Nuker Team Refereed Publications

1. A Family of Models for Spherical Stellar Systems.
S. Tremaine, D. O. Richstone, Y. Byun, A. Dressler, S. M. Faber, C. Grillmair, J. Kormendy, & T. R. Lauer (1994). AJ, 107, 634.

We describe a one-parameter family of models of stable spherical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts (rho propto r-4 and central power-law density cusps, rho propto r3-eta, 0< eta le 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.
Full Refereed Journal Article

2. The Centers of Early-Type Galaxies with HST. I. An Observational Survey.
T. R. Lauer, E. A. Ajhar, Y. Byun, A. Dressler, S. M. Faber, C. Grillmair, J. Kormendy, D. Richstone, & S. Tremaine (1995). AJ, 110, 2622.

We have obtained V-band images of 45 nearby elliptical galaxies and bulges using the original Planetary Camera of the Hubble Space Telescope. The majority of the sample is at distances of 10 to 20 Mpc. This represents a substantial increase in the number of galaxies that have been studied at a resolution of a few parsecs. At this resolution, many galaxies reveal previously unknown central disks, dust clouds, and nuclear components. We find that galaxies have two types of brightness profiles. The first type consists of galaxies that have cores. These galaxies have brightness profiles that ``break'' from steep outer power-laws to shallow inner cusps. The Core class includes many galaxies that had cores apparently resolved from the ground. The second type consists of galaxies that have profiles that continue into the resolution limit as steep power-laws, showing no evidence of cores of any sort. We thus find that all galaxies studied so far have singular brightness profiles in the sense that I(r)\sim r^-gamma}as r->0.1'' with 0< gamma< 0.3 at the few parsec scale for galaxies with cores, and gamma~1 for Power-law galaxies. No galaxies in our sample have a central region that is constant in surface brightness. This implies that the stellar density in these systems is still increasing steeply at the HST resolution limit. Many galaxies reach stellar mass-densities of ~5X104MSun pc-3 at the resolution limit, appearing similar in form to M32 at radii of a few parsecs. The Core and Power-law profile classes correspond to the Jaffe et al. (1994) Type I and II profiles; however, we disagree with their suggestion that the presence of a central stellar disk is closely related to, or even determines, profile type. Power-law galaxies are seen at all ellipticities, and the majority of them show no evidence for central disks.
Full Refereed Journal Article

3. HST Spectroscopic Confirmation of a 2X109MSun Black Hole in NGC 3115.
J. Kormendy, R. Bender, D. Richstone, E. A. Ajhar, A. Dressler, S. M. Faber, K. Gebhardt, C. Grillmair, T. R. Lauer, & S. Tremaine (1996). ApJ, 459, L57.

The discovery by Kormendy & Richstone of an M• ≃ 109 M&sun; massive dark object (MDO) in NGC 3115 is confirmed with higher resolution spectroscopy from the Canada-France-Hawaii Telescope (CFHT) and the Hubble Space Telescope (HST). Measurements with the CFHT and Subarcsecond Imaging Spectrograph improve the resolution from sigma * = 0."44 to sigma * = 0."244 ( sigma * = Gaussian dispersion radius of the point-spread function). The apparent central velocity dispersion rises from sigma = 295 +/- 9 km s-1 to sigma = 343 +/- 19 km s-1. The Faint Object Spectrograph and COSTAR-corrected HST provide a further improvement in resolution using a 0."21 aperture. Then, the measured sigma = 443 +/- 18 km s-1 is remarkably high, and the wings of the velocity profiles extend beyond 1200 km s-1 from the line centers. Similarly, the apparent rotation curve rises much more rapidly than is observed from the ground. Published dynamical models fit the new observations reasonably well when "observed" at the improved spatial resolution; V and sigma are at the high end of the predicted range near the center. Therefore, M• > 109 M&sun;. The spatial resolution has now improved by a factor of ~5 since the discovery observations, and the case for a central MDO has strengthened correspondingly. With HST and the Second Wide Field and Planetary Camera, NGC 3115 also shows a bright nucleus. This is very prominent and distinct from the bulge when the superposed nuclear disk is subtracted. After bulge subtraction, the nucleus has sigma = 600 +/- 37 km s-1, the largest central dispersion seen in any galaxy. If the nucleus contained only old stars and not an MDO, its escape velocity would be ~352 km s-1, much smaller than the observed velocities of the stars. This is independent proof that an MDO is present. The new observations put more stringent constraints on the radius inside which the dark mass lies and strengthen the case that it is a 2 x 109 M&sun; black hole.
Full Refereed Journal Article

