arXiv subjects

Martin D. Weinberg

Publications and source records attributed to Martin D. Weinberg.

88 records · Page 5Linked to original sources

arXiv1999

Effect of the Milky Way on Magellanic Cloud structure

A combination of analytic models and n-body simulations implies that the structural evolution of the Large Magellanic Cloud (LMC) is dominated by its dynamical interaction with the Milky Way. Although expected at some level, the scope of the involvement has significant observational consequences. First, LMC disk orbits are torqued out of the disk plane, thickening the disk and populating a spheroid. The torque results from direct forcing by the Milky Way tide and, indirectly, from the drag between the LMC disk and its halo resulting from the induced precession of the LMC disk. The latter is a newly reported mechanism that can affect all satellite interations. However, the overall torque can not isotropize the stellar orbits and their kinematics remains disk-like. Such a kinematic signature is observed for nearly all LMC populations. The extended disk distribution is predicted to increase the microlensing toward the LMC. Second, the disk's binding energy slowly decreases during this process, puffing up and priming the outer regions for subsequent tidal stripping. Because the tidally stripped debris will be spatially extended, the distribution of stripped stars is much more extended than the HI Magellanic Stream. This is consistent with upper limits to stellar densities in the gas stream and suggests a different strategy for detecting the stripped stars. And, finally, the mass loss over several LMC orbits is predicted by n-body simulation and the debris extends to tens of kiloparsecs from the tidal boundary. Although the overall space density of the stripped stars is low, possible existence of such intervening populations have been recently reported and may be detectable using 2MASS.

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arXiv1998

Effect of the Magellanic Clouds on the Milky Way disk and VICE VERSA

The satellite-disk interaction provides limits on halo properties in two ways: (1) physical arguments motivate the excitation of observable Galactic disk structure in the presence of a massive halo, although precise limits on halo parameters are scenario-dependent; (2) conversely, the Milky Way as a whole has significant dynamical effect on LMC structure and this interaction also leads to halo limits. Together, these scenarios give strong corroboration of our current gravitational mass estimates and suggests a rapidly evolving LMC.

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arXiv1998

An adaptive algorithm for n-body field expansions

An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly and provides the highest computational advantage if the lowest-order potential-density pair in the basis looks like the unperturbed galaxy or stellar system. Unfortunately, there are only a handful of such basis in the literature which limits this advantage. This paper presents an algorithm for deriving these bases to match a wide variety of galaxy models. The method is based on efficient numerical solution of the Sturm-Liouville equation and can be used for any geometry with a separable Laplacian. Two cases are described in detail. First for the spherical case, the lowest order basis function pair may be chosen to be exactly that of the underlying model. The profile may be cuspy or have a core and truncated or of infinite extent. Secondly, the method yields a three-dimensional cylindrical basis appropriate for studying galaxian disks. In this case, the vertical and radial bases are coupled; the lowest order radial part of the basis function can be chosen to match the underlying profile only in the disk plane. Practically, this basis is still a very good match to the overall disk profile and converges in a small number of terms.

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arXiv1997

Fluctuations in finite N equilibrium stellar systems

Gravitational amplification of Poisson noise in stellar systems increases the dipole noise power by roughly a factor of six and the quadrupole noise by 50% for a King model profile. The dipole noise is amplified by a factor of fifteen for the core-free Hernquist model. The predictions are computed using the dressed-particle formalism of Rostoker & Rosenbluth (1960) and are demonstrated by n-body simulation. This result implies that a collisionless n-body simulation is impossible; the fluctuation noise which causes relaxation is an intrinic part of self gravity. Applied to dark matter halos of disk galaxies, particle numbers of at least 10^6 will be necessary to suppress this noise at a level that does not dominate or significantly affect the disk response. Conversely, halos are most likely far from phase-mixed equilibrium and the resulting noise spectrum may seed or excite observed structure such as warps, spiral arms and bars. Fluctuation noise, similar to that due to a population of 10^6 solar-mass black holes can produce observable warping and possibly excite or seed other disk structure.

