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

On the Destruction and Over-Merging of Dark Halos in Dissipationless N-body Simulations

N-body simulations that follow only a collisionless dark matter component have failed to produce galaxy halos or substructure within dense environments. We investigate the `over-merging' problem analytically and with numerical simulations, by calculating dissolution timescales of halos due to physical and artificial dynamical effects. The numerical resolution that has recently been attained is such that mass-loss from two-body relaxation is negligible. We demonstrate that substructure is destroyed in present simulations as a result of large force softening combined with the heating sources of tides and encounters with dissolving substructure. In the limit of infinite numerical resolution, whether or not individual halos or substructure can survive depends sensitively on their inner density profiles. Singular isothermal halos will always survive at some level, however, if halos form with large core radii then the over-merging problem will always exist within dissipationless N-body simulations. In this latter case a dissipational component can increase the halos central density enabling galaxies to survive.Comment: submitted to ApJL. compressed postscript file includes figures

New insight on galaxy structure from GALPHAT I. Motivation, methodology, and benchmarks for Sersic models

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)Comment: Submitted to MNRAS. The submitted version with high resolution figures can be downloaded from http://www.astro.umass.edu/~iyoon/GALPHAT/galphat1.pd

Photoionization, Numerical Resolution, and Galaxy Formation

Using cosmological simulations that incorporate gas dynamics and gravitational forces, we investigate the influence of photoionization by a UV radiation background on the formation of galaxies. In our highest resolution simulations, we find that photoionization has essentially no effect on the baryonic mass function of galaxies at $z=2$, down to our resolution limit of 5e9 M_\sun. We do, however, find a strong interplay between the mass resolution of a simulation and the microphysics included in the computation of heating and cooling rates. At low resolution, a photoionizing background can appear to suppress the formation of even relatively massive galaxies. However, when the same initial conditions are evolved with a factor of eight better mass resolution, this effect disappears. Our results demonstrate the need for care in interpreting the results of cosmological simulations that incorporate hydrodynamics and radiation physics. For example, we conclude that a simulation with limited resolution may yield more realistic results if it ignores some relevant physical processes, such as photoionization. At higher resolution, the simulated population of massive galaxies is insensitive to the treatment of photoionization and star formation, but it does depend significantly on the amplitude of the initial density fluctuations. By $z=2$, an $\Omega=1$ cold dark matter model normalized to produce the observed masses of present-day clusters has already formed galaxies with baryon masses exceeding 1e11 M_\sun.Comment: 25 pages, w/ embedded figures. Submitted to ApJ. Also available at http://www-astronomy.mps.ohio-state.edu/~dhw/Docs/preprints.htm

Cosmological Simulations with TreeSPH

We describe numerical methods for incorporating gas dynamics into cosmological simulations and present illustrative applications to the cold dark matter (CDM) scenario. Our evolution code, a version of TreeSPH (Hernquist \& Katz 1989) generalized to handle comoving coordinates and periodic boundary conditions, combines smoothed--particle hydrodynamics (SPH) with the hierarchical tree method for computing gravitational forces. The Lagrangian hydrodynamics approach and individual time steps for gas particles give the algorithm a large dynamic range, which is essential for studies of galaxy formation in a cosmological context. The code incorporates radiative cooling for an optically thin, primordial composition gas in ionization equilibrium with a user-specified ultraviolet background. We adopt a phenomenological prescription for star formation that gradually turns cold, dense, Jeans-unstable gas into collisionless stars, returning supernova feedback energy to the surrounding medium. In CDM simulations, some of the baryons that fall into dark matter potential wells dissipate their acquired thermal energy and condense into clumps with roughly galactic masses. The resulting galaxy population is insensitive to assumptions about star formation; we obtain similar baryonic mass functions and galaxy correlation functions from simulations with star formation and from simulations without star formation in which we identify galaxies directly from the cold, dense gas.Comment: compressed postscript, 38 pages including 6 out of 7 embedded figures. Submitted to ApJ Supplements. Version with all 7 figures available from ftp://bessel.mps.ohio-state.edu/pub/dhw/Preprint

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'