Role of primordial black holes in the direct collapse scenario of
  supermassive black hole formation at high redshifts
  In this paper, we explore the possibility of accreting primordial black holes
as the source of heating for the collapsing gas in the context of the direct
collapse black hole scenario for the formation of super-massive black holes
(SMBHs) at high redshifts, $z\sim 6-7$. One of the essential requirements for
the direct collapse model to work is to maintain the temperature of the in
falling gas at $\approx 10^4$ K. We show that even under the existing abundance
limits, the primordial black holes of masses $\gtrsim 10^{-2} \ {\rm M}_\odot$,
can heat the collapsing gas to an extent that the ${\rm H}_2$ formation is
inhibited. The collapsing gas can maintain its temperature at $10^4$ K till the
gas reaches a critical density $n_{crit} \approx 10^3$ cm$^{-3}$, at which the
roto-vibrational states of ${\rm H}_2$ approaches local thermodynamic
equilibrium and ${\rm H}_2$ cooling becomes inefficient. In the absence of
${\rm H}_2$ cooling the temperature of the collapsing gas stays at $\approx
10^4$ K even as it collapses further. We discuss scenarios of subsequent
angular momentum removal and the route to find collapse through either a
supermassive star or a supermassive disk.
