LISA Constraints on an Intermediate-Mass Black Hole in the Galactic Center*

Nuclear star clusters in galaxies are among the potential hosts for intermediate-mass black holes (IMBHs). If present in a galactic nucleus, an IMBH will perturb the motion of other members of the nucleus. The absence of observable perturbations in our own Galactic center has resulted in a few constraints on the IMBH mass and position. In this work we show that Laser Interferometer Space Antenna (LISA) can help put complementary constraints if the IMBH forms a binary with a compact remnant (white dwarf, neutron star, or a stellar black hole). The gravitational-wave signal from the binary will exhibit Doppler-shift variations as the binary orbits around the supermassive black hole (SMBH) at the center of the Milky Way. The signal and its Doppler shift will help constrain the mass and position of the IMBH, respectively. We argue that this method is the most effective in a region of the parameter space which remains partially unconstrained: for IMBHs with masses between 10³ and 10⁵ solar masses and located between 0.1 mpc and 2 mpc from the SMBH. We show that in this region, if the binary is detected, its Doppler shift is most likely measurable. We also discuss possible ways for an IMBH to form a binary in the Galactic center, and we argue that the most efficient channel is gravitational-wave captures of stellar black holes and neutron stars.