2015MNRAS.451.2174T

We perform numerical simulations on the merger of multiple black holes (BHs) in primordial gas at early cosmic epochs. We consider two cases of BH mass: MBH = 30 and 10⁴M_☉. Attention is concentrated on the effect of the dynamical friction by gas in a host object. The simulations incorporate such general relativistic effects as the pericentre shift and gravitational wave emission. As a result, we find that multiple BHs are able to merge into one BH within 100 Myr in a wide range of BH density. The merger mechanism is revealed to be categorized into three types: gas-drag-driven merger (type A), interplay-driven merger (type B), and three-body-driven merger (type C). We find the relation between the merger mechanism and the ratio of the gas mass within the initial BH orbit (Mgas) to the total BH mass (∑MBH). Type A merger occurs if Mgas ≳ 10⁵∑MBH, type B if Mgas ≲ 10⁵∑MBH, and type C if Mgas ≪ 10⁵∑MBH. Supposing the gas and BH density based on the recent numerical simulations on first stars, all the BH remnants from first stars are likely to merge into one BH in ∼ 10⁷yr through the type B or C mechanism. Also, we find that multiple massive BHs (MBH = 10⁴M_☉) distributed over several parsec can merge into one BH through the type B mechanism, if the gas density is higher than 5x10⁶/cm3. The present results imply that the BH merger may contribute significantly to the formation of supermassive BHs at high-redshift epochs.