Buoyancy and g-modes in young superfluid neutron stars

TL;DR

This paper investigates the dynamics of g-modes in young superfluid neutron stars, considering composition, thermal effects, and superfluidity, providing detailed equations and analyzing their evolution with star cooling.

Contribution

It offers a comprehensive derivation of the governing equations for g-modes in superfluid neutron star cores, including effects of composition gradients and thermal excitations, with explicit results for specific models.

Findings

Composition gradients are dominated by muons when present.

G-modes supported by thermal gradients become relevant below the superfluid transition.

G-mode instability is weak and short-lived during star cooling.

Abstract

We consider the local dynamics of a realistic neutron star core, including composition gradients, superfluidity and thermal effects. The main focus is on the gravity g-modes, which are supported by composition stratification and thermal gradients. We derive the equations that govern this problem in full detail, paying particular attention to the input that needs to be provided through the equation of state and distinguishing between normal and superfluid regions. The analysis highlights a number of key issues that should be kept in mind whenever equation of state data is compiled from nuclear physics for use in neutron star calculations. We provide explicit results for a particular stellar model and a specific nucleonic equation of state, making use of cooling simulations to show how the local wave spectrum evolves as the star ages. Our results show that the composition gradient is effectively dominated by the muons whenever they are present. When the star cools below the superfluid transition, the support for g-modes at lower densities (where there are no muons) is entirely thermal. We confirm the recent suggestion that the g-modes in this region may be unstable, but our results indicate that this instability will be weak and would only be present for a brief period of the star's life. Our analysis accounts for the presence of thermal excitations encoded in entrainment between the entropy and the superfluid component. Finally, we discuss the complete spectrum, including the normal sound waves and, in superfluid regions, the second sound.