Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Abstract

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

New Developments in Flavor Evolution of a Dense Neutrino Gas

“…Hydrodynamical simulations of core collapse have approached the 3D frontier (79,80). Given the challenges involved in the modeling of neutrino flavor conversion physics, the neutrino transport equations in hydrodynamical simulations do not include flavor conversions (81). Instead, flavor conversions are investigated in a postprocessing phase.…”

On the Time Distribution of Supernova Antineutrino Flux

“…For a few recent and useful review articles on supernova neutrinos, please see [9][10][11][12][13][14][15][16][17][18][19][20][21][22]45] and references therein.…”

“…Decades-long discussion about their internal mechanism has made it clear that a specific kind of supernova occurs as a result of a gravitational collapse, which leads to the formation of compact stellar remnants accompanied by a brief and very intense neutrino emission [9][10][11][12][13][14][15][16][17][18][19][20][21][22], and likely by a burst of gravitational waves [23][24][25][26][27][28] (it is now widely accepted that a supernova explosion is an intrinsic multidimensional phenomenon, i.e., essential deviations from the spherical symmetry, with three-dimensional features crucial for triggering an explosion [16,19,29,30]). In this paper, we will discuss neutrino emission from this type of supernovae, which is observable in terrestrial detectors if the supernova occurs in our galaxy, and which is the main diagnostics of events following core collapse.…”

A Multifluid Perspective on Multimessenger Modeling

“…This is a crucial issue for both supernova core collapse (where neutrinos are thought to provide the key explosion mechanism) and neutron star mergers (where the merger remnant heats up to temperatures similar to those reached in high-energy colliders). The problem of neutrino transport is extremely challenging (Mezzacappa et al, 2020), but it has one simple and intuitive limit. At high temperatures, the neutrinos are trapped by the matter and they may have a short enough mean-free path that we can meaningfully describe them as a fluid (Pomraning, 1973;Hsieh and Spiegel, 1976).…”

“…The formalism for this is well-developed and the issues associated with it are well-understood (in the context of kinetic theory). The actual challenge is computational (Kotake et al, 2012;Mezzacappa et al, 2020), given the added dimensions associated with the radiation phase space. This is why practical implementations (Stone et al, 1992;Shibata and Sekiguchi, 2012;Skadowski et al, 2013;Anninos and Fragile, 2020) typically involve simplifying the problem by integrating out momentum aspects, leading to a well-defined moment expansion.…”