General relativistic neutrino transport using spectral methods

TL;DR

This paper introduces Lorene's Ghost, a spectral method-based code for neutrino transport in supernovae, capable of handling full energy dependence and relativistic effects with high accuracy and efficiency.

Contribution

The paper develops a new spectral method framework for relativistic neutrino transport, including derivation of the Liouville operator and implementation in a spherical shell with energy dependence.

Findings

Demonstrates convergence and conservation properties in test cases

Validates the treatment of relativistic effects in Schwarzschild metric

Shows efficient computation in six-dimensional settings

Abstract

We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general-relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.