Merger of Black Holes in the Galactic Center

We present the results of three body simulations focused on understanding the fates of intermediate mass black holes (IBH) that drift within the central 0.5 pc of the Galaxy. In particular, we modeled the interactions between pairs of $4000 {\rm M}_{\odot}$ black holes as they orbit a central blac k hole of mass $4 \times 10^6 {\rm M}_{\odot}$. The simulations performed assume a Schwarzschild geometry and account for Chandrasekhar dynamical friction as well as acceleration resulting from energy lost due to gravitational radiation. We found the branching ratio for one of the orbiting IBHs to merge with the CBH was 0.95 and is independent of the inner IBH's initial eccentricity as well as the rate of sinking. This, coupled with an infall rate of $\sim 10^7 $ yrs for an IBH to drift into the Galactic center, results in an IBH-CBH merger every $\lesssim 11$ Myrs. Lastly we found that the IBH-IBH-CBH triple body system ``resets'' itself, in the sense that a system with an inner I BH with an initially circular orbit generally left behind an IBH with a large eccentricity, whereas a system in which the inner IBH had a high eccentricity ($e_0 \sim 0.9$) usually left a remnant with low eccentricity. Branching ratios for different outcomes are also similar in the two cases.