Probability distribution of σ_BH for the host environment of GW190521 obtained using the formalism in Section 4 with σ_i = σ_BH (red and blue curves). Gray histograms show observational constraints on σ_BH based on rescaling stellar velocity dispersions via the equipartition theorem (see the main text for details). The relative heights of the GC and NSC distributions are also rescaled for better visualization.