Making a supermassive star by stellar bombardment
  Approximately two hundred supermassive black holes (SMBHs) have been
discovered within the first $\sim$Gyr after the Big Bang. One pathway for the
formation of SMBHs is through the collapse of supermassive stars (SMSs). A
possible obstacle to this scenario is that the collapsing gas fragments and
forms a cluster of main-sequence stars. Here we raise the possibility that
stellar collisions may be sufficiently frequent and energetic to inhibit the
contraction of the massive protostar, avoiding strong UV radiation driven
outflows, and allowing it to continue growing into an SMS. We investigate this
scenario with semianalytic models incorporating star formation, gas accretion,
dynamical friction from stars and gas, stellar collisions, and gas ejection. We
find that when the collapsing gas fragments at a density of $\lesssim 3\times
10^{10}\,\mathrm{cm^{-3}}$, the central protostar contracts due to infrequent
stellar mergers, and in turn photoevaporates the remaining collapsing gas,
resulting in the formation of a $\lesssim 10^4~{\rm M_\odot}$ object. On the
other hand, when the collapsing gas fragments at higher densities (expected for
a metal-poor cloud with $Z\lesssim10^{-5}\,{\rm Z_\odot}$ with suppressed ${\rm
H_2}$ abundance) the central protostar avoids contraction and keeps growing via
frequent stellar mergers, reaching masses as high as $\sim 10^5-10^6\,{\rm
M_\odot}$. We conclude that frequent stellar mergers represent a possible
pathway to form massive BHs in the early universe.
