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Neutron star heating vs. HST observations

Luis E. Rodríguez, Andreas Reisenegger, Denis González-Caniulef, Cristóbal Petrovich, George Pavlov, Sébastien Guillot, Oleg Kargaltsev, Blagoy Rangelov

TL;DR

This work tackles the heating puzzle of old neutron stars by integrating three internal heating mechanisms—rotochemical heating (RH), vortex creep (VC), and crustal heating—into NS thermal evolution models, with and without nucleon Cooper pairing. It demonstrates that no single mechanism suffices to explain all UV observations from HST, but a hybrid model combining RH with a large isotropic pairing gap of about $\Delta \approx 1.5$ MeV and VC can simultaneously account for PSR J0437-4715 and PSR B0950+08, while remaining consistent with upper limits for the others. The results emphasize that late-time NS temperatures are governed by heating-cooling balance and that the initial spin period $P_0$ crucially determines RH activation in the presence of strong pairing. The authors predict that deeper UV and multi-wavelength observations should reveal temperatures near current limits if the proposed scenario is correct, enabling a strong test of the combined RH+VC model with pairing.

Abstract

Passively cooling neutron stars (NSs) should reach undetectably low surface temperatures $T_s<10^4$ K in less than $10^7$ yr. However, HST observations have revealed likely thermal UV emission from the Gyr-old millisecond pulsars PSR~J0437$-$4715 and PSR~J2124$-$3358, and from the $\sim10^{7-8}$ yr-old classical pulsars PSR~B0950$+$08 and PSR~J0108$-$1431, implying $T_s\sim10^5$ K and the need for heating mechanisms. We compute the thermal evolution of these NSs including rotochemical heating (RH) in the core with normal or Cooper-paired matter, vortex creep (VC) in the inner crust, and crustal heating through nuclear reactions, and compare the results with observations and with the upper limit for PSR~2144$-$3933. No single mechanism explains all sources. The high temperature of PSR~J0437$-$4715 can be reproduced by RH with a large Cooper pairing gap $Δ_i\sim1.5$ MeV for either neutrons or protons, but this requires an unrealistically short initial period $P_0\lesssim1.8$ ms to activate the same mechanism in PSR~B0950$+$08. Conversely, the latter can be explained by RH with modified Urca reactions in normal matter or by VC with an excess angular momentum $J\sim3\times10^{43}$ erg,s, but these models underpredict PSR~J0437$-$4715. A model combining RH with a large pairing gap and VC matches both pulsars and is consistent with the upper limits for the remaining three. It further predicts that their temperatures should lie close to these limits, suggesting that deeper or broader-wavelength observations would provide a strong test of this scenario.

Neutron star heating vs. HST observations

TL;DR

This work tackles the heating puzzle of old neutron stars by integrating three internal heating mechanisms—rotochemical heating (RH), vortex creep (VC), and crustal heating—into NS thermal evolution models, with and without nucleon Cooper pairing. It demonstrates that no single mechanism suffices to explain all UV observations from HST, but a hybrid model combining RH with a large isotropic pairing gap of about MeV and VC can simultaneously account for PSR J0437-4715 and PSR B0950+08, while remaining consistent with upper limits for the others. The results emphasize that late-time NS temperatures are governed by heating-cooling balance and that the initial spin period crucially determines RH activation in the presence of strong pairing. The authors predict that deeper UV and multi-wavelength observations should reveal temperatures near current limits if the proposed scenario is correct, enabling a strong test of the combined RH+VC model with pairing.

