The basic dimensional properties of the centers of elliptical galaxies, suc
h as length scale, luminosity, and velocity dispersion, lie on a fundamenta
l plane similar to that of elliptical galaxies as a whole. The orientation
of this plane, and the distribution of core parameters within it, point to
a strong correlation of core density with either core or total luminosity,
and indicate that low-luminosity ellipticals are much denser than high-lumi
nosity galaxies (Hubble Space Telescope data suggest that this relationship
may be as steep as rho(c) proportional to L-2). In addition, low-luminosit
y ellipticals have a much smaller length scale than their high-luminosity c
ounterparts. Since we think that small galaxies are occasionally accreted b
y big ones, the high density of these galaxies and their likely durability
against the time-varying tidal field of the bigger ones suggests that they
will survive substantially intact in the cores of larger galaxies and would
be easily visible. Their presence would destroy the observed correlation.
Motivated by this apparent inconsistency between an observed fact and a sim
ple physical argument, we have developed an effective simulation method and
applied it to the problem of the accretion of very dense secondary compani
ons by tenuous primaries. We have studied the accretion of objects of varyi
ng luminosity ratios, with sizes and densities drawn from the fundamental p
lane under the assumption that the mass distribution in the central parts o
f the galaxies follows the light. The results indicate that in mergers with
mass ratios greater than 10, chosen with an appropriate central density de
pendence on luminosity, the smaller object is only stripped down to the hig
hest density encountered in the primary during the accretion process. Thus,
the form of the core fundamental plane suggests that the mass distribution
in galaxy centers is different from the light distribution, or that an und
erstanding of secondary survival requires more than the dynamics of visible
stars.