Self-Similar Hot Accretion Flow onto a Neutron Star

Abstract

We consider hot, two-temperature, viscous accretion onto a rotating, unmagnetized neutron star. We assume Coulomb coupling betweenthe protons and electrons, and free-free cooling from the electrons. We show that the accretion flow has an extended settling region which can be described by means of two analytical self-similar solutions: a two-temperature solution which is valid in an inner zone, r<10^{2.5}, where r is the radius in Schwarzchild units; and a one-temperature solution which is valid in an outer zone, r>10^{2.5}. In both zones the density varies as \rho ~ r^{-2} and the angular velocity as \Omega ~ r^{-3/2}. We solve the flow equations numerically and confirm that the analytical solutions are accurate. The settling flow radiates the energy dissipated by viscosity; so it is not advection-dominated. Except for the radial velocity, all other gas properties - density, angular velocity, temperature, luminosity, angular momentum flux - are independent of the mass accretion rate; these quantities do depend sensitively on the spin of the neutron star. The angular momentum flux is outward under most conditions; therefore, the central star is nearly always spun-down. The luminosity of the settling zone arises from the rotational energy that is released as the star is braked by viscosity, and the contribution from gravity is small; hence the radiative efficiency can be arbitrarily large at low $\mdot$. For reasonable values of the gas adiabatic index, the Bernoulli parameter is negative; therefore, a strong outflow or wind is not expected. The flow is convectively stable, but may be thermally unstable. The described solution is not advection-dominated; however, when the spin of the star is small enough, it transforms smoothly to an advection-dominated branch of solution.