Carbon Flashes in the Heavy Element Ocean on Accreting Neutron Stars

We show that burning of a small mass fraction of carbon in a neutron star ocean is thermally unstable at low accumulated masses when the ocean contains heavy ashes from the hydrogen burning rapid proton (rp) process. The key to early unstable ignition is the low thermal conductivity of a heavy element ocean. The instability requires accretion rates in excess of one-tenth the Eddington limit when the carbon mass fraction is 0.1 or less. The unstable flashes release 10^{42} to 10^{43} ergs over hours to days, and are likely the cause of the recently discovered large Type I X-ray bursts (so-called ``superbursts'') from six Galactic low mass X-ray binaries. In addition to explaining the energetics, recurrence times, and durations of the superbursts, these mixed carbon/heavy element flashes have an accretion rate dependence of unstable burning similar to that observed. Though the instability is present at accretion rates near Eddington, there is less contrast with the accretion luminosity there, explaining why most detections are made at accretion rates between 0.1 and 0.3 Eddington. Future comparisons of time dependent calculations with observations will provide new insights into the rp process.