Abstract

Passively cooling neutron stars (NSs) should reach undetectably low surface temperatures K in less than yr. However, HST observations have revealed likely thermal UV emission from the Gyr-old millisecond pulsars PSR~J04374715 and PSR~J21243358, and from the yr-old classical pulsars PSR~B095008 and PSR~J01081431, implying K and the need for heating mechanisms. We compute the thermal evolution of these NSs including rotochemical heating (RH) in the core with normal or Cooper-paired matter, vortex creep (VC) in the inner crust, and crustal heating through nuclear reactions, and compare the results with observations and with the upper limit for PSR~21443933. No single mechanism explains all sources. The high temperature of PSR~J04374715 can be reproduced by RH with a large Cooper pairing gap MeV for either neutrons or protons, but this requires an unrealistically short initial period ms to activate the same mechanism in PSR~B095008. Conversely, the latter can be explained by RH with modified Urca reactions in normal matter or by VC with an excess angular momentum erg,s, but these models underpredict PSR~J04374715. A model combining RH with a large pairing gap and VC matches both pulsars and is consistent with the upper limits for the remaining three. It further predicts that their temperatures should lie close to these limits, suggesting that deeper or broader-wavelength observations would provide a strong test of this scenario.

Paper Structure

This paper contains 13 sections, 23 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Observational data
  3. Thermal evolution models
  4. Heating mechanisms
  5. Rotochemical heating
  6. Vortex Creep
  7. Crustal heating
  8. Thermal evolution simulations for the observed NSs
  9. Assumptions and setup
  10. Results of simulations and comparison to observations
  11. Sensitivity to initial conditions
  12. Conclusions
  13. Thermal oscillations

Figures (2)

  • Figure 1: Surface temperature evolution curves for each observed pulsar considering models with different reheating mechanisms. In each panel, all curves were calculated assuming magnetic dipole spin-down with a constant dipole moment inferred from the measured spin-down parameters $P$ and $\dot P$ of the respective pulsars. B0950 and J0108 are plotted together, because they have nearly the same inferred dipole field. Their curves were generated with the magnetic field of B0950. For the MSPs (J0437 and J2124), the initial conditions were taken as $P_0=1$ ms and $T_0^\infty=10^{9}$ K, whereas for the CPs (B0950, J0108, and J2144) we assumed $P_0=5~\mathrm{ms}$ and $T_0^\infty=10^{11}$ K. The error bars or upper limits for the pulsars are placed at the times at which the present spin parameters are reached. The models used for Murca and Durca reactions are given in Table \ref{['table:parameters']} as Model M and Model D, respectively. The labels correspond to the following cases: I- Passive cooling with Murca reactions in normal (non-superfluid and non-superconducting) matter. II- Passive cooling with Durca reactions in normal matter. III- Rotochemical heating with Murca reactions in normal matter. IV- Rotochemical heating with Durca reactions in normal matter. V- Vortex creep with Murca reactions setting $J=3\times 10^{43}$ erg s and assuming normal particles in the core. VI- Same as V, but with Durca reactions. VII- Crustal heating (only present in MSPs) with Murca reactions and normal particles in the core. VIII- Same as VII, but with Durca reactions. IX- Rotochemical heating with Murca reactions considering normal protons and superfluid neutrons with a uniform energy gap $\Delta_n=1.5$ MeV, with reaction rates reduced by a factor $f=10^{-2}$. X- Same as IX, but with Durca reactions and reaction rates reduced by a factor $f=10^{-8}$. XI- Rotochemical heating with Murca reactions considering normal protons and superfluid neutrons with $\Delta_n=1.5\,\mathrm{MeV}$ and reaction rates reduced by a factor $f=10^{-2}$, as well as vortex creep with $J=3\times 10^{43}$ erg s.
  • Figure 2: Evolution of the chemical imbalances and the temperature for an MSP with initial conditions $P_0=1\,\mathrm{ms}$, $T_0^\infty=10^9\,\mathrm{K}$, and $\eta_{e,0}^\infty=\eta_{\mu,0}^\infty=0$, considering the effect of rotochemical heating with Murca reactions, normal protons, and superfluid neutrons with $\Delta_n^\infty=1.5\,\mathrm{MeV}$. Each panel has the reaction rates reduced by a different factor $f=1,10^{-1},10^{-2},10^{-5}$, respectively.