Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; the mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentially-anisotropic state induced by the binary. We show that density profiles similar to those observed at the center of the Milky Way and M32 can regenerate themselves in several Gyr following infall of a second black hole; the presence of density cusps at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter than M_V ~ -18.5 that contain supermassive black holes, but the cusps have not been detected outside of the Local Group since their angular sizes are less than 0.1". We show that the presence of a cusp implies a lower limit of \~10^{-4} per year on the rate of stellar tidal disruptions, and discuss the consequences of the cusps for gravitational lensing and the distribution of dark matter on sub-parsec scales.Comment: Accepted for publication in The Astrophysical Journa

Supermassive Black Holes in Active Galactic Nuclei. I. The Consistency of Black Hole Masses in Quiescent and Active Galaxies

We report the first results of a program to measure accurate stellar velocity dispersions in the bulges of the host galaxies of active galactic nuclei (AGNs) for which accurate black hole (BH) masses have been determined via reverberation mapping. We find good agreement between BH masses obtained from reverberation mapping, and from the M(BH) - sigma relation as defined by quiescent galaxies, indicating a common relationship between active and quiescent black holes and their large-scale environments.Comment: Submitted to ApJ

The Black Hole Mass of NGC 4151: Comparison of Reverberation Mapping and Stellar Dynamical Measurements

We present a stellar dynamical estimate of the black hole (BH) mass in the Seyfert 1 galaxy, NGC 4151. We analyze ground-based spectroscopy as well as imaging data from the ground and space, and we construct 3-integral axisymmetric models in order to constrain the BH mass and mass-to-light ratio. The dynamical models depend on the assumed inclination of the kinematic symmetry axis of the stellar bulge. In the case where the bulge is assumed to be viewed edge-on, the kinematical data give only an upper limit to the mass of the BH of ~4e7 M_sun (1 sigma). If the bulge kinematic axis is assumed to have the same inclination as the symmetry axis of the large-scale galaxy disk (i.e., 23 degrees relative to the line of sight), a best-fit dynamical mass between 4-5e7 M_sun is obtained. However, because of the poor quality of the fit when the bulge is assumed to be inclined (as determined by the noisiness of the chi^2 surface and its minimum value), and because we lack spectroscopic data that clearly resolves the BH sphere of influence, we consider our measurements to be tentative estimates of the dynamical BH mass. With this preliminary result, NGC 4151 is now among the small sample of galaxies in which the BH mass has been constrained from two independent techniques, and the mass values we find for both bulge inclinations are in reasonable agreement with the recent estimate from reverberation mapping (4.57[+0.57/-0.47]e7 M_sun) published by Bentz et al.Comment: 20 pages, including 11 low-res figures. Accepted for publication in ApJ. High resolution version available upon reques

Ejection of Supermassive Black Holes from Galaxy Cores

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.Comment: 18 pages, The Astrophysical Journal, in press. Replaced with revised versio

Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation-Mapping Database

We present improved black hole masses for 35 active galactic nuclei (AGNs) based on a complete and consistent reanalysis of broad emission-line reverberation-mapping data. From objects with multiple line measurements, we find that the highest precision measure of the virial product is obtained by using the cross-correlation function centroid (as opposed to the cross-correlation function peak) for the time delay and the line dispersion (as opposed to full width half maximum) for the line width and by measuring the line width in the variable part of the spectrum. Accurate line-width measurement depends critically on avoiding contaminating features, in particular the narrow components of the emission lines. We find that the precision (or random component of the error) of reverberation-based black hole mass measurements is typically around 30%, comparable to the precision attained in measurement of black hole masses in quiescent galaxies by gas or stellar dynamical methods. Based on results presented in a companion paper by Onken et al., we provide a zero-point calibration for the reverberation-based black hole mass scale by using the relationship between black hole mass and host-galaxy bulge velocity dispersion. The scatter around this relationship implies that the typical systematic uncertainties in reverberation-based black hole masses are smaller than a factor of three. We present a preliminary version of a mass-luminosity relationship that is much better defined than any previous attempt. Scatter about the mass-luminosity relationship for these AGNs appears to be real and could be correlated with either Eddington ratio or object inclination.Comment: 61 pages, including 8 Tables and 16 Figures. Accepted for publication in The Astrophysical Journa

Chaos and Elliptical Galaxies

Recent results on chaos in triaxial galaxy models are reviewed. Central mass concentrations like those observed in early-type galaxies -- either stellar cusps, or massive black holes -- render most of the box orbits in a triaxial potential stochastic. Typical Liapunov times are 3-5 crossing times, and ensembles of stochastic orbits undergo mixing on time scales that are roughly an order of magnitude longer. The replacement of the regular orbits by stochastic orbits reduces the freedom to construct self-consistent equilibria, and strong triaxiality can be ruled out for galaxies with sufficiently high central mass concentrations.Comment: uuencoded gziped PostScript, 12 pages including figure

