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We describe a one-parameter family of models of stable sperical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts (rho propotional to r(exp -4)) and central power-law density cusps, rho proportional to r(exp 3-eta), 0 less than eta less than or = 3. The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole.

Low resolution spectra have been obtained of eight R is approximately equal to 19 mag galaxies located within 1 arcmin of the low-redshift, high luminosity quasar H1821 + 643. Six of the eight galaxies belong to a cluster that has the same redshift, within the observational errors, as the quasar. Five of the six cluster members have the spectra of early type galaxies; the spectrum of the sixth cluster member contains H-alpha, semiforbidden O III, and possibly O II emission lines. The other two objects are an emission line foreground galaxy and a background galaxy. The cluster has a Galactocentric redshift of 0.299 +/- 0.002 and a radial velocity dispersion of 1050 +/- 320 km/s. The photometric and spectroscopic data suggest that H1821 + 643 is associated with a rich cluster of galaxies.