arXiv subjects

Martin D. Weinberg

Publications and source records attributed to Martin D. Weinberg.

At least 55 records · Page 3Linked to original sources

arXiv2013

Direct Simulation Monte Carlo for astrophysical flows: II. Ram pressure dynamics

We use the Direct Simulation Monte Carlo (DSMC) method combined with an n-body code to study the dynamics of the interaction between a gas-rich spiral galaxy and intracluster or intragroup medium, often known as the ram pressure scenario. The advantage of this gas kinetic approach over traditional hydrodynamics is explicit treatment of the interface between the hot and cold, dense and rarefied media typical of astrophysical flows and the explicit conservation of energy and momentum and the interface. This approach yields some new physical insight. Owing to the shock and backward wave that forms at the point ICM--ISM contact, ICM gas is compressed, heated and slowed. The shock morphology is Mach-disk-like. In the outer galaxy, the hot turbulent post-shock gas flows around the galaxy disk, while heating and ablating the initially cool disk gas. The outer gas and angular momentum are lost to the flow. In the inner galaxy, the hot gas pressurizes the neutral ISM gas causing a strong two-phase instability. As a result, the momentum of the wind is no longer impulsively communicated to the cold gas as assumed in the Gunn-Gott (1972) formula, but oozes through the porous disk, transferring its linear momentum to the disk en masse. The escaping gas mixture has a net positive angular momentum and forms a slowly rotating sheath. The shear flow caused by the post-shock ICM flowing through the porous multiphase ISM creates a strong Kelvin-Helmholtz instability in the disk that results in Cartwheel-like ring and spoke morphology.

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arXiv2013

Creation of Peanut-Shaped Bulges via the Slow Mode of Bar Growth

Recent theoretical work has implicated fast bar formation modes and subsequent evolution as the creation mechanism for the observed peanut-shaped bulges in some edge-on disk galaxies. We demonstrate an N-body simulation of a disk undergoing a contrasting slow mode of bar growth, unsubjected to a buckling instability, which nonetheless grows the 4:1 orbit family responsible for a peanut-shaped bulge. We also present a simulation with fast mode bar growth, which exhibits thickening similar to other work. A novel orbit classification method that finds dynamically distinct families is presented, allowing for a detailed analysis of angular momentum transfer channels within the disk.

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arXiv2013

Computational statistics using the Bayesian Inference Engine

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organise and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasises hybrid tempered MCMC schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE is implements a full persistence or serialisation system that stores the full byte-level image of the running inference and previously characterised posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GPL.

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arXiv2013

Inferring the Andromeda Galaxy's mass from its giant southern stream with Bayesian simulation sampling

M31 has a giant stream of stars extending far to the south and a great deal of other tidal debris in its halo, much of which is thought to be directly associated with the southern stream. We model this structure by means of Bayesian sampling of parameter space, where each sample uses an N-body simulation of a satellite disrupting in M31's potential. We combine constraints on stellar surface densities from the Isaac Newton Telescope survey of M31 with kinematic data and photometric distances. This combination of data tightly constrains the model, indicating a stellar mass at last pericentric passage of log(M_s / Msun) = 9.5+-0.1, comparable to the LMC. Any existing remnant of the satellite is expected to lie in the NE Shelf region beside M31's disk, at velocities more negative than M31's disk in this region. This rules out the prominent satellites M32 or NGC 205 as the progenitor, but an overdensity recently discovered in M31's NE disk sits at the edge of the progenitor locations found in the model. M31's virial mass is constrained in this model to be log(M200) = 12.3+-0.1, alleviating the previous tension between observational virial mass estimates and expectations from the general galactic population and the timing argument. The techniques used in this paper, which should be more generally applicable, are a powerful method of extracting physical inferences from observational data on tidal debris structures.

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arXiv2013

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.

