Monte-Carlo neutrino transport in neutron star merger simulations

TL;DR

This paper introduces a Monte-Carlo neutrino transport method for neutron star merger simulations, providing more accurate predictions of matter and neutrino outflows compared to traditional approximate schemes.

Contribution

It presents the first neutron star merger simulation using Monte-Carlo techniques for neutrino transport, improving accuracy and quantifying errors of approximate methods.

Findings

Monte-Carlo method yields more accurate neutrino and matter outflow properties.

Approximate M1 scheme has about 10-20% uncertainty in key quantities.

Heavy-lepton neutrino luminosity differs by a factor of ~2 between methods.

Abstract

Gravitational waves and electromagnetic signals from merging neutron star binaries provide valuable information about the the properties of dense matter, the formation of heavy elements, and high-energy astrophysics. To fully leverage observations of these systems, we need numerical simulations that provide reliable predictions for the properties of the matter unbound in these mergers. An important limitation of current simulations is the use of approximate methods for neutrino transport that do not converge to a solution of the transport equations as numerical resolution increases, and thus have errors that are impossible to quantify. Here, we report on a first simulation of a binary neutron star merger that uses Monte-Carlo techniques to directly solve the transport equations in low-density regions. In high-density regions, we use approximations inspired by implicit Monte-Carlo to greatly reduce the cost of simulations, while only introducing errors quantifiable through more expensive convergence studies. We simulate an unequal mass neutron star binary merger up to $5\,{\rm ms}$ past merger, and report on the properties of the matter and neutrino outflows. Finally, we compare our results to the output of our best approximate `M1' transport scheme, demonstrating that an M1 scheme that carefully approximates the neutrino energy spectrum only leads to $\sim 10\%$ uncertainty in the composition and velocity of the ejecta, and $\sim20\%$ uncertainty in the $\nu_e$ and $\bar\nu_e$ luminosities and energies. The most significant disagreement found between M1 and Monte-Carlo results is a factor of $\sim 2$ difference in the luminosity of heavy-lepton neutrinos.