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Transient neutron star (NS) LMXBs undergo episodes of accretion, alternatedwith quiescent periods. During an accretion outburst, the NS heats up due toexothermic accretion-induced processes taking place in the crust. Besides thelong-known deep crustal heating of nuclear origin, a likely non-nuclear sourceof heat, dubbed 'shallow heating', is present at lower densities. Most of theaccretion-induced heat slowly diffuses into the core on a timescale of years.Over many outburst cycles, a state of equilibrium is reached when the coretemperature is high enough that the heating and cooling (photon and neutrinoemission) processes are in balance. We investigate how stellar characteristicsand outburst properties affect the long-term temperature evolution of atransiently accreting NS. For the first time the effects of crustal propertiesare considered, particularly that of shallow heating. Using our code NSCool, wetracked the thermal evolution of a NS undergoing outbursts over a period of$10^5$ yr. The outburst sequence is based on the regular outbursts observedfrom Aql X-1. For each model, we calculated the timescale over whichequilibrium was reached and we present these timescales along with thetemperature and luminosity parameters of the equilibrium state. We find thatshallow heating significantly contributes to the equilibrium state. Increasingits strength raises the equilibrium core temperature. We find that if deepcrustal heating is replaced by shallow heating alone, the core would still heatup, reaching only a 2% lower equilibrium core temperature. Deep crustal heatingmay therefore not be vital to the heating of the core. Additionally, shallowheating can increase the quiescent luminosity to values higher than previouslyexpected.

Long-term temperature evolution of neutron stars undergoing episodic accretion outbursts