Weinberg, Martin

Job Title

Professor, Department of Astronomy

Last Name

Weinberg

First Name

Martin

Discipline

Astrophysics and Astronomy

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Now showing 1 - 10 of 70

ADIABATIC INVARIANTS IN STELLAR DYNAMICS .1. BASIC CONCEPTS
(1994) Weinberg, MD
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slow varying perturbation is exponentially small. Recent mathematical results precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. the mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.
Effect of the Magellanic Clouds on the Milky Way disk and VICE VERSA
(1999) Weinberg, Martin D
We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy PHotometric ATtributes), to provide full posterior probability distributions and reliable confidence intervals for all model parameters. GALPHAT is designed to yield a high speed and accurate likelihood computation, using grid interpolation and Fourier rotation. We benchmark this approach using an ensemble of simulated Sersic model galaxies over a wide range of observational conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the PSF and the image size, and errors in the assumed PSF; and a range of structural parameters: the half-light radius $r_e$ and the Sersic index $n$. We characterise the strength of parameter covariance in Sersic model, which increases with S/N and $n$, and the results strongly motivate the need for the full posterior probability distribution in galaxy morphology analyses and later inferences. The test results for simulated galaxies successfully demonstrate that, with a careful choice of Markov chain Monte Carlo algorithms and fast model image generation, GALPHAT is a powerful analysis tool for reliably inferring morphological parameters from a large ensemble of galaxies over a wide range of different observational conditions. (abridged)
High-accuracy minimum relaxation N-body simulations using orthogonal series force computation
(1996) Weinberg, MD
This report describes a modification of orthogonal function Poisson solver for n body simulations that minimize relaxation caused by small particle number fluctuations. With the standard algorithm, the noise leading to relaxation can e reduced by making the expansion basis similar to the particle distribution and by carefully choosing the maximum order in the expansion. The proposed algorithm accomplishes both task simultaneously while the simulation is running. This procedure is asymptotically equivalent to expanding in an orthogonal series which is matched to the distribution to start and truncating a low order. Because the modified algorithm adapts to a time evolving distribution, it has advantage over a fixed basis. The required changes to the standard algorithm are minor and do not affect its overall structure or scalability. Tests show that the overhead in CPU time is small in practical applications. The decrease in relaxation rate is demonstrated for both axisymmetric and non axisymmetric system and the robustness of the algorithm is demonstrated by following the evolution of unstable generalized polytropes. Finally the empirically based moment analysis which leads to the uncorrelated basis is an ideal tool for investigating structure and modes in n body simulations and an examples is provided.
The Dynamics of the Galatic bar
(1996) Weinberg, Martin D
Evolution of the galactic globular cluster system
(1997) Murali, C; Weinberg, MD
We study the dynamical evolution of disk and halo globular clusters in the Milky Way using a series of Fokker-Planck calculations combined with parametric statistical models. Our sample of 113 clusters with velocity data is predicted to descend from an initial population of 250 clusters, implying more than a factor of two decrease in population size due to evolution. Approximately 200 of these clusters are in a halo component and 50 in a disk component. The estimated initial halo population follows a coreless R−3.38 density profile in good agreement with current estimates for the distribution of halo field stars. The observed core in the present-day distribution of halo clusters results from the rapid evaporation of clusters in the inner regions of the Galaxy. The initial halo population is also predicted to have a radially biased orbit distribution in rough agreement with the observed kinematics of halo field stars. The isotropy of the present-day halo cluster distribution results from the evaporation of clusters on elongated orbits. Similarly, the initial disk component has a nearly isotropic initial distribution that becomes more tangentially biased with time. However, the inferred initial characteristics of the disk component do not match the kinematics of the rapidly rotating thin or thick disk stellar populations. These characteristics may be more indicative of the flattened halo component discussed by Zinn (1993). Detailed examination of cluster evolution confirms the importance of disk heating. Clusters on low-inclination orbits experience the strongest disk heating because of optimal matches in resonant frequencies. Disk heating on high-inclination orbits is weaker but still dominates over spheroidal heating. Evaporation times depend weakly on initial concentration, density and height of oscillation above the disk.
ADIABATIC INVARIANTS IN STELLAR DYNAMICS .2. GRAVITATIONAL SHOCKING
(1994) Weinberg, MD
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of the disk shocking of star clusters.
A Bayesian approach to the semi-analytic model of galaxy formation: methodology
(2010-01) Lu, Yu; Mo, H.J.; Weinberg, Martin D.; Katz, N
We believe that a wide range of physical processes conspire to shape the observed galaxy population but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper, we develop a generalized SAM using the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov-Chain Monte-Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterize galaxy formation in the current $\Lambda$CDM cosmology using stellar mass function of galaxies as observational constraints. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters. It is common practice to reduce the SAM dimensionality by fixing various parameters. However, this can lead to biased inferences and to incorrect interpretations of data owing to this parameter covariance. This suggests that some conclusions obtained from early SAMs may not be reliable. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.
