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As some neutron star transients require an additional unknown heat source (referred to as “shallow heating”) to explain their high temperatures at the beginning of quiescence, we investigate the effect of shallow heating as well as compressional heating on the thermal state of transiently accreting neutron stars with the use of evolutionary calculations in the present work. Through comparing our theoretical predictions of the equilibrium redshifted luminosities $(L_{\gamma}^{\infty})$ produced by both deep crustal heating and shallow heating/compressional heating for different time-averaged mass-accretion rates $\langle\dot{M}\rangle$ with 35 updated observations of soft X-ray transients, the results show that both shallow heating and compressional heating make significant contributions to the equilibrium redshifted luminosity. The hotter sources (XTE J1701, MAXI J0556, EXO 0748, Aql X-1 etc.) with higher accretion rates are more likely to be explained with the effect of shallow heating or compressional heating. In addition, for a proper shallow heat $q_\mathrm{sh}$ and mass-accretion rate $\dot{M}$, the effect of shallow heating could be simulated by compressional heating.

Thermal state of transiently accreting neutron stars with additional heating beyond deep crustal heating