Carbon Synthesis in Steady-State Hydrogen and Helium Burning On Accreting Neutron Stars

Abstract: Superbursts from accreting neutron stars probe nuclear reactions at extreme densities ($\rho \approx 10<sup>{9}~g\,cm<sup>{-3}$) and temperatures ($T&gt;10<sup>9~K$). These bursts ($\sim$1000 times more energetic than type I X-ray bursts) are most likely triggered by unstable ignition of carbon in a sea of heavy nuclei made during the rp-process of regular type I X-ray bursts (where the accumulated hydrogen and helium are burned). An open question is the origin of sufficient amounts of carbon, which is largely destroyed during the rp-process in X-ray bursts. We explore carbon production in steady-state burning via the rp-process, which might occur together with unstable burning in systems showing superbursts. We find that for a wide range of accretion rates and accreted helium mass fractions large amounts of carbon are produced, even for systems that accrete solar composition. This makes stable hydrogen and helium burning a viable source of carbon to trigger superbursts. We also investigate the sensitivity of the results to nuclear reactions. We find that the $<sup>{14}$O($\alpha$,p)$<sup>{17}$F reaction rate introduces by far the largest uncertainties in the $<sup>{12}$C yield.