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arXiv2012

Bayesian inference of galaxy formation from the K-band luminosity function of galaxies: tensions between theory and observation

We conduct Bayesian model inferences from the observed K-band luminosity function of galaxies in the local Universe, using the semi-analytic model (SAM) of galaxy formation introduced in Lu et al (2011). The prior distributions for the 14 free parameters include a large range of possible models. We find that some of the free parameters, e.g. the characteristic scales for quenching star formation in both high-mass and low-mass halos, are already tightly constrained by the single data set. The posterior distribution includes the model parameters adopted in other SAMs. By marginalising over the posterior distribution, we make predictions that include the full inferential uncertainties for the colour-magnitude relation, the Tully-Fisher relation, the conditional stellar mass function of galaxies in halos of different masses, the HI mass function, the redshift evolution of the stellar mass function of galaxies, and the global star formation history. Using posterior predictive checking with the available observational results, we find that the model family (i) predicts a Tully-Fisher relation that is curved; (ii) significantly over predicts the satellite fraction; (iii) vastly over predicts the HI mass function; (iv) predicts high-z stellar mass functions that have too many low mass galaxies and too few high mass ones. and (v) predicts a redshift evolution of the stellar mass density and the star formation history that are in moderate disagreement. These results suggest that some important processes are still missing in the current model family and we discuss a number of possible solutions to solve the discrepancies, such as interactions between galaxies and dark matter halos, tidal stripping, the bimodal accretion of gas, preheating, and a redshift-dependent initial mass function.

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arXiv2011

A Bayesian approach to the semi-analytic model of galaxy formation: methodology

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 parameterisations 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 SAM in 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 characterise galaxy formation in the current $Λ$CDM cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. 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.

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arXiv2011

On the algorithms of radiative cooling in semi-analytic models

We study the behaviour of multiple radiative cooling algorithms implemented in seven Semi-Analytic Models (SAMs) of galaxy formation, including a new model we propose in this paper. We use versions of the models without feedback and apply them to dark matter haloes growing in a cosmological context, which have final masses that range from 10^{11}Msun to 10^{14}Msun. First, using simplified smoothly-growing halo models, we demonstrate that the different algorithms predict cooling rates and final cold gas masses that differ by a factor of ~5 for massive haloes (>10^{12}Msun). The algorithms are in better agreement for less massive haloes because they cool efficiently and, therefore, their cooling rates are largely limited by the halo accretion rate. However, for less massive haloes, all the SAMs predict less cooling than corresponding 1D hydrodynamic models. Second, we study the gas accretion history of the central galaxies of dark matter haloes using merger trees. The inclusion of mergers alters the cooling history of haloes by locking up gas in galaxies within small haloes at early times. For realistic halo models, the dispersion in the cold gas mass predicted by the algorithms is 0.5 dex for high mass haloes and 0.1 dex for low mass haloes, while the dispersion in the accretion rate is about two times larger. Comparing to cosmological SPH simulations, we find that most SAMs systematically under-predict the gas accretion rates for low-mass haloes but over-predict the gas accretion rates for massive haloes. Although the models all include both "rapid" and "slow" mode accretion, the transition between the two accretion modes varies between models and also differs from the simulations. Finally, we construct a new model that explicitly incorporates cold halo gas to illustrate that such a class of models can better match the results from cosmological hydrodynamic simulations.

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arXiv2010

Computing the Bayesian Factor from a Markov chain Monte Carlo Simulation of the Posterior Distribution

Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by careful attention to the numerics of the probability integral. Posing the expression for the marginal likelihood as a Lebesgue integral, we may convert the harmonic mean approximation from a sample statistic to a quadrature rule. As a quadrature, the harmonic mean approximation suffers from enormous truncation error as consequence . In addition, I demonstrate that the integral expression for the harmonic-mean approximation converges slowly at best for high-dimensional problems with uninformative prior distributions. These observations lead to two computationally-modest families of quadrature algorithms that use the full generality sample posterior but without the instability. The first algorithm automatically eliminates the part of the sample that contributes large truncation error. The second algorithm uses the posterior sample to assign probability to a partition of the sample space and performs the marginal likelihood integral directly. This eliminates convergence issues. The first algorithm is analogous to standard quadrature but can only be applied for convergent problems. The second is a hybrid of cubature: it uses the posterior to discover and tessellate the subset of that sample space was explored and uses quantiles to compute a representive field value. Neither algorithm makes strong assumptions about the shape of the posterior distribution and neither is sensitive outliers. [abridged]

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arXiv2009

The dynamics of satellite disruption in cold dark matter haloes

We investigate the physical mechanisms of tidal heating and satellite disruption in cold dark matter host haloes using N-body simulations based on cosmological initial conditions. We show the importance of resonant shocks and resonant torques with the host halo to satellite heating. A resonant shock (torque) couples the radial (tangential) motion of a satellite in its orbit to its phase space. For a satellite on a circular orbit, an ILR-like resonance dominates the heating and this heating results in continuous satellite mass loss. We estimate the requirements for simulations to achieve these dynamics using perturbation theory. Both resonant shocks and resonant torques affect satellites on eccentric orbits. We demonstrate that satellite mass loss is an outside-in process in energy space; a satellite's stars and gas are thus protected by their own halo against tidal stripping. We simulate the evolution of a halo similar to the Large Magellanic Cloud (LMC) in our Galactic dark matter halo and conclude that the LMC stars have not yet been stripped. Finally, we present a simple algorithm for estimating the evolution of satellite mass that includes both shock heating and resonant torques.

