Hydrogen Electron Capture in Accreting Neutron Stars and the Resulting   g-Mode Oscillation Spectrum
  We investigate hydrogen electron capture in the oceans of neutron stars accreting at rates appropriate for most Low-Mass X-Ray Binaries. These stars burn the accreted hydrogen and helium unstably in the upper atmosphere and accumulate material which usually contains some small amount of hydrogen (mass fractions are typically 10%) mixed in with the heavier iron group ashes. The subsequent evolution of this matter is determined by compression towards higher densities until electron capture on the hydrogen occurs. We construct steady-state models of the electron captures and the subsequent neutron recombinations onto the heavy nuclei. The density discontinuity from these captures gives rise to a new g-mode (much like a surface wave), which has a lowest order (l=1) frequency of 35 Hz when X=0.1 on a slowly rotating star. We also discuss, for the first time, a new set of non-radial g-modes unique to these neutron stars. These modes have most of their nodes in the finite thickness layer where the electron captures are occurring. The lowest order mode frequencies are in the 1-10 Hz range for a few radial nodes on a slowly rotating star. We conclude by discussing how the dispersion relations for these modes are modified for a rapidly rotating neutron star. Whether any of these modes are observable depends on their excitation and damping mechanisms and the ability to excite them, issues we will address in a future paper. 
Lars Bildsten and Andrew Cumming (University of California, Berkeley)