4. The Centers of Early-Type Galaxies with HST. II. Empirical Models and Structural Parameters.
Y. Byun, C. Grillmair, S. M. Faber, E. A. Ajhar, A. Dressler, J. Kormendy, T. R. Lauer, D. Richstone, & S. Tremaine (1996). AJ, 111, 1889.

We present a set of structural parameters for the central parts of 57 early-type galaxies observed with the Planetary Camera of the Hubble Space Telescope. These parameters are based on a new empirical law that successfully characterizes the centers of early type galaxies. This empirical law assumes that the surface brightness profile is a combination of two power laws with different slopes gamma and beta for the inner and outer regions. Conventional structural parameters such as core radius and central surface brightness are replaced by break radius r_b, where the transition between power-law slopes takes place, and surface brightness mu_b at that radius. An additional parameter alpha describes the sharpness of the break. The structural parameters are derived using a chi-squared minimization process applied to the mean surface brightness profiles. The resulting model profiles generally give very good agreement to the observed profiles out to the radius of 10 arcseconds imaged by the Planetary Camera. Exceptions include galaxies which depart from pure power-laws at large radius, those with strong nuclear components, and galaxies partly obscured by dust. The uncertainties in the derived parameters are estimated using Monte-Carlo simulations which test the stability of solutions in the face of photon noise and the effects of the deconvolution process. The covariance of the structural parameters is examined by computing contours of constant chi squared in multi-dimensional parameter space.
Full Refereed Journal Article

5. The Centers of Early-Type Galaxies with HST. III. Non-Parametric Recovery of Stellar Luminosity Distributions.
K. Gebhardt, D. Richstone, E. A. Ajhar, T. R. Lauer, Y. Byun, J. Kormendy, A. Dressler, S. M. Faber, C. Grillmair, & S. Tremaine (1996). AJ, 112, 105.

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.
Full Refereed Journal Article

6. Hubble Space Telescope Observations of the Double Nucleus of NGC 4486B.
T. R. Lauer, S. Tremaine, E. A. Ajhar, R. Bender, A. Dressler, S. M. Faber, K. Gebhardt, C. J. Grillmair, J. Kormendy, & D. Richstone (1996). ApJ, 471, L79.

Hubble Space Telescope WFPC2 images show that the low-luminosity elliptical galaxy companion to M87, NGC 4486B, has a double nucleus that resembles the one discovered in M31. The NGC 4486B nucleus comprises two peaks separated by ~0."15 or 12 pc. Neither peak is coincident with the galaxy photocenter, which falls between them. The nuclear morphology is independent of color; thus, the double structure is not likely to arise from dust absorption. It is also unlikely that the peaks are a binary stellar system (such as an ongoing merger of the nucleus of a less luminous system with the nucleus of NGC 4486B), since the decay timescale is short (<108 yr) and the present environment of NGC 4486B should inhibit mergers. We suggest that the nuclear morphology of NGC 4486B may be explained by the eccentric-disk model of Tremaine, which was originally advanced to account for the central structure of M31. This model requires that NGC 4486B contains a central massive dark object, which is suggested by the spectroscopic observations of Kormendy et al. The eccentric disk might be related to the symmetric disk seen at larger radii.
Full Refereed Journal Article

7. Hubble Space Telescope Spectroscopic Evidence for a 1X109MSun Black Hole in NGC 4594.
J. Kormendy, R. Bender, E. A. Ajhar, A. Dressler, S. M. Faber, K. Gebhardt, C. Grillmair, T. R. Lauer, D. Richstone, & S. Tremaine (1996). ApJ, 473, L91.

