Neutron star heating vs. HST observations

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 $\Delta_i\sim1.5$ 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.