We present a unifying empirical description of the structural and kinematic properties of all spheroids embedded in dark matter halos .
We find that the stellar spheroidal components of galaxy clusters , which we call cluster spheroids ( CSphs ) and which are typically one hundred times the size of normal elliptical galaxies , lie on a “ fundamental plane ” as tight as that defined by ellipticals ( rms in effective radius of \sim 0.07 ) , but that has a different slope .
The slope , as measured by the coefficient of the \log \sigma term , declines significantly and systematically between the fundamental planes of ellipticals , brightest cluster galaxies ( BCGs ) , and CSphs .
We attribute this decline primarily to a continuous change in M _ { e } / L _ { e } , the mass-to-light ratio within the effective radius r _ { e } , with spheroid scale .
The magnitude of the slope change requires that it arises principally from differences in the relative distributions of luminous and dark matter , rather than from stellar population differences such as in age and metallicity .
By expressing the M _ { e } / L _ { e } term as a function of \sigma in the simple derivation of the fundamental plane and requiring the behavior of that term to mimic the observed nonlinear relationship between \log M _ { e } / L _ { e } and \log \sigma , we simultaneously fit a 2-D manifold to the measured properties of dwarf ellipticals , ellipticals , BCGs , and CSphs .
The combined data have an rms scatter in \log r _ { e } of 0.114 ( 0.099 for the combination of Es , BCGs , and CSphs ) , which is modestly larger than each fundamental plane has alone , but which includes the scatter introduced by merging different studies done in different filters by different investigators .
This “ fundamental manifold ” fits the structural and kinematic properties of spheroids that span a factor of 100 in \sigma and 1000 in r _ { e } .
While our mathematical form is neither unique nor derived from physical principles , the tightness of the fit leaves little room for improvement by other unification schemes over the range of observed spheroids .