Self-consistent Dynamical Model Research Articles

A Self-Consistent Dynamical Model for the COBE Observed Galactic Bar and Its Application to Microlensing

AbstractA self-consistent stellar dynamical model for the Galactic bar is constructed from about 500 numerically computed orbits with an extension of the Schwarzschild technique. The model fits the COBE found asymmetric boxy light distribution and the observed stellar kinematics of the bulge. The model potential is also consistent with the non-circular motions of the HI and CO velocity maps of the inner Galaxy. We also use the stellar bar model to construct an N-body model to study stability and a microlensing map towards the bulge, which can account for the observed optical depth and the event duration by the MACHO and OGLE collaborations. The technique used here can be applied to interpret light and velocity data of external bulges/bars and galactic nuclei.

Microlensing by the galactic bar

We compute the predicted optical depth and duration distribution of microlensing events towards Baade's window in a model composed of a Galactic disk and a bar. The bar model is a self-consistent dynamical model built out of individual orbits that has been populated to be consistent with the COBE maps of the Galaxy and kinematic observations of the Bulge. We find most of the lenses are at 6.25 kpc in BW. The microlensing optical depth of a 2E10 Msun bar plus a truncated disk is (2.2+-0.3)E-6, consistent with the very large optical depth (3.2+-1.2)E-6 found by Udalski et al. (1994). This prediction doubles that of axisymmetric models by Kiraga and Paczynski (1994) since the bar is elongated along the line-of-sight. The large Einstein radius and small transverse velocity dispersion also predict a longer event duration in the bar model than the KP model. The event rate and duration distribution also depend on the lower mass cutoff of the lens mass function. With a 0.1Msun cutoff, 5-7 events of typical 20 days duration are expected for the OGLE experiment according to our model, while Udalski et al. observed 9 events with durations from 8-62 days. On the other hand, if most of the lenses are brown dwarfs, our model predicts too many short duration events; a KS test finds only 7% probability for the model with 0.01Msun cutoff to be consistent with current data.

Velocity profiles of galaxies with claimed black holes -- I. Observations of M31, M32, NGC 3115 and NGC 4594

The presence of a massive black hole has been invoked to match the observed rotation velocities and velocity dispersions at the centres of M31, M32, NGC 3115 and NGC 4594, Here we determine stellar line-of-sight velocity profiles of these galaxies, from high spatial resolution, high S/N spectra centred on the G-band, the Mg b triplet and the Ca II IR triplet. For all spectra we determine rotation velocities, V, velocity dispersions, |$\sigma$|⁠, and deviations of the velocity profiles from a Gaussian shape, as quantified by the Gauss-Hermite moments |$h_3, \ldots, h_6$|⁠. Significant deviations of the velocity profiles from a Gaussian are present in all objects. The strongest deviations are asymmetries quantified by |$h_3$| and are found primarily along the major axis. The amplitude of |$h_3$| is typically |$|h_3| \lesssim 0.15$| and is correlated with |$V/\sigma$|⁠. Its sign always indicates an excess of stars at low rotation velocities, and results in the mean stellar streaming velocity being lower than the mean of the best-fitting Gaussian, the quantity conventionally used to characterize rotation. The difference is |$\sim 10$| per cent for M31, M32 and NGC 3115, and |$\sim 20$| per cent for NGC 4594. It is thus important that models take the observed velocity profile shapes into account. We demonstrate that the observed deviations from Gaussian velocity profiles are for the most part not the result of projection and seeing convolution. We calculate the velocity profiles predicted by Tonry's model for M32, taking seeing and projection into account, but assuming the local (unprojected) velocity distributions to be Gaussian. The predicted velocity profiles are nearly Gaussian, in conflict with our data. Self-consistent dynamical models must thus be constructed to fit the observed velocity profiles. Such models should constrain the central structure quite strongly, and will hence provide improved constraints on the mass and presence of a supermassive central object.

On the velocity fields of elliptical galaxies

A family of self-consistent maximum entropy dynamical models is presented for the triaxial 'perfect ellipsoids'. These models are projected in different viewing geometries to explore the possible morphologies of the 2D radial-velocity fields of elliptical galaxies. It is found that, typically, about half the time an 'ordinary' velocity field is seen with a mixture of major- and minor-axis rotation. For other lines of sight, the velocity fields are more complicated, showing multiple peaks, steep gradients, strongly twisted contours, or kinematically distinct or counter-rotating cores. The origin of each of these velocity field morphologies is explained in terms of competing contributions from the major families of tube orbits.

