  When embedded in dense cluster cores, intermediate mass black holes (IMBHs)
acquire close stellar or stellar-remnant companions. These companions are not
only gravitationally bound, they tend to hierarchically isolate from other
cluster stars through series of multibody encounters. In this paper, we study
the demographics of IMBH companions in compact star clusters through direct
$N$-body simulation. We study clusters initially composed of $10^5$ or $2\times
10^5$ stars with IMBHs of 75 and 150 solar masses, and follow their evolution
for 6-10 Gyr. A tight innermost binary pair of IMBH and stellar object rapidly
forms. The IMBH has a companion with orbital semi-major axis at least three
times tighter than the second-most bound object over 90% of the time. These
companionships have typical periods of order years and are subject to cycles of
exchange and destruction. The most frequently observed, long-lived pairings
persist for $\sim 10^7$ yr. The demographics of IMBH companions in clusters are
diverse; they include both main sequence, giant stars, and stellar remnants.
Companion objects may reveal the presence of an IMBH in a cluster in one of
several ways. Most-bound companion stars routinely suffer grazing tidal
interactions with the IMBH, offering a dynamical mechanism to produce repeated
flaring episodes like those seen in the IMBH candidate HLX-1. Stellar winds of
companion stars provide a minimum quiescent accretion rate for IMBHs, with
implications for radio searches for IMBH accretion in globular clusters.
Finally, gravitational wave inspirals of compact objects are found to occur
with promising frequency.