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arXiv1997

Dynamics of an interacting luminous disk, dark halo, and satellite companion

This paper explores the dynamical interaction between extended halo and spheroid components of a disk galaxy and an environmental disturbance. One finds that resonant interaction between a galaxy and passing interlopers or satellite companions can carry the disturbance inward, deep inside the halo, where it can perturb the disk. Applied to the Milky Way for example, the LMC and SMC appear to be sufficient to cause the observed Galactic warp and possibly seed other asymmetries. A polar satellite orbit produces the largest warp and therefore the inferred LMC orbit is nearly optimal for maximum warp production. Both the magnitude and morphology of the response depend on the details of the disk and halo models. The results and prognosis for N-body simulations are discussed. Discreteness noise in the halo, similar to that due to a population of $10^6M_\odot$ black holes, can produce observable warping.

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arXiv1997

A rigorous reanalysis of the IRAS variable population: scale lenghts, asymmetries, and microlensing

Previous work reported a bar signature in color-selected IRAS variable stars. Here, we estimate the source density of these variables while consistently accounting for spatial incompleteness in data using a likelihood approach. The existence of the bar is confirmed with shoulder of 4 kpc and position angle of 19 +/- 1 degrees. The ratio of non-axisymmetric to axisymmetric components gives similar estimate for the bar size 3.3 +/- 0.1 kpc and position angle 24 +/- 2 degrees. We estimate a scale length 4.00 +/- 0.55 kpc for the IRAS variable population, suggesting that these stars represent the old disk population. We use this density reconstruction to estimate the optical depth to microlensing for the large-scale bar in the Galactic disk. We find an enhancement over an equivalent axisymmetric disk by 30% but still too small to account for the MACHO result. In addition, we predict a significant asymmetry at positive and negative longitudes along lines of sight through the end of the bar with optical depths comparable to that in Baade's window. An infrared microlensing survey may be a sensitive tool for detecting or constraining structural asymmetries. More generally, this is a pilot study for Bayesian star count analyses. Bayesian approach allows the assessment of prior probabilities to the unknown parameters of the model; the resulting likelihood function is straightforwardly modified to incorporate all available data.

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arXiv1996

Evolution of Galactic Globular Clusters

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.

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arXiv1996

The fate of cannibalized fundamental-plane ellipticals

Evolution and disruption of galaxies orbiting in the gravitational field of a larger cluster galaxy are driven by three coupled mechanisms: 1) the heating due to its time dependent motion in the primary; 2) mass loss due to the tidal strain field; and 3) orbital decay. Previous work demonstrated that tidal heating is effective well inside the impulse approximation limit. Not only does the overall energy increase over previous predictions, but the work is done deep inside the secondary galaxy, e.g. at or inside the half mass radius in most cases. Here, these ideas applied to cannibalization of elliptical galaxies with fundamental-plane parameters. In summary, satellites which can fall to the center of a cluster giant by dynamical friction are evaporated by internal heating by the time they reach the center. This suggests that true merger-produced multiple nuclei giants should be rare. Specifically, secondaries with mass ratios as small as 1\% on any initial orbit evaporate and those on eccentric orbits with mass ratios as small as 0.1\% evolve significantly and nearly evaporate in a galaxian age. Captured satellites with mass ratios smaller than roughly 1\% have insufficient time to decay to the center. After many accretion events, the model predicts that the merged system has a profile similar to that of the original primary with a weak increase in concentration.

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arXiv1995

The Dynamics of the Galactic Bar

I selectively review the various dynamical scenarios that have been explored to date, especially those that illustrate the conundrums. In short, although the existence of asymmetries are convincing enough, the interpretation remains ambiguous. A coherent picture for the Milky Way asymmetries is an obvious lack; each mechanism is considered independently of all others. With this motivation, I will present a nonstandard picture which has the potential to explain some of the signatures and a few of the conundrums. Moreover, it illustrates global features are dynamically connected and I believe that it is time to revisit the Milky Way in this context. Finally, I will end with a wish list for future work---both observational and theoretical---designed to help us pin down the Milky Way.