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arXiv2007

The dynamics of tidal tails from massive satellites

(Abbreviated) We investigate the dynamical mechanisms responsible for producing tidal tails from dwarf satellites using N-body simulations. We identify two important dynamical co-conspirators: 1) the points where the attractive force of the host halo and satellite are balanced do not occur at equal distances from the satellite centre or at the same equipotential value for massive satellites, breaking the morphological symmetry of the leading and trailing tails; and 2) the escaped ejecta in the leading (trailing) tail continues to be decelerated (accelerated) by the satellite's gravity leading to large offsets of the ejecta orbits from the satellite orbit. The effect of the satellite's self gravity decreases only weakly with a decreasing ratio of satellite mass to host halo mass, demonstrating the importance of these effects over a wide range of subhalo masses. Not only will the morphology of the leading and trailing tails for massive satellites be different, but the observed radial velocities of the tails will be displaced from that of the satellite orbit; both the displacement and the peak radial velocity is proportional to satellite mass. If the tails are assumed to follow the progenitor satellite orbits, the tails from satellites with masses greater than 0.0001 of the host halo virial mass in a spherical halo will appear to indicate a flattened halo. Therefore, a constraint on the Milky Way halo shape using tidal streams requires mass-dependent modelling. Similarly, we compute the the distribution of tail orbits both in E_{r}-r^{-2} space and in E-L_{z} space, advocated for identifying satellite stream relics. The acceleration of ejecta by a massive satellite during escape spreads the velocity distribution and obscures the signature of a well-defined ``moving group'' in phase space.

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arXiv2006

Dark matter halo response to the disk growth

We consider the sensitivity of the circular-orbit adiabatic contraction approximation to the baryon condensation rate and the orbital structure of dark matter halos in the $Λ$CDM paradigm. Using one-dimensional hydrodynamic simulations including the dark matter halo mass accretion history and gas cooling, we demonstrate that the adiabatic approximation is approximately valid even though halos and disks may assemble simultaneously. We further demonstrate the validity of the simple approximation for $Λ$CDM halos with isotropic velocity distributions using three-dimensional N-body simulations. This result is easily understood: an isotropic velocity distribution in a cuspy halo requires more circular orbits than radial orbits. Conversely, the approximation is poor in the extreme case of a radial orbit halo. It overestimates the response a core dark matter halo, where radial orbit fraction is larger. Because no astronomically relevant models are dominated by low-angular momentum orbits in the vicinity of the disk and the growth time scale is never shorter than a dynamical time, we conclude that the adiabatic contraction approximation is useful in modeling the response of dark matter halos to the growth of a disk.

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arXiv2006

On the origin of cold dark matter halo density profiles

N-body simulations predict that CDM halo-assembly occurs in two phases: 1) a fast accretion phase with a rapidly deepening potential well; and 2) a slow accretion phase characterised by a gentle addition of mass to the outer halo with little change in the inner potential well. We demonstrate, using one-dimensional simulations, that this two-phase accretion leads to CDM halos of the NFW form and provides physical insight into the properties of the mass accretion history that influence the final profile. Assuming that the velocities of CDM particles are effectively isotropised by fluctuations in the gravitational potential during the fast accretion phase, we show that gravitational collapse in this phase leads to an inner profile rho(r) ~ r^{-1}. Slow accretion onto an established potential well leads to an outer profile with rho(r) ~ r^{-3}. The concentration of a halo is determined by the fraction of mass that is accreted during the fast accretion phase. Using an ensemble of realistic mass accretion histories, we show that the model predictions of the dependence of halo concentration on halo formation time, and hence the dependence of halo concentration on halo mass, and the distribution of halo concentrations all match those found in cosmological N-body simulations. Using a simple analytic model that captures much of the important physics we show that the inner r^{-1} profile of CDM halos is a natural result of hierarchical mass assembly with a initial phase of rapid accretion.

