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David Merritt

Publications and source records attributed to David Merritt.

At least 163 records · Page 9Linked to original sources
arXiv2001

Dynamics of the Globular Cluster System Associated with M87 (NGC 4486). II. Analysis

We present a dynamical analysis of the globular cluster system associated with M87 (= NGC 4486), the cD galaxy near the dynamical center of the Virgo cluster. The analysis utilizes a new spectroscopic and photometric database which is described in a companion paper (Hanes et al. 2001). Using a sample of 278 globular clusters with measured radial velocities and metallicities, and new surface density profiles based on wide-field Washington photometry, we study the dynamics of the M87 globular cluster system both globally --- for the entire cluster sample --- and separately --- for the metal-rich and metal-poor globular cluster samples. This constitutes the largest sample of radial velocities for pure Population II tracers yet assembled for any galaxy. We discuss the implications of our findings for models for the formation of giant elliptical galaxies, globular cluster systems, and the Virgo cluster. (ABRIDGED)

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arXiv2001

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.

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arXiv2001

Brownian Motion of a Massive Binary

The dynamical friction and diffusion coefficients are derived for a massive binary that moves against a uniform background of stars. The random impulses exerted on the binary's center of mass by the field stars are greater than those exerted on a point particle due to inelastic scattering. The frictional force acting on the binary is less than that acting on a point particle due to randomization of the trajectories of field stars that pass near the binary. Both effects tend to increase the random motion of a binary compared with that of a point mass. If the maximum effective impact parameter for gravitational encounters is comparable to the radius of gravitational influence of the binary, its Brownian velocity can be increased by a modest factor compared with that of a single particle. This condition is probably fulfilled in the case of binary supermassive black holes in galactic nuclei.

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arXiv2001

Formation of Galactic Nuclei

We investigate a model in which galactic nuclei form via the coalescence of pre-existing stellar systems containing supermassive black holes. Merger simulations are carried out using N-body algorithms that can follow the formation and decay of a black-hole binary and its effect on the surrounding stars down to sub-parsec scales. Our initial stellar systems have steep central density cusps similar to those in low-luminosity elliptical galaxies. Formation of a black-hole binary transfers energy to the stars and lowers the central density; continued decay of the binary creates a ~1/r density cusp similar to those observed in bright elliptical galaxies, with a break radius that extends well beyond the sphere of gravitational influence of the black holes. The decay of the black hole binary is followed over a factor of ~20 in separation after formation of a hard binary, considerably farther than in previous simulations. We see almost no dependence of the binary's decay rate on number of particles in the simulation, contrary to earlier studies in which a lower initial density of stars led to a more rapid depletion of the binary's loss cone. We nevertheless argue that the decay of a black hole binary in a real galaxy would be expected to stall at separations of 0.01-1 pc unless some additional mechanism is able to extract energy from the binary. Our results support a picture in which the observed dependence of nuclear cusp slope on galaxy luminosity is a consequence of galaxy interactions. We also discuss the implications of our results for the survivability of dark-matter cusps.

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arXiv2001

Cusp Disruption in Minor Mergers

We present 0.55 x 10^6 particle simulations of the accretion of high-density dwarf galaxies by low-density giant galaxies, using models that contain both power-law central density cusps and point masses representing supermassive black holes. The cusp of the dwarf galaxy is disrupted during the merger, producing a remnant with a central density that is only slightly higher than that of the giant galaxy initially. Removing the black hole from the giant galaxy allows the dwarf galaxy to remain intact and leads to a remnant with a high central density, contrary to what is observed. Our results support the hypothesis that the persistence of low-density cores in giant galaxies is a consequence of supermassive black holes.

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arXiv2001

Black Hole Demographics from the M(BH)-sigma Relation

We analyze a sample of 32 galaxies for which a dynamical estimate of the mass of the hot stellar component, M_bulge, is available. For each of these galaxies, we calculate the mass of the central black hole, M_BH, using the tight empirical correlation between M_BH and the bulge stellar velocity dispersion. The frequency function N(log M_BH/M_bulge) is reasonably well described as a Gaussian with ~ -2.90 and standard deviation 0.45; the implied mean ratio of black hole to bulge mass is a factor 5 smaller than generally quoted in the literature. We present marginal evidence for a lower, average black-hole mass fraction in more massive galaxies. The total mass density in black holes in the local Universe is estimated to be 5 x 10^5 solar masses per cubic megaparsec, consistent with that inferred from high redshift (z ~ 2) AGNs.

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arXiv2000

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.

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arXiv2000

A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies

The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges, M(BH) ~ sigma^alpha, where alpha =4.8 +/- 0.5$. The relation is much tighter than the relation between M(BH) and bulge luminosity, with a scatter no larger than expected on the basis of measurement error alone. Black hole masses estimated by Magorrian et al. (1998) lie systematically above the M(BH)-sigma relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the M(BH)-sigma relation implies a strong link between black hole formation and the properties of the stellar bulge.

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arXiv1999

Orbital instability and relaxation in stellar systems

The orbits of stars in galaxies are generically chaotic: the chaotic behavior arises in part from the intrinsically grainy nature of a potential that is composed of point masses. Even if the potential is assumed to be smooth, however, orbits in non-axisymmetric galaxies can be chaotic due to the presence of central density cusps or black holes. The chaotic nature of orbits implies that perturbations will grow exponentially and this in turn is expected to result in a diffusion in phase space. We show that the degree of orbital evolution is not well predicted by the growth rate of infinitesimal perturbations, i.e. by the Liapunov exponent. A more useful criterion is whether perturbations continue to grow exponentially until their scale is of order the size of the system. We illustrate these ideas in a potential consisting of N fixed point masses. Liapunov exponents are large for all values of N, but orbits become increasingly regular in their behavior as N increases; the reason is that the exponential divergence saturates at smaller and smaller distances as N is increased. The objects which impede diffusion are the invariant tori. When there are few stable tori, an ensemble of chaotic orbits evolves rapidly toward a nearly stationary state. This mixing process occurs on timescales of a few crossing times in triaxial potentials containing massive central singularities, consistent with the rapid evolution observed in N-body simulations of galaxies with central black holes.