Structure of bright 2MASS galaxies: 2D fits to the K-S-band surface brightness profiles
(2003-01) McIntosh, DH; Maller, AH; Katz, N; Weinberg, MD
The unprecedented sky coverage and photometric uniformity of the Two Micron All Sky Survey (2MASS) provides a rich resource for obtaining a detailed understanding of the galaxies populating our local (z<0.1) Universe. A full characterization of the physical structure of nearby galaxies is essential for theoretical and observational studies of galaxy evolution and structure formation. We have begun a quantified description of the internal structure and morphology of 10,000 bright (10<11) 2MASS galaxies through multi-component model fits to the 2D surface brightness profiles using GIM2D. From our initial Monte Carlo tests on 77 galaxies drawn at random from the RC3, we find that the model derived structural parameter errors due to sky uncertainies are typically less than 10%.
A Two Micron All Sky Survey view of the Sagittarius dwarf galaxy. I. Morphology of the Sagittarius core and tidal arms
(2003-01) Majewski, SR; Skrutskie, MF; Weinberg, MD; Ostheimer, JC
We present the first all-sky view of the Sagittarius (Sgr) dwarf galaxy mapped by M-giant star tracers detected in the complete Two Micron All Sky Survey (2MASS). Near-infrared photometry of Sgr's prominent M-giant population permits an unprecedentedly clear view of the center of Sgr. The main body is fitted with a King profile of limiting major-axis radius 30°—substantially larger than previously found or assumed—beyond which is a prominent break in the density profile from stars in the Sgr tidal tails; thus the Sgr radial profile resembles that of Galactic dwarf speroidal (dSph) satellites. Adopting traditional methods for analyzing dSph light profiles, we determine the brightness of the main body of Sgr to be MV = -13.27 (the brightest of the known Galactic dSph galaxies) and the total Sgr mass-to-light ratio to be 25 in solar units. However, we regard the latter result with suspicion and argue that much of the observed structure beyond the King-fit core radius (224') may be outside the actual Sgr tidal radius as the former dwarf spiral/irregular satellite undergoes catastrophic disruption during its last orbits. The M-giant distribution of Sgr exhibits a central density cusp at the same location as, but not due to, the old stars constituting the globular cluster M54. A striking trailing tidal tail is found to extend from the Sgr center and arc across the south Galactic hemisphere with approximately constant density and mean distance varying from ~20 to 40 kpc. A prominent leading debris arm extends from the Sgr center northward of the Galactic plane to an apogalacticon ~45 kpc from the Sun and then turns toward the north Galactic cap (NGC), from where it descends back toward the Galactic plane, becomes foreshortened, and, at brighter magnitudes, covers the NGC. The leading and trailing Sgr tails lie along a well-defined orbital plane about the Galactic center. The Sun lies within a kiloparsec of that plane and near the path of leading Sgr debris; thus, it is possible that former Sgr stars are near or in the solar neighborhood. We discuss the implications of this new view of the Sgr galaxy and its entrails for the character of the Sgr orbit, mass, mass-loss rate, and contribution of stars to the Milky Way halo. The minimal precession displayed by the Sgr tidal debris along its inclined orbit supports the notion of a nearly spherical Galactic potential. The number of M giants in the Sgr tails is at least 15% that contained within the King limiting radius of the main Sgr body. The fact that M giants, presumably formed within the past few gigayears in the Sgr nucleus, are nevertheless so widespread along the Sgr tidal arms not only places limits on the dynamical age of these arms but also poses a timing problem that bears on the recent binding energy of the Sgr core and that is most naturally explained by recent and catastrophic mass loss. Sgr appears to contribute more than 75% of the high-latitude, halo M giants, despite substantial reservoirs of M giants in the Magellanic Clouds. No evidence of extended M-giant tidal debris from the Magellanic Clouds is found. Generally good correspondence is found between the M-giant, all-sky map of the Sgr system and all previously published detections of potential Sgr debris, with the exception of Sgr carbon stars, which must be subluminous compared with counterparts in other Galactic satellites in order to resolve the discrepancy.
Noise-driven evolution in stellar systems - II. A universal halo profile
(2001-01) Weinberg, MD
Disc instabilities such as arm and bar formation, minor mergers and tidal encounters drive a galaxy from equilibrium. Using the theory that describes the evolution of a galaxy halo as a result of stochastic fluctuations developed in the companion paper to this one, we show that this sort of noise evolves a halo toward a standard profile, independent of its initial profile and concentration. This process can substantially redistribute the mass in dark-matter haloes in the 10 Gyr since formation. Three different noise processes are studied: (i) a bombardment by blobs of mass that are small compared to the halo mass (‘shrapnel’); (ii) orbital evolution of substructure by dynamical friction (‘satellites’) and (iii) noise caused by the orbit of blobs in the halo (‘black holes’). The power spectrum in the shrapnel and satellite cases is continuous and produces the universal form by exciting the same discrete modes independent of the noise source. These modes dominate the evolution of the mass profile. The power spectrum for black holes is discrete and has a different form with a much slower rate of evolution. The predicted convergence in evolution may help explain the similarity of galaxy properties in widely differing environments.