A Survey of Chemical Separation in Accreting Neutron Stars

The heavy element ashes of rp-process hydrogen and helium burning in accreting neutron stars are compressed to high density where they freeze, forming the outer crust of the star. We calculate the chemical separation on freezing for a number of different nuclear mixtures resulting from a range of burning conditions for the rp-process. We confirm the generic result that light nuclei are preferentially retained in the liquid and heavy nuclei in the solid. This is in agreement with the previous study of a 17-component mixture of rp-process ashes by Horowitz et al. (2007), but extends that result to a much larger range of compositions. We also find an alternate phase separation regime for the lightest ash mixtures which does not demonstrate this generic behaviour. With a few exceptions, we find that chemical separation reduces the expected $Q_{\rm imp}$ in the outer crust compared to the initial rp-process ash, where $Q_{\rm imp}$ measures the mean-square dispersion in atomic number $Z$ of the nuclei in the mixture. We find that the fractional spread of $Z$ plays a role in setting the amount of chemical separation and is strongly correlated to the divergence between the two/three-component approximations and the full component model. The contrast in $Y_e$ between the initial rp-process ashes and the equilibrium liquid composition is similar to that assumed in earlier two-component models of compositionally driven convection, except for very light compositions which produce nearly negligible convective driving. We discuss the implications of these results for observations of accreting neutron stars.