The discovery by Kormendy of a M• ~= 109 Msolar massive dark object (MDO) in NGC 4594 is confirmed with higher resolution spectroscopy from the Canada-France-Hawaii Telescope (CFHT) and the Hubble Space Telescope (HST). CFHT measurements with the Subarcsecond Imaging Spectrograph improve the resolution from sigma * = 0."40 to 0."27 Gaussian dispersion radius of the point-spread function (PSF). The apparent central velocity dispersion rises from sigma = 250 +/- 7 km s-1 to sigma = 286 +/- 7 km s-1. As observed with the COSTAR-corrected HST, the Faint Object Spectrograph, and a 0."21 aperture, sigma = 321 +/- 7 km s-1 is still higher, and the central rotation curve is very steep. The highest-M• published dynamical model fits the new observations reasonably well when "observed" at HST resolution. The spatial resolution has now improved by a factor of ~5 since the discovery measurements, and the case for a black hole (BH) has strengthened correspondingly. We confirm that NGC 4594 has a Seyfert spectrum; H alpha is ~5200 km s-1 wide at zero intensity. However, gas velocities are lower than the circular velocities implied by the stars, so they cannot be used to test the BH case in NGC 4594. The gas may be in a ring, or it may be associated with patchy dust. HST images with the Wide Field and Planetary Camera 2 show dust at some aperture positions. NGC 4594 appears to have a bright point nucleus. However, the central absorption-line strengths are low, consistent with dilution by enough nonthermal light to explain the "nucleus." There is no evidence for a distinct nuclear star cluster. NGC 4594 is similar to M87, which also has a nonthermal nuclear source, and not to M31 and NGC 3115, which have quiescent BHs and nuclear star clusters.
Full Refereed Journal Article

8. Spectroscopic Evidence for a Supermassive Black Hole in NGC 4486B.
J. Kormendy, R. Bender, J. Magorrian, S. Tremaine, K. Gebhardt, D. Richstone, A. Dressler, S. M. Faber, R. Green, C. Grillmair, & T. R. Lauer (1997). ApJ, 482, L139.

The stellar kinematics of the dwarf elliptical galaxy NGC 4486B have been measured in seeing sigma_* =0.22 arcsec with the Canada-France-Hawaii Telescope. Lauer et al. 1996, ApJ, 471, L79 have shown that NGC 4486B is similar to M31 in having a double nucleus. We show that it also resembles M31 in its kinematics. The velocity dispersion gradient is very steep: sigma increases from 116 +- 6 km/s at r = 2" - 6" to 281 +- 11 km/s at the center. This is much higher than expected for an elliptical galaxy of absolute magnitude M_B = -16.8: NGC 4486B is far above the scatter in the Faber-Jackson correlation between sigma and bulge luminosity. Therefore the King core mass-to-light ratio, M/L_V = 20, is unusually high compared with normal values for old stellar populations. We construct dynamical models with isotropic velocity dispersions and show that they reproduce black hole (BH) masses derived by more detailed methods. We also fit axisymmetric, three-integral models. Isotropic models imply that NGC 4486B contains a central dark object, probably a BH, of mass M_BH = 6(+3 -2) x 10^8 M_sun. However, anisotropic models fit the data without a BH if the ratio of radial to azimuthal dispersions is ~ 2 at 1". Therefore this is a less strong BH detection than the ones in M31, M32, and NGC 3115. A 6 x 10^8 M_sun BH is 9% of the mass M_bulge in stars; even if M_BH is smaller than the isotropic value, M_BH/M_bulge is likely to be unusually large. Double nuclei are a puzzle because the dynamical friction timescales for self-gravitating star clusters in orbit around each other are short. Since both M31 and NGC 4486B contain central dark objects, our results support models in which the survival of double nuclei is connected with the presence of a BH (e. g., Tremaine 1995, AJ, 110, 628).
Full Refereed Journal Article

9. The Centers of Early-Type Galaxies with HST. IV. Central Parameter Relations.
S. M. Faber, S. Tremaine, E. A. Ajhar, R. Bender, Y. Byun, A. Dressler, K. Gebhardt, C. Grillmair, J. Kormendy, T. R. Lauer, J. Magorrian, & D. Richstone (1997). AJ, 114, 1771.

