#### Spherical accretion onto black hole

The interstellar matter is influenced by the presence of compact stars due to their strong gravitational field. Therefore some of the matter falls down onto the compact star. In case of neutron star, the matter hits its solid surface, for black hole, the matter crosses the horizon and plunges inside the black hole. This process is called accretion.

Generally, the accreting matter interact with itself and the surroundings also through electromagnetic interaction, so the accretion is very complicated process influenced by many factors. The exact form of equation of state of the matter (gas) and the physical principle responsible for the angular momentum transport play crucial role for describing this violent environment correctly. This is demanding both from the theoretical point of view, because complex physics needs to be taken into account, and from the numerical standpoint.

The simplest situation is spherically symmetric accretion of inviscid gas which is at rest at infinity. This issue was addressed analytically by Bondi in 1952 and since then is called the Bondi accretion. Later also pseudo-Newtonian potentials (e.g. Paczynski-Wiita potential) were used to mimic the general relativistic effects caused by the presence of the compact star near the horizon. This simple situation is one of the benchmarks for the hydro-dynamical codes used for the simulations of the acreating gas behaviour.

Below on the left, the 2D slice of density profile is given. On the right the hydro-dynamical simulation (crosses are data points) is compared to the analytical solution (solid lines) along the equatorial plane. The horizontal axis is the radial distance to the compact star in geometrical units — Schwarzschild radius r_S=2M, where M is the mass of the compact star. The position of the sonic point (radius, where the velocity of the gas equals the local sound speed) is indicated by the vertical pink line together with the velocity and density at the sonic point and the line y=1 (horizontal lines). The Mach number U (dark orange crosses) is given by the ratio of the velocity of the gas to the local sound speed. The numeric solution is stationary and in very good agreement with the analytical solution.