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 The fiducial Bondi model offers initial guidance, but is subject to additional systematic uncertainties and should be superseded by hydrodynamical simulations of gas flows in GCs.