A Theoretical Model for the Mbh−σM_{\rm bh}-\sigma Relation for Supermassive Black Holes in Galaxies

We construct a model for the formation of black holes within galactic bulges. The initial state is a slowly rotating isothermal sphere, characterized by effective transport speed \aeff and rotation rate $\Omega$. The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation between black hole masses and galactic velocity dispersions, \mbh \approx 10^8 M_\odot (\sigma/200 \kms)^4, where \sigma = \sqrt{2} \aeff. This model also predicts the ratio \mrat of black hole mass to host mass: \mrat $\approx$ 0.004 (\sigma/200 \kms).Comment: 9 pages, 2 figures, submitted to Astrophysical Journal Letter

The M(BH)-Sigma Relation for Supermassive Black Holes

We investigate the differences in the M(BH)-sigma relation derived recently by Ferrarese & Merritt (2000) and Gebhardt et al. (2000). The shallower slope found by the latter authors (3.75 vs. 4.8) is due partly to the use of a regression algorithm that ignores measurement errors, and partly to the value of the velocity dispersion adopted for a single galaxy, the Milky Way. A steeper relation is shown to provide a better fit to black hole masses derived from reverberation mapping studies. Combining the stellar dynamical, gas dynamical, and reverberation mapping mass estimates, we derive a best-fit relation M(BH) = 1.30 (+/- 0.36) X 10^8 (sigma_c/200)^{4.72(+/- 0.36)}, where M(BH) is in solar masses, and sigma in km/s.Comment: The Astrophysical Journal, in pres

Formation of Supermassive Black Holes in Galactic Bulges: A Rotating Collapse Model Consistent with the \mbh-\sigma Relation

Motivated by the observed correlation between black hole masses \mbh and the velocity dispersion $\sigma$ of host galaxies, we develop a theoretical model of black hole formation in galactic bulges (this paper generalizes an earlier ApJ Letter). The model assumes an initial state specified by a a uniform rotation rate $\Omega$ and a density distribution of the form \rho = \aeff^2 / 2 \pi G r^2 (so that \aeff is an effective transport speed). The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole (for Schwarzschild geometry). This model reproduces the observed correlation between the estimated black hole masses and the velocity dispersions of galactic bulges, i.e., \mbh \approx 10^8 M_\odot (\sigma/200 {\rm km s^{-1}})^4, where \sigma = \sqrt{2} \aeff. To obtain this normalization, the rotation rate $\Omega \approx 2 \times 10^{15}$ rad/s. The model also defines a bulge mass scale $M_B$. If we identify the scale $M_B$ with the bulge mass, the model determines the ratio \mrat of black hole mass to the host mass: \mrat $\approx$ 0.0024 $(\sigma/200 {\rm km s^{-1}})$, again in reasonable agreement with observed values. In this scenario, supermassive black holes form quickly (in $\sim10^5$ yr) and are born rapidly rotating (with $a/M \sim 0.9$). This paper also shows how these results depend on the assumed initial conditions; the most important quantity is the initial distribution of specific angular momentum in the pre-collapse state.Comment: 31 pages, 4 figures, accepted to Ap

Nuclear Cusps and Cores in Early-type Galaxies As Relics of Binary Black Hole Mergers

We present an analysis of the central cusp slopes and core parameters of early-type galaxies using a large database of surface brightness profiles obtained from Hubble Space Telescope observations. We examine the relation between the central cusp slopes, core parameters, and black hole masses in early-type galaxies, in light of two models that attempt to explain the formation of cores and density cusps via the dynamical influence of black holes. Contrary to the expectations from adiabatic-growth models, we find that the cusp slopes do not steepen with increasing black hole mass fraction. Moreover, a comparison of kinematic black hole mass measurements with the masses predicted by the adiabatic models shows that they overpredict the masses by a factor of approximately 3. Simulations involving binary black hole mergers predict that both the size of the core and the central mass deficit correlate with the final black hole mass. These relations are qualitatively supported by the present data.Comment: To appear in ApJ. 8 page

Evidence of a Supermassive Black Hole in the Galaxy NGC 1023 from the Nuclear Stellar Dynamics

