Accessing Intermediate-Mass Black Holes in 728 Globular Star Clusters in
  NGC\,4472
  Intermediate-mass black holes (IMBHs) by definition have masses of $M_{\rm
IMBH} \sim 10^{2-5}~M_\odot$, a range with few observational constraints.
Finding IMBHs in globular star clusters (GCs) would validate a formation
channel for massive black-hole seeds in the early universe. Here, we simulate a
60-hour observation with the next-generation Very Large Array (ngVLA) of 728 GC
candidates in the Virgo Cluster galaxy NGC\,4472. Interpreting the radio
detection thresholds as signatures of accretion onto IMBHs, we benchmark IMBH
mass thresholds in three scenarios and find the following: (1) Radio analogs of
ESO\,243-49 HLX-1, a strong IMBH candidate with $M_{\rm IMBH}^{\rm HLX} \sim
10^{4-5}~M_\odot$ in a star cluster, are easy to access in all 728 GC
candidates. (2) For the 30 GC candidates with extant X-ray detections, the
empirical fundamental-plane relation involving black hole mass plus X-ray and
radio luminosities suggests access to $M_{\rm IMBH}^{\rm FP} \sim
10^{1.7-3.6}~M_\odot$, with an uncertainty of 0.44 dex. (3) A fiducial Bondi
accretion model was applied to all 728 GC candidates and to radio stacks of GC
candidates. This model suggests access to IMBH masses, with a statistical
uncertainty of 0.39 dex, of $M_{\rm IMBH}^{\rm B} \sim 10^{4.9-5.1}~M_\odot$
for individual GC candidates and $M_{\rm IMBH}^{\rm B,stack} \sim
10^{4.5}~M_\odot$ for radio stacks of about 100-200 GC candidates. The fiducial
Bondi model offers initial guidance, but is subject to additional systematic
uncertainties and should be superseded by hydrodynamical simulations of gas
flows in GCs.
