Advection Algorithms for Quantum Neutrino Moment Transport

TL;DR

This paper introduces a novel Riemann solver for quantum moments in neutrino transport, improving computational efficiency and accuracy in modeling flavor transformation in compact astrophysical objects.

Contribution

We generalize a Riemann solver for quantum moments by decomposing complex numbers into magnitude and phase, enabling better simulations of neutrino flavor dynamics.

Findings

Smaller growth rates of flavor transformation compared to previous algorithms

Larger length-scales of flavor instability, aligning better with multi-angle codes

Improved match with multi-angle code growth rates

Abstract

Neutrino transport in compact objects is an inherently challenging multi-dimensional problem. This difficulty is compounded if one includes flavor transformation -- an intrinsically quantum phenomenon requiring one to follow the coherence between flavors and thus necessitating the introduction of complex numbers. To reduce the computational burden, simulations of compact objects that include neutrino transport often make use of momentum-angle-integrated moments (the lowest order ones being commonly referred to as the energy density and flux) and these quantities can be generalized to include neutrino flavor, i.e., they become quantum moments. Numerous finite-volume approaches to solving the moment evolution equations for classical neutrino transport have been developed based on solving a Riemann problem at cell interfaces. In this paper we describe our generalization of a Riemann solver for quantum moments, specifically decomposing complex numbers in terms of a (signed) magnitude and phase instead of real and imaginary parts. We then test our new algorithm in numerous cases showing a neutrino fast flavor instability, varying from toy models with analytic solutions to snapshots from neutron star merger simulations. Compared to previous algorithms for neutrino transport with flavor mixing, we find uniformly smaller growth rates of the flavor transformation along with concomitantly larger length-scales, and that the results are a better match with the growth rates seen from multi-angle codes.