The Bar--Halo Interaction--I. From Fundamental Dynamics to Revised N-body Requirements

Only through resonances can non-axisymmetric features such as spiral arms and bars exert torques over large scales and change the overall structure of a near-equilibrium galaxy. We describe the resonant interaction mechanism in detail and derive explicit criteria for the particle number required to simulate these dynamical processes accurately using N-body simulations and illustrate them with numerical experiments. To do this, we perform direct numerical solution of perturbation theory and make detailed comparisons with N-body simulations. The criteria include: sufficient particle coverage in phase space near the resonance and enough particles to minimize gravitational potential fluctuations that will change the dynamics of the resonant encounter. Some of our more surprising findings are as follows. First, the Inner-Lindblad-like resonance (ILR), responsible for coupling the bar to the central halo cusp, requires almost 10^9 equal mass particles within the virial radius for a Milky-Way-like bar in an NFW profile. Second, orbits that linger near the resonance receive more angular momentum than orbits that move through the resonance quickly. Small-scale fluctuations present in state-of-the-art particle-particle simulations can knock orbits out of resonance, preventing them from lingering and, thereby, decrease the torque. The required particle numbers are sufficiently high for scenarios of interest that apparent convergence in particle number is misleading: the convergence is in the noise-dominated regime. State-of-the-art simulations are not adequate to follow all aspects of secular evolution driven by the bar-halo interaction. We present a procedure to test the requirements for individual N-body codes for the actual problem of interest. [abridged]Comment: 30 pages, 19 figures, submitted to Monthly Notices. For paper with figures at full resolution: http://www.astro.umass.edu/~weinberg/weinberg_katz_1.ps.g

The Bar-Halo Interaction - II. Secular evolution and the religion of N-body simulations

This paper explores resonance-driven secular evolution between a bar and dark-matter halo using N-body simulations. We make direct comparisons to our analytic theory (Weinberg & Katz 2005) to demonstrate the great difficulty that an N-body simulation has representing these dynamics for realistic astronomical interactions. In a dark-matter halo, the bar's angular momentum is coupled to the central density cusp (if present) by the Inner Lindblad Resonance. Owing to this angular momentum transfer and self-consistent re-equilibration, strong realistic bars WILL modify the cusp profile, lowering the central densities within about 30% of the bar radius in a few bar orbits. Past results to the contrary (Sellwood 2006, McMillan & Dehnen 2005) may be the result of weak bars or numerical artifacts. The magnitude depends on many factors and we illustrate the sensitivity of the response to the dark-matter profile, the bar shape and mass, and the galaxy's evolutionary history. For example, if the bar length is comparable to the size of a central dark-matter core, the bar may exchange angular momentum without changing its pattern speed significantly. We emphasise that this apparently simple example of secular evolution is remarkably subtle in detail and conclude that an N-body exploration of any astronomical scenario requires a deep investigation into the underlying dynamical mechanisms for that particular problem to set the necessary requirements for the simulation parameters and method (e.g. particle number and Poisson solver). Simply put, N-body simulations do not divinely reveal truth and hence their results are not infallible. They are unlikely to provide useful insight on their own, particularly for the study of even more complex secular processes such as the production of pseudo-bulges and disk heating.Comment: 23 pages, 18 figures, submitted to Monthly Notices. For paper with figures at full resolution: http://www.astro.umass.edu/~weinberg/weinberg_katz_2.ps.g

Simulating Cosmic Structure Formation

We describe cosmological simulation techniques and their application to studies of cosmic structure formation, with particular attention to recent hydrodynamic simulations of structure in the high redshift universe. Collisionless N-body simulations with Gaussian initial conditions produce a pattern of sheets, filaments, tunnels, and voids that resembles the observed large scale galaxy distribution. Simulations that incorporate gas dynamics and dissipation form dense clumps of cold gas with sizes and masses similar to the luminous parts of galaxies. Models based on inflation and cold dark matter predict a healthy population of high redshift galaxies, including systems with star formation rates of 20 M_{\sun}/year at z=6. At z~3, most of the baryons in these models reside in the low density intergalactic medium, which produces fluctuating Lyman-alpha absorption in the spectra of background quasars. The physical description of this ``Lyman-alpha forest'' is particularly simple if the absorption spectrum is viewed as a 1-dimensional map of a continuous medium instead of a collection of lines. The combination of superb observational data and robust numerical predictions makes the Lyman-alpha forest a promising tool for testing cosmological models.Comment: Latex w/ paspconf.sty, 25 pages, 8 ps figs. To appear in Origins, eds. J. M. Shull, C. E. Woodward, & H. Thronson (ASP Conference Series

