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, $L_X < 10^{36}\usp\ergspersecond (\simeq 0.01\ensuremath{L_{\mathrm{Edd}}}$), 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 $\mdot \lesssim 10^{-2}\medd$ (for which the ignition of H is unstable), where $\medd = 8.8\times 10^{4}\nsp\gpscps$, the helium and CNO elements sediment out of the accreted fuel before reaching a temperature where 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 $F = 0.1\nsp\MeV(\dot{m}/\mb)$, the range is $3\times 10^{-3}\medd\lesssim\mdot\lesssim 10^{-2}\medd$. We speculate that sources accreting in this range will build up a massive He layer that later produces 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 $\mdot \gtrsim 0.1\medd$, 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 \iso{12}{C}--an important ingredient for subsequent superbursts.