Relativistic Hydrodynamics 2025, 15 - Non-Spherical Accretion
At strong winds with small angular momentum transporting matter toward an accreting compact objects, the accretion is non-spherical. Accreting potential flows originate from an ultrastiff equation of state p = e, and a sound speed at light speed. The general solution is a superposition of Legendre functions
The Bondi-Hoyle-Lyttleton accretion develops for compact objects moving relative to a uniform gas cloud. The flow speed is subsonic everywhere without shock waves forming, due to the speed of sound being equal to light speed. If the flow is expected to be supersonic at least at somewhere, shocks can be produced. When a homogeneous flow of matter moves non-radially toward a compact object, a shock wave may form in the neighbourhood of the accretor. In the case of an ideal-fluid eq. of state, for chosen asymptotic sound speed, the rest-mass density can be set to a constant, so pressure is derived from the relativistic definition of the sound speed. For increasingly stiff fluids (adiabatic index larger than the critical one) a bow shock forms upstream of the accretor. The accretion is a near spherical detached shock. For strong shocks, the accretion rate is no longer guaranteed to be negative everywhere and the spherical accretion radius is replaced by the BHL radius. One possible instability leading to the oscillation of the shock cone across the accretor. Another is the development of quasi-periodic oscillations of sonic nature in the cone.
The flip-flop instability shows up in the BHL flow, as an instability of the shock cone. It grows very slowly, so the simulations of the problem are carried out over long times. Once a system has relaxed to the stationary state, a shock cone can form in the downstream region and induce a quasi-periodic oscillation. The stationary state is a pre-requisite for the development of such QPOs, so this phenomenon is mutually exclusive with a flip-flop instability. The resulting oscillations are numerically found to be global eigenmodes of the system with power spectral densities, essentially independent of the position within the shock cone. When flip-flop instability develops, the power spectrum of the oscillations within the shock cone changes, accompanied with nonlinear couplings.
Introductiton of radiation pressure greatly reduces the density of the fluid in the vicinity of the black hole, suppressing the accretion rates.
Assume a fluid configuration is around a black hole, but stationary and at equilibrium, and thus non-accreting. The properties of such a fluid rotating in a circular motion is best described in polar coordinates, so the choice for the metric falls easily on the Kerr metric with normalization condition for the 4-velocity u. The dimensionless specific angular momentum is defined as the fraction of the Φ and t-coordinate of u. The angular velocity of equatorial circular motion is equal to the Keplerian frequency Ω = Ω(l), with signs denoting rotation and counter-rotation.