Modelling rich clusters of galaxies

We develop a self-consistent dynamical model for spherically-symmetric clusters of galaxies. The total mass profile and velocity dispersion profiles of galaxies are derived by taking both, galaxies and intracluster gas, in hydrostatic equilibrium, and by assuming the latter to follow a polytropic distributionT∼ρλ−1. We use the strongest and better established correlations among observed properties of clusters to fix the values of the resulting free parameters, and so, to reduce the general freedom of the model.

On the orbit structure of the logarithmic potential

view Abstract Citations (112) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Orbit Structure of the Logarithmic Potential Miralda-Escude, Jordi ; Schwarzschild, M. Abstract The consequences of replacing centrophilic box orbits with centrophobic boxlets in the scale-free logarithmic potential are examined. Particular attention is given to the possibility that exact triaxial self-consistent dynamical models do not exist for density figures corresponding to the logarithmic potential. It is suggested that the central cusp of the logarithmic potential destroys the box orbits at high energy and replaces them with boxlets which are too wide to reproduce the triaxial density figure of the model in a self-consistent manner. Publication: The Astrophysical Journal Pub Date: April 1989 DOI: 10.1086/167333 Bibcode: 1989ApJ...339..752M Keywords: Computational Astrophysics; Orbital Mechanics; Stellar Motions; Branching (Mathematics); Density Distribution; Hubble Diagram; Logarithms; Orbital Resonances (Celestial Mechanics); Astrophysics; GALAXIES: INTERNAL MOTIONS; STARS: STELLAR DYNAMICS full text sources ADS |

A combined optical/X-ray study of the Galaxy cluster Abell 2256

view Abstract Citations (83) References (37) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Combined Optical/X-Ray Study of the Galaxy Cluster Abell 2256 Fabricant, Daniel G. ; Kent, Stephen M. ; Kurtz, Michael J. Abstract The dynamics of Abell 2256 (z = 0.06) are investigated by combining X-ray observations of the intracluster gas with optical observations of the galaxy distribution and kinematics. We present magnitudes and positions for 172 galaxies and new redshifts for 75. Abell 2256 is similar to the Coma Cluster in its X-ray luminosity, mass, and galaxy density. Both the X-ray surface brightness and the galaxy surface density distributions exhibit an elliptical morphology. The radial galaxy distribution is steeper than the density profile of the X-ray-emitting gas, yet the galaxy velocity dispersion is higher than the equivalent value for the gas. Under the simplest assumptions that the galaxy velocity distribution is isotropic and the gas is isothermal, the galaxies and gas cannot be in hydrostatic equilibrium in a common gravitational potential. Self-consistent dynamical models can be constructed that are in agreement with the available X-ray and optical data; these models have the common features that the mass-to-light ratio increases with radius and that the galaxy orbits are anisotropic with a radial bias. We consider, in addition, the possibility that the high apparent line-of-sight galaxy velocity dispersion may be the result of substructure in the cluster, contamination by interloper galaxies, or an extremely flattened geometry. If any of the latter three situations pertained, there would be no need to invoke radially increasing mass-to-light ratios or anisotropic galaxy orbits. Publication: The Astrophysical Journal Pub Date: January 1989 DOI: 10.1086/166995 Bibcode: 1989ApJ...336...77F Keywords: Galactic Clusters; Intergalactic Media; Red Shift; X Ray Sources; Line Of Sight; Mass To Light Ratios; Morphology; Spatial Distribution; Astrophysics; GALAXIES: CLUSTERING; GALAXIES: INTERGALACTIC MEDIUM; GALAXIES: REDSHIFTS; X-RAYS: SOURCES full text sources ADS | data products NED (175) SIMBAD (137)

Gas Dynamics and Formation of the Broad Line Region of QSOS

Observational and theoretical constraints on self-consistent gas dynamical models of the line emitting regions of QSOs and AGNs are reviewed. General equations governing the global flows are analysed and models for the formation and acceleration of the line emitting “clouds” are discussed.

