Contrasting neutron star heating mechanisms with

Passively cooling neutron stars (NSs) are expected to reach undetectably low surface temperatures, Ts < 104 K, within less than 107 yr. However, Hubble Space Telescope (HST) observations have revealed likely thermal ultraviolet emission from the gigayear-old millisecond pulsars PSR J0437−4715 and PSR J2124−3358 and the ∼107 − 8 year-old classical pulsars PSR B0950+08 and PSR J0108−1431, implying temperatures of Ts ∼ 105 K and thus suggesting the presence of some heating mechanism. In this work, the thermal evolution for each of these NSs was computed considering rotochemical heating in the NS core with normal or Cooper-paired matter, vortex creep in the inner crust, and crustal heating through nuclear processes. The results were contrasted with the observations while also including the stringent upper limit on the temperature of PSR J2144−3933. No single heating mechanism alone was found to account for all the observations. The high temperature of PSR J0437−4715 can be explained by rotochemical heating in the presence of a large Cooper pairing gap, Δi ∼ 1.5 MeV, for either neutrons or protons (or an equivalent combination of both), but this mechanism would require an unrealistically short initial rotation period, P0 ≲ 1.8 ms, to account for the high temperature of the classical pulsar PSR B0950+08. Conversely, the latter can be explained by rotochemical heating with modified Urca reactions in normal matter or by vortex creep with an excess angular momentum parameter, J ∼ 3 × 1043 erg s, but these models are insufficient to account for the former. However, a model that includes rotochemical heating with a large Cooper pairing gap together with vortex creep is consistent with the temperature measurements of these two pulsars as well as the upper limits for the other three. Moreover, this scenario predicts that the temperatures of the other three pulsars should be close to these upper limits, suggesting that deeper observations and/or a wider wavelength coverage for these and other old nearby pulsars should yield a strong probe of this model.