Soft X-ray transient sources are binary systems containing a neutron star and a low-mass star. Neutron stars undergo periods of accretion from low-mass components and periods of quiescence. The accreted matter can penetrate deeply into the neutron star crust and warm up the entire star due to nuclear transformations in this matter, particularly due to pycnonuclear reactions. Radiation from the warmed up surface is detectable during quiescent periods and carries information on the physical state of superdense matter in neutron star cores.
The physics of heating in the accreted matter is outlined. The theory is compared with observations of thermal radiation from neutron stars in soft X-ray transients during quiescent periods. The constraints on the properties of superdense matter which result from this comparison are summarized.