Sedimentation and type I X-ray bursts at low accretion rates

Neutron stars, with their strong surface gravity, have interestingly short timescales for the sedimentation of heavy elements. Motivated by observations of Type I X-ray bursts from sources with extremely low persistent accretion luminosities, L-X < 10(36) ergs s(-1) (similar or equal to 0.01 L-Edd), we study how sedimentation affects the distribution of isotopes and the ignition of H and He in the envelope of an accreting neutron star. For local mass accretion rates (m) over dot less than or similar to 10(-2)(m) over dot (Edd) (for which the ignition of H is unstable), where. (m) over dot (Edd) = 8.8 x 10(4) g cm(-2) s(-1), the helium and CNO elements sediment out of the accreted fuel before reaching a temperature at which H would ignite. Using one-zone calculations of the thermonuclear burning, we find a range of accretion rates for which the unstable H ignition does not trigger unstable He burning. This range depends on the emergent flux from reactions in the deep neutron star crust; for F = (0.1 MeV)((m) over dot / m(u)), the range is 3 x 10(-3) (m) over dot (Edd). We speculate that sources accreting in this range would build up a massive He layer that would later produce an energetic and long X-ray burst. At mass accretion rates lower than this range, we find that the H flash leads to a strong mixed H/He flash. Surprisingly, even at accretion rates (m) over dot 0.1 (m) over dot (Edd), although the H and He do not completely segregate, the H abundance at the base of the accumulated layer is still reduced. While following the evolution of the X-ray burst is beyond the scope of this introductory paper, we note that the reduced proton-to-seed ratio favors the production of C-12 - an important ingredient for subsequent superbursts.