The role of stellar relaxation in the formation and evolution of the first massive black holes
Abstract
We present calculations on the formation of massive black holes with 105 Msun at z > 6 that 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 Msun can undergo rapid core-collapse leading to the formation of very massive stars (VMSs) with ~1000 Msun which directly collapse into black holes with similar masses. Star clusters in halos of > 109 Msun 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. 2-body relaxation efficiently re-fills the loss cones of stellar orbits at larger radii and resonant relaxation at small radii is the main driver for accretion of stars onto black holes. As a result, more than ninety 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 to 105 Msun at z <~ 15. Major merging of galaxies of >~ 4*108 Msun at z ~ 20 successfully leads to the formation of >~ 105 Msun BHs by z >~ 10 which can be the potential seeds of supermassive black holes seen today.
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