r-mode instability of neutron stars in low-mass X-ray binaries: effects of Fermi surface depletion and superfluidity of dense matter

TL;DR

This paper investigates how Fermi surface depletion and superfluidity in dense nuclear matter influence the viscosity and $r$-mode instability of neutron stars in low-mass X-ray binaries, providing insights into their thermal states and gravitational wave emission.

Contribution

It introduces the combined effects of Fermi surface depletion and superfluidity on neutron star viscosity and $r$-mode instability, offering a more comprehensive understanding of neutron star dynamics.

Findings

Fermi surface depletion reduces bulk viscosity in neutron stars.

Superfluidity significantly lowers core temperature estimates.

Some neutron stars remain in the $r$-mode instability region despite effects.

Abstract

The nucleon-nucleon correlation between nucleons leads to the Fermi surface depletion measured by a $Z$-factor in momentum distribution of dense nuclear matter. The roles of the Fermi surface depletion effect ($Z$-factor effect) and its quenched neutron triplet superfluidity of nuclear matter in viscosity and hence in the gravitational-wave-driven $r$-mode instability of neutron stars (NSs) are investigated. The bulk viscosity is reduced by both the two effects, especially the superfluid effect at low temperatures which is also able to reduce the inferred core temperature of NSs. Intriguingly, due to the neutron superfluidity, the core temperature of the NSs in known low-mass X-ray binaries (LMXBs) are found to be clearly divided into two groups: high and low temperatures which correspond to NSs with short and long recurrence times for nuclear-powered bursts respectively. Yet, a large number of NSs in these LMXBs are still located in the $r$-mode instability region. If the density-dependent symmetry energy is stiff enough, the occurence of direct Urca process reduces the inferred core temperature by about one order of magnitude. Accordingly, the contradiction between the predictions and observations is alleviated to some extent, but some NSs are still located inside the unstable region.