We analyze the nuclear stellar dynamics of the SB0 galaxy NGC 1023, utilizing observational data both from the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and from the ground. The stellar kinematics measured from these long-slit spectra show rapid rotation (V = 70 km/s at a distance of 0.1 arcsec = 4.9 pc from the nucleus) and increasing velocity dispersion toward the nucleus (where sigma = 295 +/- 30 km/s). We model the observed stellar kinematics assuming an axisymmetric mass distribution with both two and three integrals of motion. Both modeling techniques point to the presence of a central dark compact mass (which presumably is a supermassive black hole) with confidence > 99%. The isotropic two-integral models yield a best-fitting black hole mass of (6.0 +/- 1.4) x 10^7 M_sun and mass-to-light ratio (M/L_V) of 5.38 +/- 0.08, and the goodness-of-fit (chi^2) is insensitive to reasonable values for the galaxy's inclination. The three-integral models, which non-parametrically fit the observed line-of-sight velocity distribution as a function of position in the galaxy, suggest a black hole mass of (3.9 +/- 0.4) x 10^7 M_sun and M/L_V of 5.56 +/- 0.02 (internal errors), and the edge-on models are vastly superior fits over models at other inclinations. The internal dynamics in NGC 1023 as suggested by our best-fit three-integral model shows that the velocity distribution function at the nucleus is tangentially anisotropic, suggesting the presence of a nuclear stellar disk. The nuclear line of sight velocity distribution has enhanced wings at velocities >= 600 km/s from systemic, suggesting that perhaps we have detected a group of stars very close to the central dark mass.Comment: 21 pages, 12 figures, accepted in the Astrophysical Journa

Central Mass Concentration and Bar Dissolution in Nearby Spiral Galaxies

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an estimate of the central mass concentration, we obtain dynamical mass estimates from SONG CO 1-0 rotation curve data. We find an inverse correlation between bar ellipticity and central mass concentration, consistent with simulations of bar dissolution.Comment: 10 pages, 2 figures and 2 tables, accepted for publication in the Astrophysical Journa

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

The Evolution of Cuspy Triaxial Galaxies Harboring Central Black Holes

We use numerical simulations to study the evolution of triaxial elliptical galaxies with central black holes. In contrast to earlier numerical studies which used galaxy models with central density ``cores,'' our galaxies have steep central cusps, like those observed in real ellipticals. As a black hole grows in these cuspy triaxial galaxies, the inner regions become rounder owing to chaos induced in the orbit families which populate the model. At larger radii, however, the models maintain their triaxiality, and orbital analyses show that centrophilic orbits there resist stochasticity over many dynamical times. While black hole induced evolution is strong in the inner regions of these galaxies, and reaches out beyond the nominal ``sphere of influence'' of a black hole, our simulations do not show evidence for a rapid {\it global} transformation of the host. The triaxiality of observed elliptical galaxies is therefore not inconsistent with the presence of supermassive black holes at their centers.Comment: 15 pages, 7 figures (1 color). Accepted for publication in Ap

A Huge Drop in X-ray Luminosity of the Non-Active Galaxy RXJ1242.6-1119A, and First Post-Flare Spectrum - Testing the Tidal Disruption Scenario

It has been suggested that an unavoidable consequence of the existence of supermassive black holes, and the best diagnostic of their presence in non-active galaxies, would be occasional tidal disruption of stars captured by the black holes. These events manifest themselves in form of luminous flares powered by accretion of debris from the disrupted star into the black hole. Candidate events among optically non-active galaxies emerged in the past few years. For the first time, we have looked with high spatial and spectral resolution at one of these most extreme variability events ever recorded among galaxies. Here, we report measuring a factor ~200 drop in luminosity of the X-ray source RXJ 1242-1119 with the X-ray observatories Chandra and XMM-Newton, and perform key tests of the favored outburst scenario, tidal disruption of a star by a supermassive black hole. We show that the detected `low-state' emission has properties such that it must still be related to the flare. The power-law shaped post-flare X-ray spectrum indicates a `hardening' compared to outburst. The inferred black hole mass, the amount of liberated energy, and the duration of the event favor an accretion event of the form expected from the (partial or complete) tidal disruption of a star (abstract abbreviated).Comment: to appear in March 1 issue of ApJ Letters (submitted Nov. 10, accepted in Dec. 2003); background information available at http://www.xray.mpe.mpg.de/~skomossa