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arXiv1999

Torus Construction

The maximally compact representation of a regular orbit is in terms of its action-angle variables. Computing the map between a trajectory's Cartesian coordinates and its action-angle variables is called torus construction. This article reviews various approaches to torus construction and their application to galactic dynamics.

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arXiv1999

Black Holes and Galaxy Dynamics

The consequences of nuclear black holes for the structure and dynamics of stellar spheroids are reviewed. Slow growth of a black hole in a pre-existing core produces a steep power-law density profile similar to the cusps seen in faint elliptical galaxies. The weaker cusps in bright ellipticals may result from ejection of stars by a coalescing black-hole binary; there is marginal kinematical evidence for such a process having occurred in M87. Stellar orbits in a triaxial nucleus are mostly regular at radii where the gravitational force is dominated by the black hole; however the orbital shapes are not conducive to reinforcing the triaxial figure, hence nuclei are likely to be approximately axisymmetric. In triaxial potentials, a ``zone of chaos'' extends outward to a radius where the enclosed stellar mass is roughly 100 times the mass of the black hole; in this chaotic zone, no regular, box-like orbits exist. At larger radii, the phase space in triaxial potentials is complex, consisting of stochastic orbits as well as regular orbits associated with stable resonances. Figure rotation tends to increase the degree of stochasticity. Both test-particle integrations and N-body simulations suggest that a triaxial galaxy responds globally to the presence of a central mass concentration by evolving toward more axisymmetric shapes; the evolution occurs rapidly when the mass of the central object exceeds roughly 2% of the mass in stars. The lack of significant triaxiality in most early-type galaxies may be a consequence of orbital evolution induced by nuclear black holes.

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arXiv1999

Resonant Orbits in Triaxial Galaxies

Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form lω_1 +mω_2+nω_3=0 between the three fundamental frequencies. Resonant orbits are confined to a membrane; they play roughly the same role, in three dimensions, that closed orbits play in two. Stable resonant orbits avoid the center of the potential; orbits that are thick enough to pass near the center are typically stochastic. Very near the center, where the gravitational potential is dominated by the black hole, resonant orbits continue to exist, including at least one family whose elongation is parallel to the long axes of the triaxial figure.

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arXiv1998

Elliptical Galaxy Dynamics

A review of elliptical galaxy dynamics, with a focus on nonintegrable models. Topics covered include torus construction; modelling axisymmetric galaxies; triaxiality; collisionless relaxation; and collective instabilities.

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arXiv1998

Regular and Chaotic Dynamics of Triaxial Stellar Systems

We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of fundamental importance in structuring phase space are found to be the 3-dimensional resonant tori; even when stable, such tori are not necessarily associated with periodic orbits as in systems with only two degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stochastic as well. The spectrum of diffusion rates for box-like orbits at a given energy is well approximated as a power law over at least six decades. Models with high central concentrations -- steep central cusps or massive black holes -- exhibit the most stochasticity. A black hole with a mass of 0.3% the mass of the galaxy is as effective as the steepest central density cusp at inducing stochastic diffusion. There is a transition to global stochasticity in box-like phase space when the mass of a central black hole exceeds 2% the galaxy mass. We predict a greater average degree of dynamical evolution in faint ellipticals, due to their high central densities and short crossing times. The evolution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about -19 or -20, consistent with the observed change in many elliptical galaxy properties at this luminosity.

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arXiv1998

Galaxies and Black Holes

Supermassive black holes containing ~0.5% of the stellar mass of their host galaxies appear to be ubiquitous components of galactic nuclei. The gravitational force from these central singularities can influence the motion of stars far outside the nucleus in non-axisymmetric, i.e. barred or triaxial, galaxies. Here, recent work concerning the influence of nuclear black holes on the large-scale structure of their host galaxies is reviewed. A number of studies point to a critical ratio of black hole mass to bulge mass, Mh/Mg, at which the black hole induces a transition to axisymmetry in the shape of the surrounding bulge or bar. This critical ratio is close to the maximum value of Mh/Mg observed in real galaxies, suggesting that black hole masses may be limited by a feedback mechanism that cuts off the supply of fuel to the nucleus once the central object grows sufficiently large.

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arXiv1997

Dynamical Evolution of Elliptical Galaxies with Central Singularities

We study the effect of a massive central singularity on the structure of a triaxial galaxy using N-body simulations. Starting from a single initial model, we grow black holes with various final masses Mh and at various rates, ranging from impulsive to adiabatic. In all cases, the galaxy achieves a final shape that is nearly spherical at the center and close to axisymmetric throughout. However, the rate of change of the galaxy's shape depends strongly on the ratio Mh/Mg of black hole mass to galaxy mass. When Mh/Mg < 0.3%, the galaxy evolves in shape on a timescale that exceeds 100 orbital periods, or roughly a galaxy lifetime. When Mh/Mg > 2%, the galaxy becomes axisymmetric in little more than a crossing time. We propose that the rapid evolution toward axisymmetric shapes that occurs when Mh/Mg > 2% provides a negative feedback mechanism which limits the mass of central black holes by cutting off their supply of fuel.

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