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 rb and break surface brightness Ib. 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 (MV < -22) have cuspy cores with steep outer power-law profiles that break at r \approx rb to shallow inner profiles I \propto r^-gamma with gamma \le 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 (MV > -20.5) show steep, largely featureless power-law profiles that lack cores. Measured values of rb and Ib 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 < MV < -20.5, core and power-law galaxies coexist, and there is a range in rb at a given luminosity of at least two orders of magnitude. Here, central properties correlate strongly with global rotation andshape: 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 intheir 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 BHs in nearby galaxies. An unresolved issue is why power-law galaxies also do not have cores if this process operates in all hot galaxies.
Full Refereed Journal Article

10. The Demography of Massive Dark Objects in Galaxy Centers.
J. Magorrian, S. Tremaine, D. Richstone, R. Bender, G. Bower, A. Dressler, S. M. Faber, K. Gebhardt, R. Green, C. Grillmair, J. Kormendy, & T. R. Lauer (1998). AJ, 115, 2285.

We construct dynamical models for a sample of 36 nearby galaxies with Hubble Space Telescope 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 mass-to-light ratio Upsilon, and a central massive dark object (MDO) of arbitrary mass MBH. They provide acceptable fits to 32 of the galaxies for some value of MBH and Upsilon; the four galaxies that cannot be fit have kinematically decoupled cores. The mass-to-light ratios inferred for the 32 well-fit galaxies are consistent with the fundamental plane correlation Upsilon propto L0.2, where L is galaxy luminosity. In all but six galaxies the models require at the 95% confidence level an MDO of mass MBH sim 0.006 M bulge equiv 0.006 Upsilon L. Five of the six galaxies consistent with MBH=0 are also consistent with this correlation. The other (NGC 7332) has a much stronger upper limit on MBH. We predict the second-moment profiles that should be 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(MBH/M bulge) of mean -2.28 and standard deviation ~0.51. There is also marginal evidence that MBH is distributed differently for ``core'' and ``power-law'' galaxies, with core galaxies having a somewhat steeper dependence on Mbulge.
Electronic Journal Article

11. Supermassive Black Holes and the Evolution of Galaxies.
D. Richstone, E. A. Ajhar, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, K. Gebhardt, R. Green, L. C. Ho, J. Kormendy, T. R. Lauer, J. Magorrian, & S. Tremaine (1998). Nat, 395, A14.

Black holes, an extreme consequence of the mathematics of General Relativity, have long been suspected of being the prime movers of quasars, which emit more energy than any other objects in the Universe. Recent evidence indicates that supermassive black holes, which are probably quasar remnants, reside at the centers of most galaxies. As our knowledge of the demographics of these relics of a violent earlier Universe improve, we see tantalizing clues that they participated intimately in the formation of galaxies and have strongly influenced their present-day structure. Postscript Version

12. Axisymmetric, 3-Integral Models of Galaxies: A Massive Black Hole in NGC 3379.
K. Gebhardt, D. Richstone, J. Kormendy, T. R. Lauer, E. A. Ajhar, R. Bender, A. Dressler, S. M. Faber, C. Grillmair, J. Magorrian, D. Richstone, & S. Tremaine (2000). AJ, 119, 1157.

We fit axisymmetric 3-integral dynamical models to NGC3379 using the line-of-sight velocity distribution obtained from HST/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 degrees (intrinsic E1) and black hole masses from 0 to 1e9 M_solar. The best-fit black hole masses range from 6e7 to 2e8 M_solar, depending on inclination. 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 mid-range radii, and tangential again at the outermost bins. For the acceptable models, the radial to tangential dispersion in the mid-range radii ranges from 1.1 < sigma_r / sigma_t < 1.7. Compared with these 3-integral models, 2-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/L and spheroidal symmetry-requiring yet more models to study black hole properties in complete generality.
Electronic Journal Article

13. A Relationship Between Nuclear Black Hole Mass and Velocity Dispersion.
K. Gebhardt, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, C. Grillmair, L. C. Ho, J. Kormendy, T. R. Lauer, J. Magorrian, J. Pinkney, D. Richstone, & S. Tremaine (2000). ApJ, 539, L13.

