Panel a: series of equilibria of the Brownian population with total mass M_b embedded in a Plummer host cluster with total mass, M_⋆, for three different individual mass ratios. The x-axis is the dimensionless density at the center. The presence of a maximum at each curve designates an instability. No equilibrium exists above the maximum at each case, while the dotted curves correspond to equilibria that cannot be supported by inhomogeneous Brownian pressure alone. Panel b: three curves of panel a merge to a single one when scaled properly with the individual mass ratios. The y-axis variable is the Spitzer parameter S. In Brownian inhomogeneous diffusion, equilibria exist above the Spitzer instability threshold S_Spitzer = 0.16. The instability sets in at S = 0.25, p̃_b(0)(m_⋆/m_b)^3/2 = 140 in the case of a Plummer host cluster.