Accretion onto Black Holes from Large Scales Regulated by Radiative Feedback. III. Enhanced Luminosity of Intermediate-mass Black Holes Moving at Supersonic Speeds

In this third paper of a series, we study the growth and luminosity of black holes (BHs) in motion with respect to their surrounding medium. We run a large set of two-dimensional axis-symmetric simulations to explore a large parameter space of initial conditions and formulate an analytical model for the accretion. Contrary to the case without radiation feedback, the accretion rate increases with increasing BH velocity v _bh reaching a maximum value at v _bh = 2c _{s, in} ~ 50 km s^-1, where c _{s, in} is the sound speed inside the "cometary-shaped" H II region around the BH, before decreasing as v_bh^{-3} when the ionization front (I-front) becomes R-type (rarefied) and the accretion rate approaches the classical Bondi-Hoyle-Lyttleton solution. The increase of the accretion rate with v _bh is produced by the formation of a D-type (dense) I-front preceded by a standing bow shock that reduces the downstream gas velocity to transonic values. There is a range of densities and velocities where the dense shell is unstable producing periodic accretion rate peaks which can significantly increase the detectability of intermediate-mass BHs. We find that the mean accretion rate for a moving BH is larger than that of a stationary BH of the same mass if the medium temperature is T _∞ < 10⁴ K. This result could be important for the growth of seed BHs in the multi-phase medium of the first galaxies and for building an early X-ray background that may affect the formation of the first galaxies and the reionization process.