Long type I X-ray bursts and neutron star interior physics

Two types of long-duration type I X-ray bursts have been discovered by long-term monitoring observations of accreting neutron stars: superbursts and "intermediate duration" bursts. We investigate the sensitivity of their ignition conditions to the interior thermal properties of the neutron star. First, we compare the observed superburst light curves to cooling models. Our fits require ignition column depths in the range (0.5-3) x 10(12) g cm(-2) and an energy release approximate to 2 x 10(17) ergs g(-1). The implied carbon fraction is X-C > 10%, constraining models of rp-process hydrogen burning. Neutrino emission and inwards conduction of heat lead to a characteristic surface fluence of 10(42) ergs, in good agreement with observations. Next, we compare ignition models to observations of superbursts. Consistent with our light-curve fits, carbon fractions X-C greater than or similar to 0.2 are needed to avoid stable burning at the lowest rates for which superbursts have been observed. Unstable carbon ignition at the observed depths requires crust temperatures approximate to 6 x 10(8) K, which implies that neutrino emission from the interior is inefficient, and the crust has a poor thermal conductivity. In particular, we cannot match observed superburst properties when Cooper pair neutrino emission from the crust is included. We conclude that an extra ingredient, for example additional heating of the accumulating fuel layer, is required to explain the observed properties of superbursts. If Cooper pair emission is less efficient than currently thought, the observed ignition depths for superbursts imply that the crust is a poor conductor, and the core neutrino emission is not more efficient than modified Urca. The observed properties of helium bursts support these conclusions, requiring inefficient crust conductivity and core neutrino emission.