Self-regulation of black hole accretion via jets in early protogalaxies

The early growth of black holes (BHs) in high-redshift galaxies is likely feedback regulated. While radiative feedback has been extensively studied, the role of mechanical feedback has received less scrutiny to date. Here, we use high-resolution parsec-scale hydrodynamical simulations to study jet propagation and its effect on 100 M_⊙ BH accretion in the dense, low-metallicity gas expected in early protogalaxies. As the jet propagates, it shocks the surrounding gas forming a jet cocoon. The cocoon consists of a rapidly cooling cold phase at the interface with the background gas and an overpressured subsonic phase of reverse shock-heated gas filling the interior. We vary the background gas density and temperature, BH feedback efficiency, and the jet model. We found that the width of the jet cocoon roughly follows a scaling derived by assuming momentum conservation in the jet-propagation direction and energy conservation in the lateral directions. Depending on the assumed gas and jet properties, the cocoon either stays elongated to large radii or isotropizes before reaching the Bondi radius, forming a nearly spherical bubble. Lower jet velocities and higher background gas densities result in self-regulation to higher momentum fluxes and elongated cocoons. In all cases, the outward cocoon momentum flux balances the inward inflowing gas momentum flux near the Bondi radius, which ultimately regulates BH accretion. The time-averaged accretion rate always remains below the Bondi rate, and exceeds the Eddington rate only if the ambient medium is dense and cold, and/or the jet is weak (low velocity and mass loading).