Analytic solutions for spherical gravitational gas accretion on to a solid body

The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic self-similar regimes, where the shock wave propagates outwards according to two similarity laws, initially accelerating, then decelerating (and eventually vanishing). Lastly, we study the final static state. Our purpose is to attain a global picture of the process.