ 1), which depend on the "00" and the "0i" components (see e.g. [49]).…”

On the Occurrence of Crossings between the Angular Distributions of Electron Neutrinos and Antineutrinos in the Supernova Core

“…In order to be certain that our simple SN model reproduces flavor-dependent neutrino angular distributions in agreement with the literature, we tested that our simple model gives numerical results in agreement with the analytical ones presented in Murchikova et al (2017) for the case of a uniform sphere emitting blackbody radiation, see Appendix for details.…”

“…As neutrinos and anti-neutrinos propagate outwards they are absorbed at a constant rate, κ ν e ,ν e , inside R ν e and Rν e respectively. Under these assumptions the total number of neutrinos emitted by the neutrinosphere is N ν e ,ν e = 4πR 2 ν e ,ν e ∞ 0 E 2 e (E−µ νe ,νe )/T + 1 ∼ R 2 ν e ,ν e T 3 ; Analytical ν e Our code ν e Analytical ν e Our code ν e of the neutrino-sphere is (Murchikova et al 2017) n ν e ,ν e (cos θ) ∝…”