Stellar collisions in flattened and rotating Pop. III star clusters
  Fragmentation often occurs in disk-like structures, both in the early
Universe and in the context of present-day star formation. Supermassive black
holes (SMBHs) are astrophysical objects whose origin is not well understood;
they weigh millions of solar masses and reside in the centers of galaxies. An
important formation scenario for SMBHs is based on collisions and mergers of
stars in a massive cluster, in which the most massive star moves to the center
of the cluster due to dynamical friction. This increases the rate of collisions
and mergers since massive stars have larger collisional cross sections. This
can lead to runaway growth of a very massive star which may collapse to become
an intermediate-mass black hole. Here we investigate the dynamical evolution of
Miyamoto-Nagai models that allow us to describe dense stellar clusters,
including flattening and different degrees of rotation. We find that the
collisions in these clusters depend mostly on the number of stars and the
initial stellar radii for a given radial size of the cluster. By comparison,
rotation seems to affect the collision rate by at most $20\%$. For flatness, we
compared spherical models with systems that have a scale height of about $10\%$
of their radial extent, in this case finding a change in the collision rate of
less than $25\%$. Overall, we conclude that the parameters only have a minor
effect on the number of collisions. Our results also suggest that rotation
helps to retain more stars in the system, reducing the number of escapers by a
factor of $2-3$ depending on the model and the specific realization. After two
million years, a typical lifetime of a very massive star, we find that about
$630$ collisions occur in typical models with $N=10^4$, $R=100$ $\rm~R_\odot$
and a half-mass radius of $0.1$ $\rm~pc$, leading to a mass of about
$6.3\times10^3$ $\rm~M_\odot$ for the most massive object.
