Fragmentation inside atomic cooling haloes exposed to Lyman-Werner
  radiation
  Supermassive stars born in pristine environments in the early Universe hold
the promise of being the seeds for the supermassive black holes observed as
high redshift quasars shortly after the epoch of reionisation. H$_2$
suppression is thought to be crucial in order to negate normal Population III
star formation and allow high accretion rates to drive the formation of
supermassive stars. Only in the cases where vigorous fragmentation is avoided
will a monolithic collapse be successful giving rise to a single massive
central object. We investigate the number of fragmentation sites formed in
collapsing atomic cooling haloes subject to various levels of background
Lyman-Werner flux. The background Lyman-Werner flux manipulates the chemical
properties of the gas in the collapsing halo by destroying H$_2$. We find that
only when the collapsing gas cloud shifts from the molecular to the atomic
cooling regime is the degree of fragmentation suppressed. In our particular
case we find that this occurs above a critical Lyman-Werner background of J
$\sim 10$ J$_{21}$. The important criterion being the transition to the atomic
cooling regime rather than the actual value of J, which will vary locally. Once
the temperature of the gas exceeds T $\gtrsim$ 10$^4$ K and the gas transitions
to atomic line cooling, then vigorous fragmentation is strongly suppressed.
