The Stability of Material Accreting onto a Neutron Star

We present a global linear stability analysis of nuclear fuel accumulating on the surface of an accreting neutron star and we identify the conditions under which thermonuclear bursts are triggered. The analysis reproduces all the recognized regimes of hydrogen and helium bursts, and in addition shows that at high accretion rates, near the limit of stable burning, there is a regime of ``delayed mixed bursts'' which is distinct from the more usual ``prompt mixed bursts.'' In delayed mixed bursts, a large fraction of the fuel is burned stably before the burst is triggered. Bursts thus have longer recurrence times, but do not have correspondingly larger fluences. Therefore, the parameter $\alpha$, which measures the ratio of the energy released via accretion to that generated through nuclear reactions in the burst, can be up to an order of magnitude larger than for prompt bursts. This increase in $\alpha$ near the threshold of stable burning has been seen in observations. We explore a wide range of mass accretion rates, neutron star radii and core temperatures, and calculate a variety of burst properties. From a preliminary comparison with data, we suggest that bursting neutron stars may have hot cores, with temperature of order 10^8 to 10^{8.5} K, consistent with interior cooling via the modified Urca process. However, this result needs to be confirmed by comparing more careful calculations with better data