Propagation of nuclear burning fronts on accreting neutron stars: X-ray bursts and sub-hertz noise

We identify a new regime of time dependent helium burning for high accretion rate neutron stars and suggest that this burning is the origin of the low-level luminosity variations (on timescales of 10-10(exp 4) s, designated the 'very low-frequency noise'(VLFN) by van der Klis and collaborators) always detected in the brightest accreting X-ray sources. Only two nuclear burning regimes were previously recognized. At accretion rates in excess of the Eddington limit (dot-M approximately greater than (1-3) x 10(exp -8) solar mass/yr), the accreted matter fuses steadily. At very low dot-M, the star's entire surface is rapidly (approximately less than 10 s) burned by a fast propagating convective burning front at regular intervals, giving quasi-periodic Type I X-ray bursts. We show that for the observationally interesting range of 5 x 10(exp -10) solar mass/yr approximately less than dot-M approximately less than 10(exp -8) solar mass/yr, parts of the stellar surface burn slowly. At these accretion rates, a local thermonuclear instability starts a fire which propagates horizontally at v approximately 300 cm/s. The fire propagates around the flammable surface in roughly the same time it takes to accrete enough fuel for the next instability (approximately 10(exp 3)-10(exp 4), so that only a few fires are burning at once, giving rise to large luminosity flares. Nuclear burning is always time dependent for sub-Eddington local accretion rates: a local patch undergoes a recurrent cycle, accumulation fuel for hours until it becomes thermally unstable or is 'ignited' by a nearby burning region. The global pattern of burning and the resulting luminosity are thus very dependent on how fast nuclear fires spread around the star. The nuclear burning luminosity is not uniform over the stellar surface and so may provide a handle on measuring, or constraining, the spin periods of these neutron stars.