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A number of ongoing surveys are likely to discover star-black hole binariesin our Galaxy in the near future. A fraction of them may be triple systemscomprising an inner binary, instead of a single black hole, which might beprogenitors of binary black holes (BBHs) routinely discovered now from thegravitational wave. We extend our previous proposal to locate inner BBHs fromthe short-term radial-velocity (RV) variation of a tertiary star in coplanartriples, and we consider noncoplanar triples and their long-term RV variationsas well. Specifically, we assume coplanar and noncoplanar triples with an innerBBH of the total mass $20~M_\odot$, whose outer and inner orbital periods are80 days and 10 days, respectively. We perform a series of N-body simulationsand compare the results with analytic approximate solutions based on quadrupoleperturbation theory. For coplanar triples, the pericenter shift of the outerstar can be used to detect the hidden inner BBH. For noncoplanar triples, thetotal RV semi-amplitude of the outer star is modulated periodically on theorder of $100$km/s due to its precession over roughly the Kozai-Lidovoscillation timescale. Such long-term modulations would be detectable within adecade, independent of the short-term RV variations on the order of of $100$m/s at roughly twice the orbital frequency of the inner binary. Thus the RVmonitoring of future star-black hole binary candidates offers a promisingmethod for searching for their inner hidden BBHs in optical bands.

astrophysical journal/the astrophysical journal

Radial-velocity variation of a tertiary star orbiting a binary black  hole in coplanar and non-coplanar triples: short- and long-term anomalous  behavior