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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 (2D) 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 $\vbh$ reaching a maximum value at $\vbh=2c_{\rm s,in}\sim 50$ km/s, where $c_{\rm s,in}$ is the sound speed inside the "cometary-shaped" \hii region around the BH, before decreasing as $\vbh^{-3}$ when the I-front becomes {\it R}-type (rarefied) and the accretion rate approaches the classical Bondi-Hoyle-Lyttleton solution. The increase of the accretion rate with $\vbh$ is produced by the formation of a {\it D}-type (dense) ionization front (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 $T_\infty<10^4$ K. This result could be important for the growth of seed BHs in the multi-phase medium of the first galaxies and for building and early X-ray background that may affect the formation of the first galaxies and the reionization process.