A general method for constructing spherical galaxy models

view Abstract Citations (146) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A general method for constructing spherical galaxy models Richstone, D. O. ; Tremaine, S. Abstract The self-consistent dynamical models of spherically symmetric galaxies presently constructed by means of Schwarzschild's (1979) linear programming method have mass-to-light ratios that are independent of radius, and surface brightness profiles obeying de Vaucouleurs (1948) or King (1972) laws. Although some of these models have dispersion profiles which one would not expect to see in a real galaxy, it appears impossible to determine, in the absence of very restrictive ad hoc assumptions about the dispersion profile, the mass-to-light ratio on the basis of a dispersion measurement at a single radius. Accurate determination of the mass-to-light ratio value requires a measurement of the rms dispersion in a centered aperture that contains a large fraction of the total galaxy luminosity, or a series of dispersion measurements at well separated radii spread out across the galaxy. Publication: The Astrophysical Journal Pub Date: November 1984 DOI: 10.1086/162572 Bibcode: 1984ApJ...286...27R Keywords: Astronomical Models; Galactic Rotation; Galactic Structure; Dynamic Models; Mass To Light Ratios; Schwarzschild Metric; Spheres; Velocity Distribution; Astrophysics full text sources ADS |

Techniques for detecting giant cells using spatially resolved solar velocity data

view Abstract Citations (11) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Techniques for detecting giant cells using spatially resolved solar velocity data Brown, T. M. ; Gilman, P. A. Abstract Whether giant cells exist in the convection zone of the sun, and what their properties might be, are matters of great importance for the understanding of the dynamics of the solar interior. So far, such cells have escaped detection, probably because of the small amplitude of their associated velocity fields and the large amplitudes of shorter-lived flows. Techniques for improving the detectability of giant cells are presented. These methods are based on the spatial extent and symmetry properties of giant cells as seen in self-consistent dynamical models of the solar convection zone. Simulations suggest that these techniques allow detection of giant cells with photospheric rms velocities of 2 m/s (0.4 m/s per longitudinal wavenumber), given observations spanning about one year. Publication: The Astrophysical Journal Pub Date: November 1984 DOI: 10.1086/162656 Bibcode: 1984ApJ...286..804B Keywords: Convective Flow; Solar Atmosphere; Solar Granulation; Solar Velocity; Power Spectra; Solar Activity; Solar Interior; Solar Physics full text sources ADS |

The dynamics of rich clusters of galaxies. I - The Coma cluster

The structure and dynamics of the Coma cluster are analyzed using self-consistent equilibrium dynamical models. Observational material for Coma is culled from a variety of sources. Projected surface, density, and velocity-dispersion profiles are derived extending out to a radius of 3/sup 0/ from the cluster center, which are essentially free from field contamination. Segregation of galaxies by luminosity and morphology are discussed and a quantitative estimate of the latter is made. The method of constructing self-consistent dynamical models is discussed. Four different forms of the distribution function are analyzed allowing for different possible dependences of f on energy and angular momentum. Properties of typical models that might resemble actual clusters are presented, and the importance of having velocity-dispersion information is empha sized. The effect of a central massive object such as a cD galaxy on the core structure is illustrated. A comparison of these models with Coma reveals that only models with a distribution function in which the ratio of tangential to radial velocity dispersions is everywhere constant give acceptable fits. In particular, it is possible to rule out models that have isotropic motions in the core and predominantly radial motions in the halo. For H/sub 0/ = 50, the more » best-fitting models give a total projected mass inside 3/sup 0/ of 2.9 x 10/sup 15/ M/sub sun/ , a core radius of 340--400 kpc (8.5'--10'), an upper limit to any central massive object of approx.10/sup 13/ M/sub sun/ , and a mass-to-blue-light ratio of M/L = 181. From cosmological considerations the cluster ''edge'' is determined to lie at rapprox.5/sup 0/--6/sup 0/. The possible distribution of ''dark matter'' in Coma is discussed and it is argued that this distribution cannot be significantly different from that of the galaxies. The dynamics of morphological segregation are examined quantitatively, and are explained at least qualitatively. « less

Dynamical Models of Elliptical Galaxies

Self-consistent dynamical models of elliptical galaxies have been constructed using a modification of the Prendergast-Tomer algorithm. They reproduce many of the observed properties of elliptical galaxies.