Symmetry energy expansion and the peak value of the bulk viscosity

TL;DR

This paper links the symmetry energy parameters to the bulk viscosity in neutron star matter, deriving formulas for the peak viscosity and stability limits, which are crucial for understanding neutron star oscillations and rotation.

Contribution

It introduces a method to connect symmetry energy parameters to bulk viscosity in dense matter, providing new formulas for resonance peaks and stability conditions.

Findings

Bulk viscosity peak depends strongly on the symmetry energy slope parameter L.

Derived a formula for conformal points of the zero-temperature equation of state.

Identified conditions under which neutron stars are limited in rotation frequency by bulk viscosity.

Abstract

The symmetry energy expansion is a useful way to parametrize the properties of dense matter near nuclear saturation density, and much work has been done to connect physical quantities like the neutron star radius and the core-crust transition density to the symmetry energy parameters. In this work, I connect the weak-interaction-driven bulk viscosity in neutron-proton-electron ($npe$) matter to the symmetry parameters by calculating the susceptibilities of dense matter in terms of the symmetry energy. I use this result to calculate the resonant-peak value of the bulk viscosity as a function of density, finding that it strongly depends on $L$, as does the minimum bulk-viscous dissipation timescale. Also resulting from this calculation is a formula for finding the conformal points of the zero-temperature equation of state. Finally, I determine for which values of the symmetry parameters the maximum r-mode-stable rotation frequency of an $npe$-matter neutron star is smaller than the Kepler frequency, in the high-temperature conditions where bulk viscosity is the dominant dissipation mechanism.