Massive binary black holes in galactic nuclei and their path to coalescence

Massive binary black holes form at the centre of galaxies that experience a merger episode. They are expected to coalesce into a larger black hole, following the emission of gravitational waves. Coalescing massive binary black holes are among the loudest sources of gravitational waves in the Universe, and the detection of these events is at the frontier of contemporary astrophysics. Understanding the black hole binary formation path and dynamics in galaxy mergers is therefore mandatory. A key question poses: during a merger, will the black holes descend over time on closer orbits, form a Keplerian binary and coalesce shortly after? Here we review progress on the fate of black holes in both major and minor mergers of galaxies, either gas-free or gas-rich, in smooth and clumpy circum-nuclear discs after a galactic merger, and in circum-binary discs present on the smallest scales inside the relic nucleus.Comment: Accepted for publication in Space Science Reviews. To appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

The nuclear star cluster of the Milky Way

The nuclear star cluster of the Milky Way is a unique target in the Universe. Contrary to extragalactic nuclear star clusters, using current technology it can be resolved into tens of thousands of individual stars. This allows us to study in detail its spatial and velocity structure as well as the different stellar populations that make up the cluster. Moreover, the Milky Way is one of the very few cases where we have firm evidence for the co-existence of a nuclear star cluster with a central supermassive black hole, Sagittarius A*. The number density of stars in the Galactic center nuclear star cluster can be well described, at distances $\gtrsim1$ pc from Sagittarius A*, by a power-law of the form $\rho(r)\propto r^{-\gamma}$ with an index of $\gamma\approx1.8$. In the central parsec the index of the power-law becomes much flatter and decreases to $\gamma\approx1.2$. We present proper motions for more than 6000 stars within 1 pc in projection from the central black hole. The cluster appears isotropic at projected distances $\gtrsim0.5$ pc from Sagittarius A*. Outside of 0.5 pc and out to 1.0 pc the velocity dispersion appears to stay constant. A robust result of our Jeans modeling of the data is the required presence of $0.5-2.0\times10^{6} M_{\odot}$ of extended (stellar) mass in the central parsec of the Galaxy.Comment: To appear in the proceedings of "The Universe under the Microscope - Astrophysics at High Angular Resolution", Journal of Physics:Conference Series (IOP; http://www.iop.org/EJ/conf) This version has been slightly modified (e.g. double-log plot in right hand panel of Figure 5

The Fueling and Evolution of AGN: Internal and External Triggers

In this chapter, I review the fueling and evolution of active galactic nuclei (AGN) under the influence of internal and external triggers, namely intrinsic properties of host galaxies (morphological or Hubble type, color, presence of bars and other non-axisymmetric features, etc) and external factors such as environment and interactions. The most daunting challenge in fueling AGN is arguably the angular momentum problem as even matter located at a radius of a few hundred pc must lose more than 99.99 % of its specific angular momentum before it is fit for consumption by a BH. I review mass accretion rates, angular momentum requirements, the effectiveness of different fueling mechanisms, and the growth and mass density of black BHs at different epochs. I discuss connections between the nuclear and larger-scale properties of AGN, both locally and at intermediate redshifts, outlining some recent results from the GEMS and GOODS HST surveys.Comment: Invited Review Chapter to appear in LNP Volume on "AGN Physics on All Scales", Chapter 6, in press. 40 pages, 12 figures. Typo in Eq 5 correcte

The Formation of Supermassive Black Holes and the Evolution of Supermassive Stars

The existence of supermassive black holes is supported by a growing body of observations. Supermassive black holes and their formation events are likely candidates for detection by proposed long-wavelength, space-based gravitational wave interferometers like LISA. However, the nature of the progenitors of supermassive black holes is rather uncertain. Supermassive black hole formation scenarios that involve either the stellar dynamical evolution of dense clusters or the hydrodynamical evolution of supermassive stars have been proposed. Each of these formation scenarios is reviewed and the evolution of supermassive stars is then examined in some detail. Supermassive stars that rotate uniformly during their secular cooling phase will spin up to the mass-shedding limit and eventually contract to the point of relativistic collapse. Supermassive stars that rotate differentially as they cool will likely encounter the dynamical bar mode instability prior to the onset of relativistic collapse. A supermassive star that undergoes this bar distortion, prior to or during collapse, may be a strong source of quasiperiodic, long-wavelength gravitational radiation.Comment: 6 pages, 1 figure; submitted to a Special Issue of Classical and Quantum Gravity, Proceedings of the Third LISA Symposiu