http://arxiv.org/abs/2204.08448
We present an exact $\gamma=5/3$ spherical accretion model which modifies the Bondi boundary condition of $\rho \to const.$ as $r\to \infty$ to one where $\rho \to 0$ as $r \to \infty$. This change allows for simple power law solutions on the density and infall velocity fields, ranging from a cold empty free-fall condition where pressure tends to zero, to a hot hydrostatic equilibrium limit with no infall velocity. As in the case of the Bondi solution, a maximum accretion rate appears. As in the $\gamma=5/3$ case of the Bondi solution, no sonic radius appears, this time however, because the flow is always characterised by a constant Mach number. This number equals 1 for the case of the maximum accretion rate, diverges towards the cold empty state, and becomes subsonic towards the hydrostatic equilibrium limit. Deviations from sphericity are then explored through an analytic perturbative analysis. The perturbed solution yields a rich phenomenology through density and radial velocity fields in terms of Legendre polynomials, which we begin to explore for simple angular velocity boundary conditions having zeros on the plane and pole. Infall/outflow solutions appear for the sub-sonic parameter region, closely resembling the outputs of recent numerical experiments. The strong density gradients in these cases result in significant pressure gradients which accelerate the polar outflows to many times the local escape velocity, well within the validity range of the perturbative analysis. Our results could complement our understanding of the origin of outflows in a variety of astrophysical settings surrounding infall situations, through purely hydrodynamical physics.
X. Hernandez and L. Nasser
Tue, 19 Apr 22
14/52
Comments: 7 pages, 4 figures