Mapping crustal heating with the cooling lightcurves of quasi-persistent transients
The monitoring of quiescent emission from neutron star transients with accretion outbursts long enough to significantly heat the neutron star crust has opened a new vista onto the physics of dense matter. In this paper we construct models of the thermal relaxation of the neutron star crust following the end of a protracted accretion outburst. We confirm the finding of Shternin et al., that the thermal conductivity of the neutron star crust is high, consistent with a low impurity parameter. We describe the basic physics that sets the broken power-law form of the cooling lightcurve. The initial power law decay gives a direct measure of the temperature profile, and hence the thermal flux during outburst, in the outer crust. The time of the break, at hundreds of days post-outburst, corresponds to the thermal time where the solid transitions from a classical to quantum crystal, close to neutron drip. We calculate in detail the constraints on the crust parameters of both KS 1731-260 and MXB 1659-29 from fitting their cooling lightcurves. Our fits to the lightcurves require that the neutrons do not contribute significantly to the heat capacity in the inner crust, and provide evidence in favor of the existence of a neutron superfluid throughout the inner crust. Our fits to both sources indicate an impurity parameter of order unity in the inner crust.