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In this third paper of a series, we study the growth and luminosity of blackholes (BHs) in motion with respect to their surrounding medium. We run a largeset of two-dimensional (2D) axis-symmetric simulations to explore a largeparameter space of initial conditions and formulate an analytical model for theaccretion. Contrary to the case without radiation feedback, the accretion rateincreases 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 speedinside the "cometary-shaped" \hii region around the BH, before decreasing as$\vbh^{-3}$ when the I-front becomes {\it R}-type (rarefied) and the accretionrate approaches the classical Bondi-Hoyle-Lyttleton solution. The increase ofthe 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 thatreduces the downstream gas velocity to transonic values. There is a range ofdensities and velocities where the dense shell is unstable producing periodicaccretion rate peaks which can significantly increase the detectability ofintermediate mass BHs. We find that the mean accretion rate for a moving BH islarger than that of a stationary BH of the same mass if the medium temperatureis $T_\infty<10^4$ K. This result could be important for the growth of seed BHsin the multi-phase medium of the first galaxies and for building and earlyX-ray background that may affect the formation of the first galaxies and thereionization process.

astrophysical journal/the astrophysical journal

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