We construct dynamical models for a sample of 36 nearby galaxies with Hubble Space Telescope (HST ) photometry and ground-based kinematics. The models assume that each galaxy is axisymmetric, with a two-integral distribution function, arbitrary inclination angle, a position-independent stellar massto-light ratio !, and a central massive dark object (MDO) of arbitrary mass They provide accept-M a . able Ðts to 32 of the galaxies for some value of and ! ; the four galaxies that cannot be Ðtted have M a kinematically decoupled cores. The mass-to-light ratios inferred for the 32 well-Ðtted galaxies are consistent with the fundamental-plane correlation ! P L0.2, where L is galaxy luminosity. In all but six galaxies the models require at the 95% conÐdence level an MDO of mass M a D 0.006M bulge 4 0.006!L . Five of the six galaxies consistent with are also consistent with this correlation. The other (NGC M a \ 0 7332) has a much stronger upper limit onWe predict the second-moment proÐles that should be M a . observed at HST resolution for the 32 galaxies that our models describe well.We consider various parameterizations for the probability distribution describing the correlation of the masses of these MDOs with other galaxy properties. One of the best models can be summarized thus : a fraction f^0.97 of early-type galaxies have MDOs, whose masses are well described by a Gaussian distribution in log of mean [2.28 and standard deviation D0.51. There is also marginal (M a /M bulge ) evidence that is distributed di †erently for "" core ÏÏ and "" power law ÏÏ galaxies, with core galaxies M a having a somewhat steeper dependence on M bulge .

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M BH and the velocity dispersion of the host galaxy, of the form logðM BH =M Þ ¼ þ logð = 0 Þ; however, published estimates of the slope span a wide range (3.75-5.3). Merritt & Ferrarese have argued that low slopes (d4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations and several others account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to r e =8 (r e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields ¼ 4:02 AE 0:32, ¼ 8:13 AE 0:06 for 0 ¼ 200 km s À1 . The M BH -relation has an intrinsic dispersion in log M BH that is no larger than 0.25-0.3 dex and may be smaller if observational errors have been underestimated. In an appendix, we present a simple kinematic model for the velocity-dispersion profile of the Galactic bulge.

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We analyze Hubble Space Telescope surface-brightness profiles of 61 elliptical galaxies and spiral bulges (hereafter "hot" galaxies). The profiles are parameterized by break radius r b and break surface brightness I b . These are combined with central velocity dispersions, total luminosities, rotation velocities, and isophote shapes to explore correlations among central and global properties. Luminous hot galaxies (M V < −22) have cuspy cores with steep outer power-law profiles that break at r ≈ r b to shallow inner profiles I ∝ r −γ with γ ≤ 0.3. Break radii and core luminosities for these objects are approximately proportional to effective radii and total luminosities. Scaling relations are presented for several core parameters as a function of total luminosity. Cores follow a fundamental plane that parallels the global fundamental plane for hot galaxies but is 30% thicker. Some of this extra thickness may be due to the effect of massive black holes (BHs) on central velocity dispersions. Faint hot galaxies (M V > −20.5) show steep, largely featureless power-law profiles that lack cores. Measured values of r b and I b for these galaxies are limits only. At a limiting radius of 10 pc, the centers of power-law galaxies are up to 1000 times denser in mass and luminosity than the cores of large galaxies. At intermediate magnitudes (−22 < M V < −20.5), core and power-law galaxies coexist, and there is a range in r b at a given luminosity of at least two orders of magnitude. Here, central properties correlate strongly with global rotation and shape: core galaxies tend to be boxy and slowly rotating, whereas power-law galaxies tend to be disky and rapidly rotating. A search for inner disks was conducted to test a claim in the literature, based on a smaller sample, that power laws originate from edge-on stellar disks. We find only limited evidence for such disks and believe that the difference between core and power-law profiles reflects a real difference in the spatial distribution of the luminous spheroidal component of the galaxy. The dense power-law centers of disky, rotating galaxies are consistent with their formation in gas-rich mergers. The parallel proposition, that cores are the by-products of gas-free stellar mergers, is less compelling for at least two reasons: (1) dissipationless hierarchical clustering does not appear to produce core profiles like those seen; (2) core galaxies accrete small, dense, gas-free galaxies at a rate sufficient to fill in their low-density cores if the satellites survived and sank to the center (whether the satellites survive is still an open question). An alternative model for core formation involves the orbital decay of massive black holes (BHs) that are accreted in mergers: the decaying BHs may heat and eject stars from the center, eroding a power law if any exists and scouring out a core. An average BH mass per spheroid of 0.002 times the stellar mass yields cores in fair agreement with observed cores and is consistent with the energetics of AGNs and the kinematic detection of...

We present axisymmetric, orbit superposition models for 12 galaxies using data taken with the Hubble Space Telescope (HST) and ground-based observatories. In each galaxy, we detect a central black hole (BH) and measure its mass to accuracies ranging from 10% to 70%. We demonstrate that in most cases the BH detection requires both the HST and ground-based data. Using the ground-based data alone does provide an unbiased measure of the BH mass (provided they are fit with fully general models), but at a greatly reduced significance. The most significant correlation with host galaxy properties is the relation between the BH mass and the velocity dispersion of the host galaxy; we find no other equally strong correlation, and no second parameter that improves the quality of the mass-dispersion relation. We are also able to measure the stellar orbital properties from these general models. The most massive galaxies are strongly biased to tangential orbits near the BH, consistent with binary BH models, while lower-mass galaxies have a range of anisotropies, consistent with an adiabatic growth of the BH.Comment: 25 pages, accepted for publication in The Astrophysical Journa