Spin diffusive modes and thermal transport in neutron star crusts

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 $ω= ω_0 + αq^2$, where $ω_0 = 2Δ$ is the threshold frequency and $Δ$ is the gap in the neutron fluid spectrum. For characteristic values of Landau parameters in neutron star crusts the exitonic density modes have $α< 0$, therefore they live below the pair-breaking continuum $ω_0$ and are undamped. For spin diffusive modes $α> 0$ and they exist above $ω_0$ 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 $T^{1/2} \exp(-2ω_0/T)$ in the case where their two-by-two scattering cross-section is weakly dependent on temperature.

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