Induced metal-free star formation around a massive black hole seed
  The direct formation of a massive black hole is a potential seeding mechanism
of the earliest observed supermassive black holes. We investigate how the
existence of a massive black hole seed impacts the ionization and thermal state
of its pre-galactic host halo and subsequent star formation. We show that its
X-ray radiation ionizes and heats the medium, enhancing $\rm{H}_2$ formation in
shielded regions, within the nuclear region in the span of a million years. The
enhanced molecular cooling triggers the formation of a $\sim 10^4~{\rm
M}_\odot$ metal-free stellar cluster at a star formation efficiency of $\sim
0.1\%$ in a single event. Star formation occurs near the edges of the H II
region that is partially ionized by X-rays, thus the initial size depends on
the black hole properties and surrounding environment. The simulated metal-free
galaxy has an initial half-light radius of $\sim 10$ pc but expands to $\sim
50$ pc after 10 million years because of the outward velocities of their birth
clouds. Supernova feedback then quenches any further star formation for tens of
millions of years, allowing the massive black hole to dominate the spectrum
once the massive metal-free stars die.
