Pycnonuclear burning and accreting neutron stars

We outline the phenomenon of deep crustal heating in transiently accreting neutron stars. It is produced by nuclear transformations (mostly, by pycnonuclear reactions) in accreted matter while this matter sinks to densities rho > 10^{10} g/cc under the weight of freshly accreted material. We consider then thermal states of transiently accreting neutron stars (with mean mass accretion rates \dot{M}=(10^{-14}-10^{-9}) M_\odot/yr) determined by deep crustal heating. In a simplified fashion we study how the thermal flux emergent from such stars depends on the properties of superdense matter in stellar interiors. We analyze the most important regulators of the thermal flux: strong superfluidity in the cores of low-mass stars and fast neutrino emission (in nucleon, pion-condensed, kaon-condensed, or quark phases of dense matter) in the cores of high-mass stars. We compare the results with observations of soft X-ray transients in quiescent states.