Long-period thermal oscillations in superfluid millisecond pulsars

TL;DR

This paper investigates how superfluidity and direct Urca reactions influence thermal oscillations in millisecond pulsars, revealing stable and unstable states with long-period cycles of heating and cooling.

Contribution

It introduces the first analysis of rotochemical heating with direct Urca reactions and superfluid gaps, uncovering new oscillatory behaviors and stability regimes.

Findings

Large superfluid gaps cause unstable, limit-cycle thermal oscillations.

Small gaps lead to stable quasi-steady states similar to previous models.

Oscillation periods are on the order of 1-10 million years.

Abstract

In previous papers, we have shown that, as the rotation of a neutron star slows down, it will be internally heated as a consequence of the progressively changing mix of particles (rotochemical heating). In previously studied cases (non-superfluid neutron stars or superfluid stars with only modified Urca reactions), this leads to a quasi-steady state in which the star radiates thermal photons for a long time, possibly accounting for the ultraviolet radiation observed from the millisecond pulsar J0437-4715. For the first time, we explore the phenomenology of rotochemical heating with direct Urca reactions and uniform and isotropic superfluid energy gaps of different sizes. We first do exploratory work by integrating the thermal and chemical evolution equations numerically for different energy gaps, which uncovers a rich phenomenology of stable and unstable solutions. To understand these, we perform a stability analysis around the quasi-steady state, identifying the characteristic times of growing, decaying, and oscillating solutions. For small gaps, the phenomenology is similar to the previously studied cases, in the sense that the solutions quickly converge to a quasi-steady state. For large gaps ($\gtrsim 0.05$ MeV), these solutions become unstable, leading to a limit-cycle behavior of periodicity $\sim 10^{6-7} yr, in which the star is hot ($T_s\gtrsim 10^5$ K) for a small fraction of the cycle ($\sim 5- 20 %$), and cold for a longer time.