We describe a correlation between the mass M_BH of a galaxy's central black hole and the luminosity-weighted line-of-sight velocity dispersion sigma_e within the half-light radius. The result is based on a sample of 26 galaxies, including 13 galaxies with new determinations of black hole masses from Hubble Space Telescope measurements of stellar kinematics. The best-fit correlation is M_BH = 1.2 (+-0.2) x 10^8 M_sun (sigma_e/200 km/s)^(3.75 (+-0.3))over almost three orders of magnitude in M_BH; the scatter in M_BH at fixed sigma_e is only 0.30 dex and most of this is due to observational errors. The M_BH-sigma_e relation is of interest not only for its strong predictive power but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxy's bulge.
Electronic Journal Article

14. Black Hole Mass Estimated From Reverberation Mapping and From Spatially Resolved Kinematics.
K. Gebhardt, J. Kormendy, L. C. Ho, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, C. Grillmair, T. R. Lauer, J. Magorrian, J. Pinkney, D. Richstone, & S. Tremaine (2000). ApJ, 543, L5.

Black hole (BH) masses that have been measured by reverberation mapping in active galaxies fall significantly below the correlation between bulge luminosity and BH mass determined from spatially resolved kinematics of nearby normal galaxies. This discrepency has created concern that one or both techniques suffer from systematic errors. We show that BH masses from reverberation mapping are consistent with the recently discovered relationship between BH mass and galaxy velocity dispersion. Therefore systematic errors in estimating bulge luminosities, not problems with either kind of mass measurement, are the probable source of the above disagreement. This result underscores the utility of the BH mass -- velocity dispersion relationship. Reverberation mapping can now be applied with increased confidence to galaxies whose active nuclei are too bright or whose distances are too large for BH searches based on spatially resolved kinematics.
Electronic Journal Article

15. The Slope of the Black-Hole Mass Versus Velocity Dispersion Correlation.
S. Tremaine, K. Gebhardt, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, C. Grillmair, L. C. Ho, J. Kormendy, T. R. Lauer, J. Magorrian, J. Pinkney, & D. Richstone (2002). ApJ, 574, 740.

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M and the velocity dispersion sigma of the host galaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, published estimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferrarese have argued that low slopes (<4) 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 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 b=4.02 +/- 0.32, a=8.13 +/- 0.06, for sigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log M that is no larger than 0.3 dex. In an Appendix, we present a simple model for the velocity-dispersion profile of the Galactic bulge. Electronic Journal Article

16. Galaxies with a Central Minimum in Stellar Luminosity Density.
Tod R. Lauer, Karl Gebhardt, Douglas Richstone, Scott Tremaine, Ralf Bender, Gary Bower, Alan Dressler, S. M. Faber, Alexei V. Filippenko, Richard Green, Carl J. Grillmair, Luis C. Ho, John Kormendy, John Magorrian, Jason Pinkney, S. Laine, Marc Postman, & Roeland P. van der Marel (2002). AJ, 124, 1975.

We used Hubble Space Telescope WFPC2 images to identify six early-type galaxies with surface-brightness profiles that decrease inward over a limited range of radii near their centers. The inferred luminosity density profiles of these galaxies have local minima interior to their core break radii. NGC 3706 harbors a high surface brightness ring of starlight with radius ~20 pc. Its central structure may be related to that in the double-nucleus galaxies M31 and NGC 4486B. NGC 4406 and NGC 6876 have nearly flat cores that on close inspection are centrally depressed. Colors for both galaxies imply that this is not due to dust absorption. The surface brightness distributions of both galaxies are consistent with stellar tori that are more diffuse than the sharply defined system in NGC 3706. The remaining three galaxies are the brightest cluster galaxies in A260, A347, and A3574. Color information is not available for these objects, but they strongly resemble NGC 4406 and NGC 6876 in their cores. The thin ring in NGC 3706 may have formed dissipatively. The five other galaxies resemble the endpoints of some simulations of the merging of two gas-free stellar systems, each harboring a massive nuclear black hole. In one version of this scenario, diffuse stellar tori are produced when stars initially bound to one black hole are tidally stripped away by the second black hole. Alternatively, some inward-decreasing surface-brightness profiles may reflect the ejection of stars from a core during the hardening of the binary black hole created during the merger.
Electronic Journal Article

17. Axisymmetric Dynamical Models of the Central Regions of Galaxies.
K. Gebhardt, D. Richstone, S. Tremaine, T. R. Lauer, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, C. Grillmair, L. C. Ho, J. Kormendy, J. Magorrian, & J. Pinkney (2003). ApJ, 583, 92.

