The Gas-Density Provenance of Radio Intermediate-Mass Black-Hole Limits in Globular Clusters: An Audit and a Recompute

Radio searches for intermediate-mass black holes (IMBHs) in Galactic globular clusters convert a flux-density limit into a mass limit through an assumed intracluster gas density, and the field-standard value is 0.2 cm⁻³. This paper audits where that value comes from and recomputes the limits with a gas prior for each cluster. The audit traces the 0.2 to four millisecond-pulsar dispersion measures in M15 (Freire et al. 2001), which Strader et al. (2012) adopted as a prior and Tremou et al. (2018) applied to all 50 clusters, with their assumed density n = 0.2 cm⁻³ corresponding to an electron density of half that value. Later users take the number from 47 Tuc (Abbate et al. 2018; Wrobel and Nyland 2020; Paduano et al. 2024). The recomputation uses a measured prior for 47 Tuc, a Zhang et al. (2025) prior for five clusters and a one-sided upper-envelope prior for the remaining 44; the amendment and the original-scope result appear in Section 4.3. In all three headline scenarios no cluster has a recomputed 95th-percentile limit below 10³ M_⊙, against 12 of 50 for the printed 3σ point limits, which are evaluations at the assumed density rather than percentiles; the tighter [T₃/10, T₃] variant leaves M15 alone below the threshold, at 537 M_⊙. A pulsar-timing control on 47 Tuc failed in its pre-registered form, which removes the pipeline route on M15 and leaves the radio route as the operative constraint, with the X-ray route as corroboration.