  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.