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< i>HST and ground-based data. Using the ground-based data alone does provide an unbiased measure of the BH mass (provided that they are fitted 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.
Electronic Journal Article

18. Kinematics of Ten Early-Type Galaxies from HST and Ground-Based Spectroscopy.
J. Pinkney, K. Gebhardt, R. Bender, G. Bower, A. Dressler, S.M. Faber, A. V. Filippenko, R. Green, L. C. Ho, J. Kormendy, T. Lauer, J. Magorrian, D. Richstone, S. Tremaine (2003). ApJ, 596, 903.

We present stellar kinematics for a sample of 10 early-type galaxies observed using the STIS aboard the Hubble Space Telescope, and the Modular Spectrograph on the MDM Observatory 2.4-m telescope. The spectra are used to derive line-of-sight velocity distributions (LOSVDs) of the stars using a Maximum Penalized Likelihood method. We use Gauss-Hermite polynomials to parameterize the LOSVDs and find predominantly negative h4 values (boxy distributions) in the central regions of our galaxies. One galaxy, NGC 4697, has significantly positive central h4 (high tail weight). The majority of galaxies have a central velocity dispersion excess in the STIS kinematics over ground-based velocity dispersions. The galaxies with the strongest rotational support, as quantified with v_MAX/sigma_STIS, have the smallest dispersion excess at STIS resolution. The best-fitting, general, axisymmetric dynamical models (described in a companion paper) require black holes in all cases, with masses ranging from 10^6.5 to 10^9.3 Msun. We replot these updated masses on the BH/sigma relation, and show that the fit to only these 10 galaxies has a slope consistent with the fits to larger samples. The greatest outlier is NGC 2778, a dwarf elliptical with relatively poorly constrained black hole mass. The two best candidates for pseudobulges, NGC 3384 and 7457, do not deviate significantly from the established relation between black hole and sigma. Neither do the three galaxies which show the most evidence of a recent merger, NGC 3608, 4473, and 4697.
Electronic Journal Article

19. The Centers of Early-Type Galaxies with HST. V. New WFPC2 Photometry
Tod R. Lauer, S. M. Faber, Karl Gebhardt, Douglas Richstone, Scott Tremaine, Edward A. Ajhar, M. C. Aller, Ralf Bender, Alan Dressler, Alexei V. Filippenko, Richard Green, Carl J. Grillmair, Luis C. Ho, John Kormendy, John Magorrian, Jason Pinkney, and Christos Siopis (2005). AJ, 129, 2138.

We present observations of 77 early-type galaxies imaged with the PC1 CCD of HST+WFPC2. ``Nuker law'' parametric fits to the surface brightness profiles are used to classify the central structure into ``core'' or ``power-law'' forms. Core galaxies are typically rounder than power-law galaxies. Nearly all power-laws with central ellipticity $\epsilon\geq0.3$ have stellar disks, implying that disks are present in most power-laws with $\epsilon<0.3,$ but are not visible due to unfavorable geometry. A few low-luminosity flattened core galaxies also have disks; these may be transition forms from power-laws to more luminous core galaxies, which lack disks. Several core galaxies have strong isophote twists interior to their break radii, although power-laws have interior twists of similar physical significance when the photometric perturbations implied by the twists are evaluated. Central color gradients are typically consistent with the envelope gradients; core galaxies have somewhat weaker color gradients than power-laws. Nuclei are found in 29% of the cores and 60% of the power-laws. Nuclei are typically bluer than the surrounding galaxy. While some nuclei are associated with AGN, just as many are not; conversely, not all galaxies known to have low-level AGN exhibit detectable nuclei in the broad-band filters. NGC 4073 and 4382, are found to have central minima in their intrinsic starlight distributions; NGC 4382 resembles the double nucleus of M31. In general, the peak brightness location is coincident with the photocenter of the core to a typical physical scale $<1$ pc. Five galaxies, however, have centers significantly displaced from their surrounding cores; these may be unresolved asymmetric double nuclei. Lastly, as noted by previous authors, central dust is visible in about half of the galaxies. The presence and strength of dust correlates with nuclear emission, thus dust may outline gas that is falling into the central black hole. The prevalence of dust and its morphology suggest that dust clouds form, settle to the center, and disappear repeatedly on ~10^8 yr timescales. We discuss the hypothesis that cores are created by the decay of a massive black hole binary formed in a merger. Apart from their brightness profiles, there are no strong differences between cores and power-laws that demand this scenario; however, the rounder shapes of cores, their lack of disks, and their reduced color gradients may be consistent with it.
Electronic Journal Article

