We present calculations on the formation of massive black holes of 105 M⊙ at z > 6, which can be the seeds of supermassive black holes at z ≳ 6. Under the assumption of compact star cluster formation in merging galaxies, star clusters in haloes of ˜ 108-109 M⊙ can undergo rapid core collapse, leading to the formation of very massive stars (VMSs) of ˜ 1000 M⊙ that collapse directly into black holes with similar masses. Star clusters in haloes of ≳ 109 M⊙ experience Type II supernovae before the formation of VMSs, due to long core-collapse time-scales. We also model the subsequent growth of black holes via accretion of residual stars in clusters. Two-body relaxation refills the loss cones of stellar orbits efficiently at larger radii and resonant relaxation at small radii is the main driver for accretion of stars on to black holes. As a result, more than 90 percent of stars in the initial cluster are swallowed by the central black holes before z = 6. Using dark matter merger trees, we derive black hole mass functions at z = 6-20. The mass function ranges from 103-105 M⊙ at z ≲ 15. Major merging of galaxies of ≳ 4 × 108 M⊙ at z ˜ 20 leads successfully to the formation of ≳ 105 M⊙ black holes by z ≳ 10, which could be the potential seeds of supermassive black holes seen today.
- stars: black holes
- galaxies: formation
- galaxies: high-redshift
- quasars: supermassive black holes
- galaxies: star clusters: general