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. In order to raise the temperature high enough that the disc might cool by neutrino emission, Chevalier found a small value of the $\alpha$-parameter, where the kinematic coefficient of shear viscosity is $\nu=\alpha c_s H$, with $c_s$ the velocity of sound and $H$ the disc height; namely, $\alpha\sim 10^{-6}$ was necessary for gas pressure to dominate. He also considered results with higher values of $\alpha$, pointing out that radiation pressure would then predominate. With these larger $\alpha$'s, the temperatures of the accreting material are much lower, $\lsim 0.35$ MeV. The result is that neutrino cooling during the flow is negligible, satisfying very well the advection dominating conditions. The low temperature of the accreting material means that it cannot get rid of its energy rapidly by neutrino emission, so it piles up, pushing its way through the accretion disc. An accretion shock is formed, far beyond the neutron star, at a radius $\gsim 10^8$ cm, much as in the earlier spherically symmetric calculation, but in rotation. Two-dimensional numerical simulation shows that an accretion disc is reformed inside of the accretion shock, allowing matter to accrete onto the neutron star with pressure high enough so that neutrinos can carry off the energy.