20. The Masses of Nuclear Black Holes in Luminous Elliptical Galaxies and Implications for the Space Density of the Most Massive Black Holes
Tod R. Lauer, S. M. Faber, Douglas Richstone, Kaarl Gebhardt, Scott Tremaine, Marc Postman, Alan Dressler, M. C. Aller, Alexei. V. Filippenko, Richard Green, Luis. C. Ho, John. Kormendy, John, Magorrian, & Jason. Pinkney (2007). ApJ, 662, 808.

Black hole masses predicted from the $M_\bullet-\sigma$ relationship conflict with those predicted from the $M_\bullet-L$ relationship for the most luminous galaxies, such as brightest cluster galaxies (BCGs). This is because stellar velocity dispersion, $\sigma,$ increases only weakly with luminosity for BCGs and other giant ellipticals. The $M_\bullet-L$ relationship predicts that the most luminous BCGs may harbor black holes with $M_\bullet$ approaching $10^{10}M_\odot,$ while the $M_\bullet-\sigma$ relationship essentially always predicts $M_\bullet<3\times10^9M_\odot.$ Lacking direct determination of $M_\bullet$ in a sample of the most luminous galaxies, we advance arguments that the $M_\bullet-L$ relationship is a plausible or even preferred description for BCGs and other galaxies of similar luminosity. Under the hypothesis that cores in central stellar density are formed by binary black holes, the inner-core cusp radius, $r_\gamma,$ may be an independent witness of $M_\bullet.$ Using central structural parameters derived from a large sample of early-type galaxies observed by {\it HST}, we argue that $L$ is superior to $\sigma$ as an indicator of $r_\gamma$ in luminous galaxies. Further, the observed $r_\gamma-M_\bullet$ relationship for 11 core galaxies with measured $M_\bullet$ appears to be consistent with the $M_\bullet-L$ relationship for BCGs. BCGs have large cores appropriate for their large luminosities that may be difficult to generate with the more modest black hole masses inferred from the $M_\bullet-\sigma$ relationship. $M_\bullet\sim M$ may be expected to hold for BCGs, if they were formed in dissipationless mergers, which should preserve ratio of black hole to stellar mass, $M.$ This picture appears to be consistent with the slow increase in $\sigma$ with $L$ and the more rapid increase in effective radii, $R_e,$ with $L$ seen in BCGs as compared to less luminous galaxies. If BCGs have large BHs commensurate with their high luminosities, then the local black hole mass function for $M_\bullet>3\times10^9M_\odot$ may be nearly an order of magnitude richer than what would be inferred from the $M_\bullet-\sigma$ relationship. The volume density of the most luminous QSOs at earlier epochs may favor the predictions from the $M_\bullet-L$ relationship.
Electronic Journal Article

21. The Centers of Early-Type Galaxies with HST. VI. Bimodal Central Surface Brightness Profiles.
T. R. Lauer, K. Gebhardt, S. M. Faber, D. Richstone, S. Tremaine, J. Kormendy, M. C. Aller, R. Bender, A. Dressler, A. V. Filippenko, R. Green, & L. C. Ho (2007). ApJ, 664, 226.

