Role of nucleon-nucleon correlation in transport coefficients and gravitational-wave-driven $r$-mode instability of neutron stars

TL;DR

This paper investigates how nucleon-nucleon correlations affect transport properties in neutron stars, revealing that Fermi surface depletion enhances damping of r-mode instabilities, but superfluid effects can counteract this.

Contribution

It provides a comprehensive calculation of transport coefficients considering nucleon correlations and superfluidity within the Brueckner theory framework, challenging previous assumptions about shear viscosity roles.

Findings

Fermi surface depletion increases transport coefficients at high densities.

Nucleon shear viscosity remains smaller than lepton viscosity in superfluid matter.

Shear viscosity alone cannot stabilize neutron stars against r-mode oscillations.

Abstract

The thermal conductivity and shear viscosity of dense nuclear matter, along with the corresponding shear viscosity timescale of canonical neutron stars (NSs), are investigated, where the effect of Fermi surface depletion (i.e., the $Z$-factor effect) induced by the nucleon-nucleon correlation are taken into account. The factors which are responsible for the transport coefficients, including the equation of state for building the stellar structure, nucleon effective masses, in-medium cross sections, and the $Z$-factor at Fermi surfaces, are all calculated in the framework of the Brueckner theory. The Fermi surface depletion is found to enhance the transport coefficients by several times at high densities, which is more favorable to damping the gravitational-wave-driven $r$-mode instability of NSs. Yet, the onset of the $Z$-factor-quenched neutron triplet superfluidity provides the opposite effects, which can be much more significant than the above mentioned $Z$-factor effect itself. Therefore, different from the previous understanding, the nucleon shear viscosity is still smaller than the lepton one in the superfluid NS matter at low temperatures. Accordingly, the shear viscosity cannot stablize canonical NSs against $r$-mode oscillations even at quite low core temperatures $10^6$ K.