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Thermal state of transiently accreting neutron stars

We study thermal states of transiently accreting neutron stars (with mean accretion rates $\dot{M} \sim 10^{-14}-10^{-9}$ M$_\odot$ yr$^{-1}$) determined by the deep crustal heating of accreted matter sinking into stellar interiors. We formalize a direct correspondence of this problem to the problem of cooling neutron stars. Using a simple toy model we analyze the most important factors which affect the thermal states of accreting stars: a strong superfluidity in the cores of low-mass stars and a fast neutrino emission (in nucleon, pion-condensed, kaon-condensed, or quark phases of dense matter) in the cores of high-mass stars. We briefly compare the results with the observations of soft X-ray transients in quiescence. If the upper limit on the quiescent thermal luminosity of the neutron star in SAX J1808.4-3658 (Campana et al. 2002) is associated with the deep crustal heating, it favors the model of nucleon neutron-star cores with switched-on direct Urca process.