Superbursts are thought to be powered by the unstable ignition of a carbon-enriched layer formed from the burning of accreted hydrogen and helium. As shown by Cumming & Bildsten, the short recurrence time hinges on the crust being sufficiently hot at densities > 1.0e9 g/cc. In this Letter, we self-consistently solve for the flux coming from the deep crust and core. The temperature where the carbon unstably ignites is only weakly sensitive to the composition of the ashes of H/He burning, but does depend on the thermal conductivity of the inner crust and the neutrino emissivity of the core. The observed superburst recurrence times and energetics suggest that the crust thermal conductivity is low, as if the crust were amorphous instead of crystalline. If the conductivity is higher, such as from a lattice with impurities, then matching the superburst properties require that the neutrino emissivity be not stronger than modified Urca. Observations of superbursts-energetics, recurrence times, and cooling times-therefore complement observations of isolated cooling neutron stars and soft X-ray transients in constraining properties of dense matter. Perhaps the most interesting object in this regard is KS 1731-260, which produced a superburst during its protracted accretion outburst but had a rapidly declining quiescent luminosity.
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