Douglas O. Richstone

The Demography of Massive Dark Objects in Galaxy Centers

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 mass-to-light ratio , and a central massive dark object (MDO) of arbitrary mass M•. They provide acceptable fits to 32 of the galaxies for some value of M• and ; the four galaxies that cannot be fitted have kinematically decoupled cores. The mass-to-light ratios inferred for the 32 well-fitted galaxies are consistent with the fundamental-plane correlation ∝ L0.2, where L is galaxy luminosity. In all but six galaxies the models require at the 95% confidence level an MDO of mass M• ~ 0.006Mbulge ≡ 0.006L. Five of the six galaxies consistent with M• = 0 are also consistent with this correlation. The other (NGC 7332) has a much stronger upper limit on M•. 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 (M•/Mbulge) of mean -2.28 and standard deviation ~0.51. There is also marginal evidence that M• is distributed differently for core and power law galaxies, with core galaxies having a somewhat steeper dependence on Mbulge.

A Relationship between nuclear black hole mass and galaxy velocity dispersion

We describe a correlation between the mass Mbh of a galaxys central black hole and the luminosity-weighted line-of-sight velocity dispersion σe 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 Mbh = 1.2(±0.2) × 108 M☉(σe/200 km s-1)3.75 (±0.3) over almost 3 orders of magnitude in Mbh; the scatter in Mbh at fixed σe is only 0.30 dex, and most of this is due to observational errors. The Mbh-σe 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 galaxys bulge.

THE SLOPE OF THE BLACK HOLE MASS VERSUS VELOCITY DISPERSION CORRELATION

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object MBH and the velocity dispersionof the host galaxy, of the form logðMBH=M� Þ¼ � þ � logð�=� 0Þ; how- ever, published estimates of the slopespan 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 sys- tematic 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 & Merritts extrapolation of central velocity dispersions to re= 8( re is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the mea- surements. A new determination of the slope using 31 galaxies yields � ¼ 4:02 � 0:32, � ¼ 8:13 � 0:06 for � 0 ¼ 200 km s � 1 . The MBH-� relation has an intrinsic dispersion in log MBH 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. Subject headings: black hole physics — galaxies: bulges — galaxies: fundamental parameters — galaxies: nuclei — Galaxy: bulge — Galaxy: kinematics and dynamics

THE M-σ AND M-L RELATIONS IN GALACTIC BULGES, AND DETERMINATIONS OF THEIR INTRINSIC SCATTER

We derive improved versions of the relations between supermassive black hole mass (M BH) and host-galaxy bulge velocity dispersion (σ) and luminosity (L; the M-σ and M-L relations), based on 49 M BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (e0) in both relations. We find log(M BH/M) = α + βlog(σ/200 km s-1) with (α, β, e0) = (8.12 0.08, 4.24 0.41, 0.44 0.06) for all galaxies and (α, β, e0) = (8.23 0.08, 3.96 0.42, 0.31 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-σ relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-σ relation. We estimate the M-L relationship as log(M BH/M) = α + βlog(LV /1011 L V) of (α, β, e0) = (8.95 0.11, 1.11 0.18, 0.38 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black holes sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.

The centers of early-type galaxies with HST. IV. Central parameter relations

We analyze Hubble Space Telescope surface-brightness profiles of 61 elliptical galaxies and spiral bulges (hot galaxies). Luminous hot galaxies have cuspy cores with steep outer power-law profiles that break at r ~ r_b to shallow inner profiles with logslope less than 0.3. Faint hot galaxies show steep, largely featureless power-law profiles at all radii and lack cores. The centers of power-law galaxies are up to 1000 times denser in mass and luminosity than the cores of large galaxies at a limiting radius of 10 pc. At intermediate magnitudes (-22.0 < 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. Central properties correlate 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. The dense power-law centers of disky, rotating galaxies are consistent with their formation in gas-rich mergers. The parallel proposition that cores are simply the by-products of gas-free stellar mergers is less compelling. For example, core galaxies accrete small, dense, gas-free galaxies at a rate sufficient to fill in low-density cores if the satellites survived and sank to the center. An alternative model for core formation involves the orbital decay of massive black holes (BHs): the BH 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 reasonably good agreement with the masses and radii of observed cores and in addition is consistent with the energetics of AGNs and kinematic detections of BHs in nearby galaxies.

Black Hole Mass Estimates from Reverberation Mapping and from Spatially Resolved Kinematics

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 discrepancy 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, the bulge luminosities are the probable source of the disagreement, not problems with either method of mass measurement. 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.

The Masses of Nuclear Black Holes in Luminous Elliptical Galaxies and Implications for the Space Density of the Most Massive Black Holes

Black hole (BH) masses predicted from the M•-σ relationship conflict with predictions from the M•-L relationship for high-luminosity galaxies, such as brightest cluster galaxies (BCGs). The M•-L relationship predicts that some BCGs may harbor BHs with M• approaching 1010 M☉, while the M•-σ relationship always predicts M• 3 × 109 M☉ would be nearly an order of magnitude richer than that inferred from the M•-σ relationship. The volume density of the most luminous QSOs may favor the M•-L relationship.

Axisymmetric Dynamical Models of the Central Regions of Galaxies

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 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. Subject headings: black hole physics — galaxies: general — galaxies: nuclei — galaxies: statistics — stellar dynamics On-line material: color figures

A family of models for spherical stellar systems

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 Kings 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.

Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies

Observational work conducted over the past few decades indicates that all massive galaxies have supermassive black holes at their centres. Although the luminosities and brightness fluctuations of quasars in the early Universe suggest that some were powered by black holes with masses greater than 10 billion solar masses, the remnants of these objects have not been found in the nearby Universe. The giant elliptical galaxy Messier 87 hosts the hitherto most massive known black hole, which has a mass of 6.3 billion solar masses. Here we report that NGC 3842, the brightest galaxy in a cluster at a distance from Earth of 98 megaparsecs, has a central black hole with a mass of 9.7 billion solar masses, and that a black hole of comparable or greater mass is present in NGC 4889, the brightest galaxy in the Coma cluster (at a distance of 103 megaparsecs). These two black holes are significantly more massive than predicted by linearly extrapolating the widely used correlations between black-hole mass and the stellar velocity dispersion or bulge luminosity of the host galaxy. Although these correlations remain useful for predicting black-hole masses in less massive elliptical galaxies, our measurements suggest that different evolutionary processes influence the growth of the largest galaxies and their black holes.