The Cosmological Dependence of Cluster Density Profiles

We use N-body simulations to study the shape of mean cluster density and velocity profiles formed via gravitational instability. The dependence of the final structure on both cosmology and initial density field is examined, using a grid of cosmologies and scale-free initial power spectra P\propto k^n. For each model, we stack clusters to define an average density profile in the non-linear regime. The profiles are well fit by a power law over 99% of the cluster volume, with a clear trend toward steeper slopes with both increasing n and decreasing Omega_o. For models with a Omega_o = 0.2, the profile slopes are consistently higher than those for Omega-1.0. Cluster density profiles are thus potentially useful cosmological diagnostics. We find no evidence for a constant density core in any of the models, although the density profiles do tend to flatten at small radii. Much of the flattening is due to the force softening required by the simulations, and an attempt is made to recover the unsoftened profiles assuming angular momentum invariance. The recovered profiles in the Omega=1 cosmologies are consistent with a pure power law up to the highest density contrasts (10^6) accessible with our resolution. The low density models show significant deviations from a power law above density contrasts \sim 10^5. We interpret this curvature as reflecting the non scale-invariant nature of the background cosmology in these models.Comment: uuencoded, 22 pages + 13 figs. Astrophysical Journal, in pres

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 Black Hole in the Compact, High-dispersion Galaxy NGC 1271

Located in the Perseus cluster, NGC 1271 is an early-type galaxy with a small effective radius of 2.2 kpc and a large stellar velocity dispersion of 276 km/s for its K-band luminosity of 8.9x10^{10} L_sun. We present a mass measurement for the black hole in this compact, high-dispersion galaxy using observations from the integral field spectrograph NIFS on the Gemini North telescope assisted by laser guide star adaptive optics, large-scale integral field unit observations with PPAK at the Calar Alto Observatory, and Hubble Space Telescope WFC3 imaging observations. We are able to map out the stellar kinematics on small spatial scales, within the black hole sphere of influence, and on large scales that extend out to four times the galaxy's effective radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion. Through the use of orbit-based stellar dynamical models, we determine that the black hole has a mass of (3.0^{+1.0}_{-1.1}) x 10^9 M_sun and the H-band stellar mass-to-light ratio is 1.40^{+0.13}_{-0.11} M_sun/L_sun (1-sigma uncertainties). NGC 1271 occupies the sparsely-populated upper end of the black hole mass distribution, but is very different from the Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are expected to host the most massive black holes. Interestingly, the black hole mass is an order of magnitude larger than expectations based on the galaxy's bulge luminosity, but is consistent with the mass predicted using the galaxy's bulge stellar velocity dispersion. More compact, high-dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses, as there could be systematic differences in the black hole scaling relations between these types of galaxies and the BCGs/giant ellipticals, thereby implying different pathways for black hole and galaxy growth.Comment: accepted for publication in Ap

A \u3cem\u3eChandra\u3c/em\u3e Survey of Supermassive Black Holes with Dynamical Mass Measurements

We present Chandra observations of 12 galaxies that contain supermassive black holes (SMBHs) with dynamical mass measurements. Each galaxy was observed for 30 ks and resulted in a total of 68 point-source detections in the target galaxies including SMBH sources, ultraluminous X-ray sources (ULXs), and extragalactic X-ray binaries. Based on our fits of the X-ray spectra, we report fluxes, luminosities, Eddington ratios, and slope of the power-law spectrum. Normalized to the Eddington luminosity, the 2-10 keV band X-ray luminosities of the SMBH sources range from 10-8 to 10-6, and the power-law slopes are centered at ~2 with a slight trend toward steeper (softer) slopes at smaller Eddington fractions, implying a change in the physical processes responsible for their emission at low accretion rates. We find 20 ULX candidates, of which 6 are likely (\u3e90% chance) to be true ULXs. The most promising ULX candidate has an isotropic luminosity in the 0.3-10 keV band of 1.0+0.6 - 0.3 × 1040 erg s-1

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

A \u3cem\u3eChandra\u3c/em\u3e Survey of Supermassive Black Holes with Dynamical Mass Measurements

We present Chandra observations of 12 galaxies that contain supermassive black holes (SMBHs) with dynamical mass measurements. Each galaxy was observed for 30 ks and resulted in a total of 68 point-source detections in the target galaxies including SMBH sources, ultraluminous X-ray sources (ULXs), and extragalactic X-ray binaries. Based on our fits of the X-ray spectra, we report fluxes, luminosities, Eddington ratios, and slope of the power-law spectrum. Normalized to the Eddington luminosity, the 2-10 keV band X-ray luminosities of the SMBH sources range from 10-8 to 10-6, and the power-law slopes are centered at ~2 with a slight trend toward steeper (softer) slopes at smaller Eddington fractions, implying a change in the physical processes responsible for their emission at low accretion rates. We find 20 ULX candidates, of which 6 are likely (\u3e90% chance) to be true ULXs. The most promising ULX candidate has an isotropic luminosity in the 0.3-10 keV band of 1.0+0.6 - 0.3 × 1040 erg s-1

Probing Stellar Dynamics in Galactic Nuclei

Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center. Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.Comment: 8 pages, Science white paper for the Astro2010 Decadal Surve