On spherically symmetrical accretion in fractal media

Abstract

We use fractional integrals to generalize the description of hydrodynamic accretion in fractal media. The fractional continuous medium model allows the generalization of the equations of balance of mass density and momentum density. These make it possible to consider the general case of spherical hydrodynamic accretion onto a gravitating mass embedded in a fractal medium. The general nature of the solution is similar to the "Bondi solution", but the accretion rate may vary substantially and the dependence on central mass may change significantly depending on dimensionality of the fractal medium. The theory shows consistency with the observational data and numerical simulation results for the particular case of accretion onto pre-main-sequence stars.