We combine several HST investigations on the central structure of early-type galaxies to generate a large sample of surface photometry. The studies selected were those that used the "Nuker law" to characterize the inner light distributions of the galaxies. The sample comprises WFPC1 and WFPC2 V-band observations published earlier by our group, R-band WFPC2 photometry of Rest et al., NICMOS H-band photometry by Ravindranath et al. and Quillen et al., and the brightest cluster galaxy WFPC2 I-band photometry of Laine et al. The distribution of the logarithmic slopes of the central brightness profiles strongly affirms that the central structure of elliptical galaxies with MV < -19 is bimodal, based on both parametric and nonparametric analysis. At the HST resolution limit, most galaxies are either power-law systems, which have steep cusps in surface brightness, or core systems, which have shallow cusps interior to a steeper envelope brightness distribution. A rapid transition between the two forms occurs over the luminosity range -22 < MV < -20, with cores dominating at the highest luminosities and power laws at the lowest. There are a few "intermediate" systems that have both cusp slopes and total luminosities that fall within the core/power-law transition, but they are rare and do not fill in the overall bimodal distribution.
Electronic Journal Article

22. The Black Hole Mass and Extreme Orbital Structure in NGC 1399.
K. Gebhardt, T. R. Lauer, J. Pinkney, R. Bender, D. Richstone, M. Aller, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, L. C. Ho, J. Kormendy, C. Siopis, & S. Tremaine (2007). ApJ, 671, 1321.

The largest galaxies, and in particular central galaxies in clusters, offer unique insight into understanding the mechanism for the growth of nuclear black holes. We present Hubble Space Telescope kinematics for NGC 1399, the central galaxy in Fornax. We find the best-fit model contains a black hole of (5.1±0.7)× 108MSun, (at a distance of 21.1 Mpc), a factor of over 2 below the correlation of black hole mass and velocity dispersion. We also find a dramatic signature for central tangential anisotropy. The velocity profiles on adjacent sides 0.5'' away from the nucleus show strong bimodality, and the central spectrum shows a large drop in the dispersion. Both of these observations point to an orbital distribution that is tangentially biased. The best-fit orbital model suggests a ratio of the tangential to radial internal velocity dispersions of 3. This ratio is the largest seen in any galaxy to date and will provide an important measure for the mode by which the central black hole has grown.
Electronic Journal Article

23. A Stellar Dynamical Measurement of the Black Hole Mass in the Maser Galaxy NGC 4258.
C. Siops, K. Gebhardt, T. R. Lauer, J. Kormendy, J. Pinkney, D. Richstone, S. M. Faber, S. Tremaine, M. C. Aller, R. Bender, G. Bower, A. Dressler, A. V. Filippenko, R. Green, & L. C. Ho, & J. Magorrian (2008). ApJ, submitted.

We determine the mass of the black hole at the center of the spiral galaxy NGC 4258 by constructing axisymmetric dynamical models of the galaxy. These models are constrained by high spatial resolution imaging and long-slit spectroscopy of the nuclear region obtained with the Hubble Space Telescope, complemented by ground-based observations extending to larger radii. Our best mass estimate is M&bull = (3.3±0.2) × 107MSun for a distance of 7.28 Mpc (statistical errors only). This is within 15% of (3.82±0.01)× 107MSun, the mass determined from the kinematics of water masers (rescaled to the same distance) assuming they are in Keplerian rotation in a warped disk. Unfortunately, the construction of accurate dynamical models of NGC 4258 is compromised by an unresolved active nucleus and color gradients, the latter caused by variations in the stellar population and/or obscuring dust. Depending on how these effects are treated, as well as on assumptions about the ellipticity and inclination of the galaxy, we obtain black hole masses ranging from 2.4 × 107MSun to 3.6×107MSun. This spread is mainly due to uncertainties in the stellar mass profile inside the central 2'' (~70 pc). Obscuration of high-velocity stars by circumnuclear dust (possibly associated with the masing disk) could lead to an underestimate of the black hole mass which is hard to correct. These problems are not present in the ~30 other black hole mass determinations from stellar dynamics that have been published by us and other groups; thus, the relatively close agreement between the stellar dynamical mass and the maser mass in NGC 4258 enhances our confidence in the black hole masses determined in other galaxies from stellar dynamics using similar methods and data of comparable quality.
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