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arXiv2006

A Magellanic Origin for the Warp of the Galaxy

We show that a Magellanic Cloud origin for the warp of the Milky Way can explain most quantitative features of the outer HI layer recently identified by Levine, Blitz & Heiles (2005). We construct a model similar to that of Weinberg (1998) that produces distortions in the dark matter halo, and we calculate the combined effect of these dark-halo distortions and the direct tidal forcing by the Magellanic Clouds on the disk warp in the linear regime. The interaction of the dark matter halo with the disk and resonances between the orbit of the Clouds and the disk account for the large amplitudes observed for the vertical m=0,1,2 harmonics. The observations lead to six constraints on warp forcing mechanisms and our model reasonably approximates all six. The disk is shown to be very dynamic, constantly changing its shape as the Clouds proceed along their orbit. We discuss the challenges to MOND placed by the observations.

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arXiv2006

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.

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arXiv2005

Nature and completeness of galaxies detected in the Two Micron All Sky Survey

We cross correlate the well-defined and very complete spectroscopic Main Galaxy Sample (MGS) of 156,000 bright (r<17.5 mag) galaxies from the SDSS with 2MASS sources to explore the nature and completeness of the 2MASS K-band selection of nearby galaxies. 2MASS detects 90% of the MGS brighter than r=17 mag. For r<16, 93.1% of the MGS is found in the 2MASS Extended Source Catalog (XSC). These detections span the representative range of optical and near-IR galaxy properties, but with a surface brightness-dependent bias to preferentially miss the most blue and low-concentration sources, consistent with the most morphologically late-type galaxy population. An XSC completeness of 97.5% is achievable at bright magnitudes, with blue LSBs being the only major source of incompleteness, if one follows our careful matching criteria and weeds out spurious SDSS sources. We conclude that the rapid drop in XSC completeness at r>16 reflects the sharp surface-brightness limit of the extended source detection algorithm in 2MASS. As a result, the r>16 galaxies found in the XSC are over-representative in red early types and under-representative in blue latetypes. At r>16 the XSC suffers an additional selection effect from the 2-3" spatial resolution limit of 2MASS. Therefore, 2MASS continues to detect 90% of of the MGS at 16<r<17, but with a growing fraction found in the Point Source Catalog (PSC) only. Overall, one third of the MGS is detected in the 2MASS PSC but not the XSC. A combined K<13.57 and r<16 selection provides the most representative inventory of galaxies in the local cosmos with near-IR and optical measurements, and 90.8% completeness. Using data from SDSS-DR2, this sample contains 19,156 galaxies with a median redshift of 0.052. (abridged)

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arXiv2005

The Cosmological Significance of High-Velocity Cloud Complex H

We have used infrared and radio observations to search for a dwarf galaxy associated with the high-velocity cloud (HVC) known as Complex H. Complex H is a large (> 400 deg^2) and probably nearby (d = 27 kpc) HVC whose location in the Galactic plane has hampered previous investigations of its stellar content. The HI mass of the cloud is 2.0 x 10^7 (d/27 kpc)^2 Msun, making Complex H one of the most massive HVCs if its distance is > ~20 kpc. Virtually all similar HI clouds in other galaxy groups are associated with LSB dwarf galaxies. We selected mid-IR MSX sources in the direction of Complex H that appeared likely to be star-forming regions and observed them at the wavelength of the CO 1-0 transition. 59 of the 60 observed sources show emission at Milky Way velocities, and we detected no emission at velocities consistent with that of Complex H. We use these observations to set an upper limit on the ongoing star formation rate in the HVC of < 5 x 10^-4 Msun yr^-1. We also searched the 2MASS database for evidence of any dwarf-galaxy-like stellar population in the direction of the HVC and found no trace of a distant red giant population, with an upper limit on the stellar mass of ~10^6 Msun. Given the lack of evidence for either current star formation or an evolved population, we conclude that Complex H cannot be a dwarf galaxy with properties similar to those of known dwarfs. Complex H is therefore one of the most massive known HI clouds without stars. If Complex H is self-gravitating, then it is one of the few known dark galaxy candidates. These findings may offer observational support for the idea that the Cold Dark Matter substructure problem is related to the difficulty of forming stars in low-mass dark matter halos; alternatively, Complex H could be an example of a cold accretion flow onto the Milky Way. [slightly abridged]

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arXiv2005

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]

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