Rotochemical heating of millisecond and classical pulsars with anisotropic and density-dependent superfluid gap models

TL;DR

This study investigates how anisotropic and density-dependent superfluid gaps affect rotochemical heating in neutron stars, comparing predictions with observations to constrain superfluid models.

Contribution

It extends previous models by incorporating anisotropic and density-dependent superfluid gaps, analyzing their impact on neutron star thermal evolution.

Findings

Millisecond pulsar PSR J0437-4715's temperature explained by large energy gap models.

Classical pulsars' temperatures suggest models with angle-dependent gaps.

No single superfluid model fits all neutron star observations.

Abstract

When a rotating neutron star loses angular momentum, the progressive reduction of the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium, inducing reactions that release heat (rotochemical heating). This effect has previously been studied by Fern\'andez & Reisenegger (2005) for non-superfluid neutron stars and by Petrovich & Reisenegger (2010) for superfluid millisecond pulsars. Both studies found that pulsars reach a quasi-steady state in which the compression driving the matter out of beta equilibrium is balanced by the reactions trying to restore the equilibrium. We extend previous studies by considering the effect of density-dependence and anisotropy of the superfluid energy gaps, for the case in which the dominant reactions are the modified Urca processes, the protons are non-superconducting, and the neutron superfluidity is parametrized by models proposed in the literature. By comparing our predictions with the surface temperature of the millisecond pulsar PSR J0437-4715 and upper limits for twenty-one classical pulsars, we find the millisecond pulsar can be only explained by the models with the effectively largest energy gaps (type B models), the classical pulsars require with the gap models that vanish for some angle (type C) and two different envelope compositions. Thus, no single model for neutron superfluidity can simultaneously account for the thermal emission of all available observations of non-accreting neutron stars, possibly due to our neglect of proton superconductivity.