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Abstract:

We fit axisymmetric three-integral dynamical models to NGC 3379 using the line-of-sight velocity distribution obtained from Hubble Space Telescope FOS spectra of the galaxy center and ground-based long-slit spectroscopy along four position angles, with the light distribution constrained by WFPC2 and ground-based images. We have fitted models with inclinations from 29° (intrinsic galaxy type E5) to 90° (intrinsic E1) and black hole masses from 0 to 109 M⊙. The best-fit black hole masses range from 6 × 107 to 2 × 108 M⊙, depending on inclination. The preferred inclination is 90° (edge-on); however, the constraints on allowed inclination are not very strong, owing to our assumption of constant M/LV. The velocity ellipsoid of the best model is not consistent with either isotropy or a two-integral distribution function. Along the major axis, the velocity ellipsoid becomes tangential at the innermost bin, radial in the midrange radii, and tangential again at the outermost bins. The rotation rises quickly at small radii owing to the presence of the black hole. For the acceptable models, the radial-to-tangential [(σ2θ + σ2φ)/2] dispersion in the midrange radii ranges over 1.1 < σr/σt < 1.7, with the smaller black holes requiring larger radial anisotropy. Compared with these three-integral models, two-integral isotropic models overestimate the black hole mass since they cannot provide adequate radial motion. However, the models presented in this paper still contain restrictive assumptions - namely, assumptions of constant M/LV and spheroidal symmetry - requiring yet more models to study black hole properties in complete generality.

Abstract:

In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. Previous analyses of this data set used the Jeans equation to model the projected velocity dispersion profile. However, the results of such an analysis always yield a strong degeneracy between the mass density profile and the velocity dispersion anisotropy profile. Here we analyze the full (R, v) data set of galaxy positions and velocities in an attempt to break this degeneracy. We build an "ensemble cluster" from the individual clusters under the assumption that they form a homologous sequence; if clusters are not homologous then our results are probably still valid in an average sense. To interpret the data we study a one-parameter family of spherical models with different constant velocity dispersion anisotropy, chosen to all provide the same acceptable fit to the projected velocity dispersion profile. The best-fit model is sought using a variety of statistics, including the likelihood of the data set and the shape and Gauss-Hermite moments of the grand-total velocity histogram. The confidence regions and goodness of fit for the best-fit model are determined using Monte Carlo simulations. Although the results of our analysis depend slightly on which statistic is used to judge the models, all statistics agree that the best-fit model is close to isotropic. For none of the statistics does the 1 σ confidence region extend below σr/σt = 0.74, or above σr/σt, = 1.05. This result derives primarily from the fact that the observed grand-total velocity histogram is close to Gaussian, which is not expected to be the case for a strongly anisotropic model. The best-fitting models have a mass-to-number density ratio that is approximately independent of radius over the range constrained by the data. They also have a mass density profile that is consistent with the dark matter halo profile advocated by Navarro, Frenk, & White in terms of both the profile shape and the characteristic scale length. This adds important new weight to the evidence that clusters do indeed follow this proposed universal mass density profile. We present a detailed discussion of a number of possible uncertainties in our analysis, including our treatment of interlopers and brightest cluster galaxies, our use of a restricted one-parameter family of distribution functions, our use of spherical models for what is in reality an ensemble of nonspherical clusters, and our assumption that clusters form a homologous set. These issues all constitute important approximations in our analysis. However, none of the tests that we have done indicates that these approximations influence our results at a significant level.

Abstract:

I apply constant-anisotropy spherical dynamical models to a sample of 18 round ellipticals to look for evidence of dark halos. All 18 lie along a Tully-Fisher relation parallel to that for spirals, but fainter at given upsilon(c) by about 1 mag. By constructing more general, flattened models, I show there is a degeneracy between anisotropy and flattening, and discuss its implications.