Early Type Galaxy Core Phase Densities

Early type galaxies have projected central density brightness profile logarithmic slopes, gamma^prime, ranging from about 0 to 1. We show that gamma^prime is strongly correlated, r= 0.83, with the coarse grain phase density of the galaxy core, Q_0 = rho/sigma^3. The gamma^prime-luminosity correlation is much weaker, r= -0.5. Q_0 also serves to separate the distribution of power-law profiles, gamma^prime>0.5 from nearly flat profiles, gamma^prime<0.3, although there are many galaxies of intermediate slope, at intermediate $Q_0$, in a volume limited sample. The transition phase density separating the two profile types is approximately 0.003, which is also where the relation between Q_0 and core mass shows a change in slope, the rotation rate of the central part of the galaxy increases, and the ratio of the black hole to core mass increases. These relations are considered relative to the globular cluster inspiral core buildup and binary black hole core scouring mechanisms for core creation and evolution. Globular cluster inspiral models have quantitative predictions that the data support, but no single model yet completely explains the correlations.