Millihertz quasi-periodic oscillations from marginally stable nuclear burning on an accreting neutron star

We investigate marginally stable nuclear burning on the surface of accreting neutron stars as an explanation for the mHz quasi-periodic oscillations (QPOs) observed from three low-mass X-ray binaries. At local accretion rates close to the boundary between unstable and stable burning, the temperature dependence of the nuclear heating rate and cooling rate almost cancel. The result is an oscillatory mode of burning, with an oscillation period close to the geometric mean of the thermal and accretion timescales for the burning layer. We describe a simple one-zone model that illustrates this basic physics and then present detailed multizone hydrodynamic calculations of nuclear burning close to the stability boundary using the KEPLER code. Our models naturally explain the characteristic 2minute period of the mHz QPOs and why they are seen only in a very narrow range of X-ray luminosities. The oscillation period is sensitive to the accreted hydrogen fraction and the surface gravity, suggesting a new way to probe these parameters. The accretion rate at which the oscillations appear in the theoretical models, however, is an order of magnitude larger than the rate implied by the X-ray luminosity when them Hz QPOs are seen if the accreted material covers the entire neutron star surface. Bringing the models and observations into agreement requires that the accreted material covers only part of the neutron star surface at luminosities of L-X greater than or similar to 10(37) erg s(-1) so that the local accretion rate at the burning depth can be higher than the observed average.