Tagawa, H., Umemura, M., Gouda, N., Yano, T., & Yamai, Y.
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: M$_BH$ = 30 and 10$^4$ M$_☉$. 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 (M$_gas$) to the total BH mass (\ensuremath∑M$_BH$). Type A merger occurs if M$_gas$ \ensuremath\gtrsim 10$^5$\ensuremath∑M$_BH$, type B if M$_gas$ \ensuremathłesssim 10$^5$\ensuremath∑M$_BH$, and type C if M$_gas$ \ensuremathłl 10$^5$\ensuremath∑M$_BH$. 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 ̃ 10$^7$ yr through the type B or C mechanism. Also, we find that multiple massive BHs (M$_BH$ = 10$^4$ M$_☉$) distributed over several parsec can merge into one BH through the type B mechanism, if the gas density is higher than 5 × 10$^6$ cm$^-3$. The present results imply that the BH merger may contribute significantly to the formation of supermassive BHs at high-redshift epochs.