Hypercritical Advection Dominated Accretion Flow

In this note we study the accretion disc that arises in hypercritical accretion of $\dot M\sim 10^8 M_{\rm Edd}$ onto a neutron star while it is in common envelope evolution with a massive companion. Using $\alpha\sim 0.1$, although our results would not change for a wide range of $\alpha$, we find the pressure to be radiation dominated with the result that temperatures of the accreting material are much lower, less than $\sim 0.5$ MeV. The result is that neutrino cooling during the flow is negligible, satisfying very well the advection dominating conditions. The advected material makes a "soft landing" on the neutron star, where each nucleon is bound by $\sim 200$ MeV, and simply adds to the mass of the neutron star. Temperatures become high enough for nuclear burning to rapidly take place. With the accreted matter the neutron star will evolve to the configuration of hydrostatic equilibrium appropriate for the more massive star. Neutrino emission from the neutron star acts as a thermostat keeping temperatures there $\lsim 1$ MeV. Boundary conditions on the neutron star are, therefore, not much different from those on a black hole, since in either case the accreting energy is taken away rapidly without back reaction on the system. We thus find our results to be very close to those of Mineshige et al. (1997) for black hole disc accretion, once we scale our accretion rate down to the $\sim \dot M/\dot M_{\rm Edd}\sim 10^6$ that they use.