Quasi-spherical hydrodynamic adiabatic accretion in a Keplerian
  potential
  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.
