The Guided Moments formalism: a new efficient full-neutrino treatment for astrophysical simulations

Abstract

We present the new Guided Moments ($\text{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\text{M1}$) and Monte-Carlo ($\text{MC}$) schemes have been proven to be robust and accurate in solving the Boltzmann's equation for neutrino transport. However, it is well-known that each method exhibits specific strengths and weaknesses in various physical scenarios. The $\text{GM}$ formalism effectively solves these problems, providing a comprehensive scheme capable of accurately capturing the optically thick limit through the exact $\text{M1}$ closure and the optically thin limit through a $\text{MC}$ based approach. In addition, the $\text{GM}$ method also approximates the neutrino distribution function with a reasonable computational cost, which is crucial for the correct estimation of the different neutrino-fluid interactions. Our work provides a comprehensive discussion of the formulation and application of the $\text{GM}$ method, concluding with a thorough comparison across several test problems involving the three schemes ($\text{M1}$, $\text{MC}$, $\text{GM}$) under consideration.

17+3 pages, 14 figures. Accepted in PRD

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