The birth of intermediate-mass black holes in primordial galaxies

The discovery of quasars at $z \gtrsim$ 7 poses serious challenges because it is not known how 10$^9$ \Ms\ black holes formed by this epoch. The leading candidates for the seeds of these quasars are 10$^5$ \Ms\ direct-collapse black holes forming in atomically cooled haloes at $z \sim$ 15 - 20. However, the Lyman-Werner (LW) UV backgrounds required to form such objects are extreme, $\gtrsim$ 10$^4$ $\rm J_{21}$, and may have been rare in the early universe. Here, we model the formation of Population III stars in moderate LW backgrounds of 100 and 500 $\rm J_{21}$ that were much more common at early times. We find that these backgrounds allow haloes to grow to a few 10$^6$ - 10$^7$ \Ms\ and virial temperatures of nearly 10$^4$ K before collapsing but do not completely sterilize them of H$_2$. At the onset of collapse, Ly$\alpha$ cooling dominates in the outer regions of the halo but H$_2$ cooling regulates the collapse of the core, at rates that are 10 - 50 times those in minihaloes because of higher virial temperatures. Supercharged H$_2$ cooling leads to the formation of 1800 - 2800 \Ms\ primordial stars, with radiative feedback from the star halting accretion and setting its upper limit in mass. Such stars may lead to a population of less-massive, lower luminosity quasars that could be discovered by the {\em James Webb Space Telescope}, {\em Euclid} and the {\em Roman Space Telescope} in the coming decade.