Three‐Body Dynamics with Gravitational Wave Emission

We present numerical three-body experiments that include the effects ofgravitational radiation reaction by using equations of motion that include the2.5-order post-Newtonian force terms, which are the leading order terms ofenergy loss from gravitational waves. We simulate binary-single interactionsand show that close approach cross sections for three 1 solar mass objects areunchanged from the purely Newtonian dynamics except for close approachessmaller than 1.0e-5 times the initial semimajor axis of the binary. We alsopresent cross sections for mergers resulting from gravitational radiationduring three-body encounters for a range of binary semimajor axes and massratios including those of interest for intermediate-mass black holes (IMBHs).Building on previous work, we simulate sequences of high-mass-ratio three-bodyencounters that include the effects of gravitational radiation. The simulationsshow that the binaries merge with extremely high eccentricity such that whenthe gravitational waves are detectable by LISA, most of the binaries will haveeccentricities e > 0.9 though all will have circularized by the time they aredetectable by LIGO. We also investigate the implications for the formation andgrowth of IMBHs and find that the inclusion of gravitational waves during theencounter results in roughly half as many black holes ejected from the hostcluster for each black hole accreted onto the growing IMBH.Comment: 34 pages, 14 figures, minor corrections to match version accepted by Ap