Seeding high-redshift QSOs by collisional runaway in primordial star clusters

We study how runaway stellar collisions in high-redshift, metal-poor star clusters form very massive stars (VMSs) that can directly collapse to intermediate-mass black holes (IMBHs). We follow the evolution of a pair of neighbouring high-redshift mini-haloes with high-resolution, cosmological hydrodynamical zoom-in simulations using the adaptive mesh refinement code RAMSES combined with the non-equilibrium chemistry package KROME. The first collapsing mini-halo is assumed to enrich the central nuclear star cluster (NSC) of the other to a critical metallicity, sufficient for Population II (Pop. II) star formation at redshift $z\approx27$. Using the spatial configuration of the flattened, asymmetrical gas cloud forming in the core of the metal enriched halo, we set the initial conditions for simulations of an initially non-spherical star cluster with the direct summation code NBODY6 which are compared to about 2000 NBODY6 simulations of spherical star clusters for a wide range of star cluster parameters. The final mass of the VMS that forms depends strongly on the initial mass and initial central density of the NSC. For the initial central densities suggested by our RAMSES simulations, VMSs with mass > 400 M$_{\odot}$ can form in clusters with stellar masses of $\approx10^4$ M$_{\odot}$, and this can increase to well over 1000 M$_{\odot}$ for more massive and denser clusters. The high probability we find for forming a VMS in these mini-haloes at such an early cosmic time makes collisional runaway of Pop. II star clusters a promising channel for producing large numbers of high-redshift IMBHs that may act as the seeds of supermassive black holes.