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arXiv1995

Minimum relaxation n-body simulations using orthogonal series force computation

This report describes a modification of the orthogonal function Poisson solver for n-body simulations that minimizes relaxation caused by small particle number fluctuations. With the standard algorithm, the noise leading to relaxation can be 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 tasks 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 at 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 systems 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 example is provided.

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arXiv1995

Production of Milky Way structure by the Magellanic Clouds

Previous attempts at disturbing the galactic disk by the Magellanic Clouds relied on direct tidal forcing. However, by allowing the halo to actively respond rather than remain a rigid contributor to the rotation curve, the Clouds may produce a wake in the halo which then distorts the disk. Recent work reported here suggests that the Magellanic Clouds use this mechanism to produce disk distortions sufficient to account for both the radial location, position angle and sign of the HI warp and observed anomalies in stellar kinematics towards the galactic anticenter and LSR motion.

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arXiv1994

Adiabatic Invariants in Stellar Dynamics: I. Basic concepts

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly 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.

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arXiv1994

Adiabatic Invariants in Stellar Dynamics: II. Gravitational shocking

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 disk shocking of star clusters.

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arXiv1994

Adiabatic Invariants in Stellar Dynamics: III. Application to Globular Cluster Evolution

The previous two companion papers demonstrate that slowly varying perturbations do not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with $R_g\lta8\kpc$: a concentration $c=1.5$ cluster with $R_g=8\kpc$ loses up to $95\%$ of its initial mass in $15\Gyr$. Only those with concentration $c\lta1.3$ survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will increase this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, $x$, which may be considerably larger than their initial values.

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arXiv1993

Weakly Damped Modes in Star Clusters and Galaxies

A perturber may excite a coherent mode in a star cluster or galaxy. If the stellar system is stable, it is commonly assumed that such a mode will be strongly damped and therefore of little practical consequence other than redistributing momentum and energy deposited by the perturber. This paper demonstrates that this assumption is false; weakly damped modes exist and may persist long enough to have observable consequences. To do this, a method for investigating the dispersion relation for spherical stellar systems and for locating weakly damped modes in particular is developed and applied to King models of varying concentration. This leads to the following remarkable result: King models exhibit {\it very} weakly damped $m=1$ modes over a wide range of concentration ($0.67\le c\le1.5$ have been examined). The predicted damping time is tens to hundreds of crossing times. This mode causes the peak density to shift from and slowly revolve about the initial center. The existence of the mode is supported by n-body simulation. Higher order modes and possible astronomical consequences are discussed. Weakly damped modes, for example, may provide a natural explanation for observed discrepancies between density and kinematic centers in galaxies, the location of velocity cusps due to massive black holes, and $m=1$ disturbances of disks embedded in massive halos. Gravitational shocking may excite the $m=1$ mode in globular clusters, which could modify their subsequent evolution and displace the positions of exotic remnants.

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arXiv1993

Kinematic Signature of a Rotating Bar Near a Resonance

There have been several recent suggestions that the Milky Way has rotating bar-like features based on HI and star count data. In this paper, I show that such features cause distinctive stellar kinematic signatures near OLR and ILR. The effects of these resonances may be observable far from the peak density of the pattern and relatively nearby the solar position. The details of the kinematic signatures depend on the evolutionary history of the `bar' and therefore velocity data, both systemic and velocity dispersion, may be used to probe the evolutionary history as well as the present state of the Galaxy. Kinematic models for a variety of simple scenarios are presented. Models with evolving pattern speeds show significantly stronger dispersion signatures than those with static pattern speeds, suggesting that useful observational constraints are possible. The models are applied to the proposed rotating spheroid and bar models; we find: 1) none of these models chosen to represent the proposed large-scale rotating spheroid are consistent with the stellar kinematics; and 2) a Galactic bar with semimajor axis of $3\kpc$ will cause a large increase in velocity dispersion in the vicinity of OLR ($\sim5\kpc$) with little change in the net radial motion and such a signature is suggested by K-giant velocity data. Potential future observations and analyses are discussed.

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