We calculate the thermal and dynamical evolution of the surface layers of an accreting neutron star during the rise of a superburst. For the first few hours following unstable 12C ignition, the nuclear energy release is transported by convection. However, as the base temperature rises, the heating time becomes shorter than the eddy turnover time and convection becomes inefficient. This results in a hydrodynamic nuclear runaway, in which the heating time becomes shorter than the local dynamical time. Such hydrodynamic burning can drive shock waves into the surrounding layers and may be the trigger for the normal X-ray burst found to immediately precede the onset of the superburst in both cases where the Rossi X-Ray Timing Explorer was observing.
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