  We have non-parametrically determined the luminosity density profiles and
their logarithmic slopes for 42 early-type galaxies observed with HST. Assuming
that the isodensity contours are spheroidal, then the luminosity density is
uniquely determined from the surface brightness data through the Abel equation.
For nearly all the galaxies in our sample, the logarithmic slope of the
luminosity density measured at 0.1" (the innermost reliable measurement with
the uncorrected HST) is significantly different from zero; i.e. most elliptical
galaxies have cusps. There are only two galaxies for which an analytic core
cannot be excluded. The distribution of logarithmic slopes at 0.1" appears to
be bimodal, confirming the conclusion of Lauer et al. (1995) that early-type
galaxies can be divided into two types based on their surface-brightness
profiles; i.e., those with cuspy cores and those whose steep power-law profiles
continue essentially unchanged in to the resolution limit. The peaks in the
slope distribution occur at -0.8 and -1.9. More than half of the galaxies have
slopes steeper than -1.0. Taken together with the recent theoretical work of
Merritt & Fridman, these results suggest that many (and maybe most) elliptical
galaxies are either nearly axisymmetric or spherical near the center, or slowly
evolve due to the influence of stochastic orbits.