A remarkably simple and accurate method for computing the Bayes Factor from a Markov chain Monte Carlo Simulation of the Posterior Distribution in high dimension

Weinberg (2012) described a constructive algorithm for computing the marginal likelihood, Z, from a Markov chain simulation of the posterior distribution. Its key point is: the choice of an integration subdomain that eliminates subvolumes with poor sampling owing to low tail-values of posterior probability. Conversely, this same idea may be used to choose the subdomain that optimizes the accuracy of Z. Here, we explore using the simulated distribution to define a small region of high posterior probability, followed by a numerical integration of the sample in the selected region using the volume tessellation algorithm described in Weinberg (2012). Even more promising is the resampling of this small region followed by a naive Monte Carlo integration. The new enhanced algorithm is computationally trivial and leads to a dramatic improvement in accuracy. For example, this application of the new algorithm to a four-component mixture with random locations in 16 dimensions yields accurate evaluation of Z with 5% errors. This enables Bayes-factor model selection for real-world problems that have been infeasible with previous methods.Comment: 14 pages, 3 figures, submitted to Bayesian Analysi

Group Scaling Relations From a Cosmological Hydrodynamic Simulation: No Pre-heating Required?

We investigate the X-ray vs. optical scaling relations of poor groups to small clusters (sigma~100-700 km/s) identified in a cosmological hydrodynamic simulation of a Lambda-CDM universe, with cooling and star formation but no pre-heating. We find that the scaling relations between X-ray luminosity, X-ray temperature, and velocity dispersion show significant departures from the relations predicted by simple hydrostatic equilibrium models or simulations without cooling, having steeper L_X-sigma and L_X-T_X slopes and a "break" at \~200 km/s (~0.3 keV). These departures arise because the hot (X-ray emitting) gas fraction varies substantially with halo mass in this regime. Our predictions roughly agree with observations. Thus radiative cooling is a critical physical process in modeling galaxy groups, and may present an alternative to ad hoc models such as pre-heating or entropy floors for explaining X-ray group scaling relations.Comment: 4 pages, to be puplished in the proceedings of the ''Sesto 2001-Tracing Cosmic Evolution with Galaxy Clusters'

Metal Lines in Cosmological Models of Lyman-Alpha Absorbers

The metal absorption lines found in association with \lya absorbers of moderate to high HI column density contain valuable information about the metallicity and ionization conditions within the absorbers and offer a stronger test of models of the intergalactic medium at \sim 3 than HI absorption lines alone. We have developed a method to predict the strengths of metal absorption lines within the framework of cosmological models for the \lya forest. The method consists of evaluating a quantity, the Line Observability Index, for a database of hundreds of candidate metal lines, allowing a comprehensive identification of the lines the model predicts to be detectable associated with a \lya absorber of a given HI column density and metallicity. Applying this technique to a particular class of models at \sim 2-4, we predict that the OVI(1032 \AA, 1038 \AA) doublet is the only practical probe of the metallicity of low column density absorbers (HI \simlt 10^{14.5} cm^{-2}$), that CIV (1548 \AA) is the strongest line with rest wavelength$\lambda_r > 1216$\AA{} regardless of HI$, and that the strongest metal lines should be CIII(977 \AA) and SiIII(1206.5 \AA), which peak at HI \sim 10^{17} cm^{-2}$.Comment: To appear in the proceedings from the 13th IAP Workshop (1-5 July 1997) "Evolution of the Intergalactic Medium From QSO Absorption Line Systems