Vortex Creep Heating in Neutron Star Cooling: New Insights into Thermal Evolution of Heavy Neutron Stars

TL;DR

This work addresses why some old neutron stars remain thermally bright despite fast neutrino cooling by extending neutron-star cooling models to include vortex creep heating (VCH) alongside direct Urca (DUrca) neutrino processes. The authors implement VCH in a physics-based cooling framework, solve the general-relativistic energy balance with both APR and BSk24 equations of state, and account for neutrino cooling and pairing via established gaps, exploring a wide parameter space including the initial spin $P_0$, spin-down rate $\dot{P}$, and magnetic field $B$. They find that VCH can significantly offset rapid DUrca cooling, especially for favorable $P_0$ values, and that a combined VCH+DUrca scenario can explain thermally bright old neutron stars as potentially more massive objects; a 3D visualization framework incorporating $B$ aids in capturing this interplay. The results highlight the importance of heating–cooling balance in interpreting NS temperatures and suggest new avenues for mass inferences and for refining cooling models with additional physics such as rotochemical heating and magnetic-field decay.

Abstract

Neutron stars provide unique laboratories for probing physics of dense nuclear matter under extreme conditions. Their thermal and luminosity evolution reflects key internal properties such as the equation of state (EoS), nucleon superfluidity and superconductivity, envelope composition, and magnetic field, and so on. Recent observations [\textit{e.g.}, V. Abramkin \textit{et al.,} ApJ \textbf{924}, 128 (2022)] have revealed unexpectedly warm old neutron stars, which cannot be explained by standard neutrino-photon cooling models. The failure of the standard cooling models implies the presence of additional internal heating mechanism. Building on the previous study [M. Fujiwara \textit{et al}., JCAP \textbf{03}, 051 (2024)], which proposed vortex creep heating (VCH) from the frictional motion of superfluid vortices as a viable mechanism, we extend the cooling framework to include both VCH and direct Urca (DUrca) processes. These are implemented in our code to explore their combined impact, particularly for massive neutron stars where DUrca operates. By varying rotational parameters ($P$, $\dot{P}$, $P_0$), EoS models (APR, BSk24), pairing gaps, and envelope compositions, we examine how heating-cooling interplay shapes the temperature evolution. Our results show that VCH can substantially mitigate the rapid cooling driven by DUrca, offering new evolutionary pathways for massive neutron stars.

Figures (2)

• Figure 1: Cooling curves of $2.0\,M_\odot$ neutron stars at $B$$=$$10^{12}\,$G (BSk24; Fe envelope; ns–SFB, ps–CCDK, nt–TToa). For each $P_0$$=$ 10--570 ms, the shaded band spans $J$$=$$10^{42.9}$--$10^{43.8}\,{\rm erg\,s}$; the dashed line is standard cooling without heating. Symbols show $T_\mathrm{s}^\infty$ vs. $t$ ($\log_{10}$ axes); colors denote classes. Left arrows mark characteristic-age estimates only; numbers label sources.
• Figure 2: Cooling evolutions of $1.4\,M_\odot$ neutron stars at fixed $P_0$$=$ 10 ms and $J$$=$$10^{43.8}$ erg s for different magnetic-field strengths $B$. (a) 3D representation of the cooling surface, where the conventional $(t,\,T_\mathrm{s}^\infty)$ cooling curves are extended along the magnetic-field axis. (b) Projection along the temperature axis, showing the time evolution at different $B$ values, with color indicating $\log_{10} T_\mathrm{s}^\infty$. Black circles denote observed ordinary pulsars with measured surface temperatures and estimated magnetic fields.