A re-examination of neutron star cooling in transient sources. No shallow heating required: The role of thermonuclear heating leakage

For the typical modelling of neutron-star cooling after an accretion episode in low-mass X-ray binaries, an extra heating source of unknown physical origin, i.e. the shallow heating, is invoked in order to account for the inferred highly effective temperatures of the star up to hundreds of days after the end of accretion. The amount of shallow heating generated in the crust is usually taken to be proportional to the accretion rate, although the proportionality constant may change from source to source. We intend to model the effective temperature data of eight outburst episodes from seven different sources ( H and ^ ̊xs, and ̨s) without ad hoc shallow heating but accounting for the presence of thermonuclear heating due to the burning of the accreted 1 4 He. We employed the fully relativistic code which simulates both the crust and the core of a neutron star, equipped with a new boundary condition at the envelope--crust transition that considers thermonuclear heating leakage from the envelope into the crust and depends on the mass-accretion rate. We find that the neutron star cooling for four out of eight of these outbursts can be well explained with this new boundary condition and without the requirement of extra shallow heating. For the remaining sources, an enhanced mass-accretion rate or high crustal impurities are needed to fit the observations.