Stationary neutron star envelopes at high accretion rates

In this work we model stationary neutron star envelopes at high accretion rates and describe our new code for such studies. As a first step we put special emphasis on the rp-process which results in the synthesis of heavy elements and study in detail how this synthesis depends on the mass accretion rate and the chemical composition of the accreted matter. We show that at very low accretion rate, $\dot{M} \sim 0.01 \dot{M}_{\text{Edd}}$, mostly low mass ($A\leq$ 24) elements are synthesized with a few heavier ones below the $^{40}$Ca bottleneck. However, once $\dot{M}$ is above ${\buildrel \sim \over >} 0.1 \dot{M}_{\text{Edd}}$ this bottleneck is surpassed and nuclei in the iron peak region ($A\sim$ 56) are abundantly produced. At higher mass accretion rates progressively heavier nuclei are generated, reaching $A \sim 70$ at $\dot{M}_{\text{Edd}}$ and $A \sim 90$ at $5 \dot{M}_{\text{Edd}}$. We find that when the rp-process is efficient, the nucleosynthesis it generates is independent of the accreted abundance of CNO elements as these are directly and copiously generated once the $3\alpha$-reaction is operating. We also explore the efficiency of the rp-process under variations of the relative abundances of H and He. Simultaneously, we put special emphasis on the density profiles of the energy generation rate particularly at high density beyond the hydrogen exhaustion point. Our results are of importance for the study of neutron stars in systems in which X-ray bursts are absent but are also of relevance for other systems in describing the low density region, mostly below $10^6$ g cm\mmm, inbetween bursts.