Beyond modified Urca: the nucleon width approximation for flavor-changing processes in dense matter

TL;DR

This paper introduces a nucleon width approximation method to improve calculations of flavor-changing processes in neutron star matter, resolving previous divergences and revealing significant rate enhancements at low densities.

Contribution

It presents a systematically improvable approach replacing modified Urca with nucleon width inclusion, improving accuracy in dense matter calculations.

Findings

Rate enhancement by over an order of magnitude at low densities

Agreement with direct and modified Urca where applicable

Resolution of divergence issues at the direct Urca threshold

Abstract

Flavor-changing charged current ("Urca") processes are of central importance in the astrophysics of neutron stars. Standard calculations approximate the Urca rate as the sum of two contributions, direct Urca and modified Urca. Attempts to make modified Urca calculations more accurate have been impeded by an unphysical divergence at the direct Urca threshold density. In this paper we describe a systematically improvable approach where, in the simplest approximation, instead of modified Urca we include an imaginary part of the nucleon mass (nucleon width). The total Urca rate is then obtained via a straightforward generalization of the direct Urca calculation, yielding results that agree with both direct and modified Urca at the densities where those approximations are valid. At low densities, we observe an enhancement of the rate by more than an order of magnitude, with important ramifications for neutron star cooling and other transport properties.