  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.
