Self-regulation of high-redshift black hole accretion via jets: challenges for SMBH formation

The early growth of black holes (BHs) in atomic-cooling halos is likely influenced by feedback on the surrounding gas. While the effects of radiative feedback are well-documented, mechanical feedback, particularly from AGN jets, has been comparatively less explored. Building on our previous work that examined the growth of a 100 ${M_\odot}$ BH in a constant density environment regulated by AGN jets, we expand the initial BH mass range from 1 to $10^4$ ${M_\odot}$ and adopt a more realistic density profile for atomic-cooling halos. We reaffirm the validity of our analytic models for jet cocoon propagation and feedback regulation. We identify several critical radii-namely, the terminal radius of jet cocoon propagation, the isotropization radius of the jet cocoon, and the core radius of the atomic-cooling halo-that are crucial in determining BH growth given specific gas properties and jet feedback parameters. In a significant portion of the parameter space, our findings show that jet feedback substantially disrupts the halo's core during the initial feedback episode, preventing BH growth beyond $10^4$ ${M_\odot}$. Conversely, conditions characterized by low jet velocities and high gas densities enable sustained BH growth over extended periods. We provide a prediction for the black hole mass growth as a function of time and feedback parameters. We found that, to form a supermassive BH ($>10^6 {M_\odot}$) within 1 Gyr entirely by accreting gas from an atomic-cooling halo, the jet energy feedback efficiency must be $\lesssim 10^{-4} \dot{M}_{BH} c^2$ even if the seed BH mass is $10^4 {M_\odot}$.