Spin diffusive modes and thermal transport in neutron star crusts

TL;DR

This paper reviews collective modes in neutron star crusts, focusing on density and spin perturbations, and calculates how spin diffusive modes influence thermal conductivity, revealing a specific temperature dependence.

Contribution

It introduces a method to analyze collective modes in neutron star crusts and demonstrates their impact on thermal transport properties, particularly the role of spin diffusive modes.

Findings

Density modes are undamped below the pair-breaking threshold.

Spin diffusive modes are damped above the threshold.

Thermal conductivity scales as T^{1/2} exp(-2ω_0/T).

Abstract

In this contribution we first review a method for obtaining the collective modes of pair-correlated neutron matter as found in a neutron star inner crust. We discuss two classes of modes corresponding to density and spin perturbations with energy spectra $\omega = \omega_0 + \alpha q^2$, where $\omega_0 = 2\Delta$ is the threshold frequency and $\Delta$ is the gap in the neutron fluid spectrum. For characteristic values of Landau parameters in neutron star crusts the exitonic density modes have $\alpha < 0$, therefore they live below the pair-breaking continuum $\omega_0$ and are undamped. For spin diffusive modes $\alpha > 0$ and they exist above $\omega_0$ which implies that these modes are damped. As an application of these findings we compute the thermal conductivity due to spin diffusive modes and show that it scales as $T^{1/2} \exp(-2\omega_0/T)$ in the case where their two-by-two scattering cross-section is weakly dependent on temperature.