Hydrogen electron capture in accreting neutron stars and the resulting g-mode oscillation spectrum

We investigate hydrogen electron capture in the ocean of neutron stars accreting at rates 10(-10) M-. yr(-1) less than or similar to (M) over dot less than or similar to 10(-8) M. yr(-1). These stars burn the accreted hydrogen and helium unstably in their upper atmospheres (rho less than or similar to 10(6) g cm(-3)) and accumulate material that sometimes contains small amounts of hydrogen (mass fractions are typically X-r< 0.1) mixed in with the heavier iron-group ashes. The subsequent evolution of this matter is determined by compression toward higher densities until electron capture on the hydrogen occurs. We construct steady state models of the electron captures and the subsequent neutron captures onto the heavy nuclei. The density discontinuity from these captures gives rise to a new g-mode (much like a surface wave), which has an l=1 frequency of approximate to 35 Hz (X-r/0.1)(1/2) on a slowly rotating (f(s) much less than 30 Hz) star. We also discuss, for the first time, a new set of nonradial g-modes unique to these high-accretion rate neutron stars. These modes are "trapped" in the finite thickness layer where the electron captures occur and are in the 1-10 Hz range for a few radial nodes on a slowly rotating star. Though the majority of the mode energy resides in the electron capture transition layer, the eigenmode propagates to higher altitudes above the layer and can thus be potentially observable. We also show that the density jump splits the ocean's thermal modes into two distinct sets, which have most of their energy either above or below the discontinuity. We conclude by discussing the dispersion relations for these modes on a rapidly rotating (f(s) much less than 30 Hz) neutron star. Whether any of these modes are observable depends on the damping mechanism and the star's ability to excite them.