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We have non-parametrically determined the luminosity density profiles andtheir logarithmic slopes for 42 early-type galaxies observed with HST. Assumingthat the isodensity contours are spheroidal, then the luminosity density isuniquely determined from the surface brightness data through the Abel equation.For nearly all the galaxies in our sample, the logarithmic slope of theluminosity density measured at 0.1" (the innermost reliable measurement withthe uncorrected HST) is significantly different from zero; i.e. most ellipticalgalaxies have cusps. There are only two galaxies for which an analytic corecannot be excluded. The distribution of logarithmic slopes at 0.1" appears tobe bimodal, confirming the conclusion of Lauer et al. (1995) that early-typegalaxies can be divided into two types based on their surface-brightnessprofiles; i.e., those with cuspy cores and those whose steep power-law profilescontinue essentially unchanged in to the resolution limit. The peaks in theslope distribution occur at -0.8 and -1.9. More than half of the galaxies haveslopes steeper than -1.0. Taken together with the recent theoretical work ofMerritt & Fridman, these results suggest that many (and maybe most) ellipticalgalaxies are either nearly axisymmetric or spherical near the center, or slowlyevolve due to the influence of stochastic orbits.Comment: uuencoded compressed tarfile 21 pages with 6 fig, 1 tabl

The Centers of Early-Type Galaxies With HST. III. Non-Parametric Recovery of Stellar Luminosity Distribution