Jason Pinkney

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.

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

THE CENTERS OF EARLY-TYPE GALAXIES WITH HUBBLE SPACE TELESCOPE. V. NEW WFPC2 PHOTOMETRY

We present observations of 77 early-type galaxies imaged with the PC1 CCD of the Hubble Space Telescope (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-law galaxies with central ellipticities ? 0.3 have stellar disks, implying that disks are present in power-law galaxies with < 0.3 but are not visible because of unfavorable geometry. A few low-luminosity flattened core galaxies also have disks; these may be transition forms from power-law galaxies to more luminous core galaxies, which lack disks. Several core galaxies have strong isophote twists interior to their break radii, although power-law galaxies 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-law galaxies. Nuclei are found in 29% of the core galaxies and 60% of the power-law galaxies. Nuclei are typically bluer than the surrounding galaxy. While some nuclei are associated with active galactic nuclei (AGNs), just as many are not; conversely, not all galaxies known to have a low-level AGN exhibit detectable nuclei in the broadband 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 of <1 pc. Five galaxies, however, have centers significantly displaced from their surrounding cores; these may be unresolved asymmetric double nuclei. Finally, 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 ~108 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 core galaxies and power-law galaxies that demand this scenario; however, the rounder shapes of core, their lack of disks, and their reduced color gradients may be consistent with it.

The Centers of Early-Type Galaxies with HST. V. New WFPC2 Photometry

We present observations of 77 early-type galaxies imaged with the PC1 CCD of the Hubble Space Telescope (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-law galaxies with central ellipticities ? 0.3 have stellar disks, implying that disks are present in power-law galaxies with < 0.3 but are not visible because of unfavorable geometry. A few low-luminosity flattened core galaxies also have disks; these may be transition forms from power-law galaxies to more luminous core galaxies, which lack disks. Several core galaxies have strong isophote twists interior to their break radii, although power-law galaxies 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-law galaxies. Nuclei are found in 29% of the core galaxies and 60% of the power-law galaxies. Nuclei are typically bluer than the surrounding galaxy. While some nuclei are associated with active galactic nuclei (AGNs), just as many are not; conversely, not all galaxies known to have a low-level AGN exhibit detectable nuclei in the broadband 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 of <1 pc. Five galaxies, however, have centers significantly displaced from their surrounding cores; these may be unresolved asymmetric double nuclei. Finally, 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 ~108 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 core galaxies and power-law galaxies that demand this scenario; however, the rounder shapes of core, their lack of disks, and their reduced color gradients may be consistent with it.

M33: A Galaxy with No Supermassive Black Hole

Galaxies that contain bulges appear to contain central black holes whose masses correlate with the velocity dispersion of the bulge. We show that no corresponding relationship applies in the pure disk galaxy M33. Three-integral dynamical models fit Hubble Space Telescope WFPC2 photometry and Space Telescope Imaging Spectrograph spectroscopy best if the central black hole mass is zero. The upper limit is 1500 M⊙. This is significantly below the mass expected from the velocity dispersion of the nucleus and far below any mass predicted from the disk kinematics. Our results suggest that supermassive black holes are associated only with galaxy bulges and not with their disks.

Kinematics of 10 Early-Type Galaxies from Hubble Space Telescope and Ground-based Spectroscopy*

We present stellar kinematics for a sample of 10 early-type galaxies observed using the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope, and the Modular Spectrograph on the MDM Observatory 2.4-m telescope. These observations are a part of an ongoing program to understand the co-evolution of supermassive black holes and their host galaxies. Our spectral ranges include either the calcium triplet absorption lines at 8498, 8542, and 8662 A, or the Mg b absorption at 5175 A. The lines 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 predominant ly 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 su pport, as quantified with vMAX/σST IS, 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 M⊙. We replot these updated masses on the Mbh - σ relation, and show that the fit to only these 10 galaxies has a slope consi stent with the fits to larger samples. The greatest outlier is NGC 2778, a dwarf elliptical with relatively poor ly constrained black hole mass. The two best candidates for pseudobulges, NGC 3384 and 7457, do not deviate significa ntly from the established relation between Mbh and σ. Neither do the three galaxies which show the most evidence of a recent merger, NGC 3608, 4473, and 4697. Subject headings: galaxies: elliptical and lenticular, cD — galaxies: kinema tics and dynamics