arXiv subjects

Edmund Bertschinger

Publications and source records attributed to Edmund Bertschinger.

At least 37 records · Page 2Linked to original sources

arXiv2005

GRACOS: Scalable and Load Balanced P3M Cosmological N-body Code

We present a parallel implementation of the particle-particle/particle-mesh (P3M) algorithm for distributed memory clusters. The GRACOS (GRAvitational COSmology) code uses a hybrid method for both computation and domain decomposition. Long-range forces are computed using a Fourier transform gravity solver on a regular mesh; the mesh is distributed across parallel processes using a static one-dimensional slab domain decomposition. Short-range forces are computed by direct summation of close pairs; particles are distributed using a dynamic domain decomposition based on a space-filling Hilbert curve. A nearly-optimal method was devised to dynamically repartition the particle distribution so as to maintain load balance even for extremely inhomogeneous mass distributions. Tests using $800^3$ simulations on a 40-processor beowulf cluster showed good load balance and scalability up to 80 processes. We discuss the limits on scalability imposed by communication and extreme clustering and suggest how they may be removed by extending our algorithm to include adaptive mesh refinement.

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arXiv2004

A tensor formalism for transfer and Compton scattering of polarized light

A novel covariant formalism for the treatment of the transfer and Compton scattering of partially polarized light is presented. This was initially developed to aid in the computation of relativistic corrections to the polarization generated by the Sunyaev-Zeldovich effect (demonstrated in a companion paper), but it is of more general utility. In this approach, the polarization state of a light beam is described by a tensor constructed from the time average of quadratic products of the electric field components in a local observer frame. This leads naturally to a covariant description which is ideal for calculations involving the boosting of polarized light beams between Lorentz frames, and is more flexible than the traditional Stokes parameter approach in which a separate set of polarization basis vectors is required for each photon. The covariant kinetic equation for Compton scattering of partially polarized light by relativistic electrons is obtained in the tensor formalism by a heuristic semi-classical line of reasoning. The kinetic equation is derived first in the electron rest frame in the Thomson limit, and then is generalized to account for electron recoil and allow for scattering from an arbitrary distribution of electrons.

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arXiv2004

Kinetic theory of polarization in the Sunyaev-Zeldovich effect

We apply the coherency tensor formalism to the calculation of the spectral distortions imprinted in the intensity and polarization of the cosmic microwave background radiation due to the kinematic and thermal Sunyaev-Zeldovich effects (SZE). We obtain the first relativistic corrections to the intensity produced by the kinematic and thermal SZE, and the first correction to the polarization magnitude due to electron thermal motion.

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arXiv2004

A Cosmological Kinetic Theory for the Evolution of Cold Dark Matter Halos with Substructure: Quasi-Linear Theory

We present a kinetic theory for the evolution of the phase-space distribution of dark matter particles in galaxy halos in the presence of a cosmological spectrum of fluctuations. This theory introduces a new way to model the formation and evolution of halos, which traditionally have been investigated by analytic gravitational infall models or numerical N-body methods. Unlike the collisionless Boltzmann equation, our kinetic equation contains nonzero terms on the right-hand side arising from stochastic fluctuations in the gravitational potential due to substructures in the dark matter mass distribution. Using statistics for constrained Gaussian random fields in standard cosmological models, we show that our kinetic equation to second-order in perturbation theory is of the Fokker-Planck form, with one scattering term representing drift and the other representing diffusion in velocity-space. The drift is radial, and the drift and diffusion coefficients depend only on positions and not velocities; our relaxation process in the quasilinear regime is therefore different from the standard two-body relaxation. We provide explicit expressions relating these coefficients to the linear power spectrum of mass fluctuation and present results for the currently favored cold dark matter model with a nonzero cosmological constant. Solutions to this kinetic equation will provide a complete description of the cold dark matter spatial and velocity distributions for the average halo during the early phases of galaxy halo formation.

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arXiv2003

A Hot Spot Model for Black Hole QPOs

In at least two black hole binary systems, the Rossi X-Ray Timing Explorer has detected high frequency quasi-periodic oscillations (HFQPOs) with a 2:3 frequency commensurability. We propose a simple hot spot model to explain the positions, amplitudes, and widths of the HFQPO peaks. Using the exact geodesic equations for the Kerr metric, we calculate the trajectories of massive test particles, which are treated as isotropic, monochromatic emitters in their rest frames. By varying the hot spot parameters, we are able to explain the different features observed in ``Type A'' and ``Type B'' QPOs from XTE J1550-564. In the context of this model, the observed power spectra allow us to infer values for the black hole mass and angular momentum, and also constrain the parameters of the model.

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arXiv2003

A Model for High Frequency Quasi-periodic Oscillations from Accreting Black Holes

Observations from the Rossi X-Ray Timing Explorer have shown the existence of high frequency quasi-periodic oscillations (HFQPOs) in the X-ray flux from accreting black hole binary systems. In at least two systems, these HFQPOs come in pairs with a 2:3 frequency commensurability. We propose a simple ``hot spot'' model to explain the position and amplitude of the HFQPO peaks. Using the exact geodesic equations for the Kerr metric, we calculate the trajectories of massive test particles, which are treated as isotropic, monochromatic emitters in their rest frames. Photons are traced from the accretion disk to a distant observer to produce time- and frequency-dependent images of the orbiting hot spot and background disk. The power spectrum of the X-ray light curve consists of multiple peaks at integral combinations of the black hole coordinate frequencies. In particular, if the radial frequency is one-third of the azimuthal frequency (as is the case near the inner-most stable circular orbit), beat frequencies appear in the power spectrum at two-thirds and four-thirds of the fundamental azimuthal orbital frequency, in agreement with observations. We also model the effects of shearing the hot spot in the disk, producing an arc of emission that also follows a geodesic orbit, as well as the effects of non-planar orbits that experience Lens-Thirring precession around the black hole axis. By varying the arc length, we are able to explain the different QPO features observed in ``Type A'' and ``Type B'' X-ray outbursts from XTE J1550-564. In the context of this model, the observed power spectra allow us to infer values for the black hole mass and angular momentum, and also constrain the parameters of the model, such as the hot spot size and luminosity.

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arXiv2002

Dynamics of Cosmological Perturbations in Position Space

We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of any perturbation can then be analyzed with the Green's function method. Prior to hydrogen recombination, assuming tight coupling between photons and baryons, neglecting neutrino perturbations, and taking isentropic (adiabatic) initial conditions, the obtained Green's functions for all metric, density, and velocity perturbations vanish beyond the acoustic horizon. A localized primordial cosmological perturbation expands as an acoustic wave of photon-baryon density perturbation with narrow spikes at its acoustic wavefronts. These spikes provide one of the main contributions to the cosmic microwave background radiation anisotropy on all experimentally accessible scales. The gravitational interaction between cold dark matter and baryons causes a dip in the observed temperature of the radiation at the center of the initial perturbation. We first model the radiation by a perfect fluid and then extend our analysis to account for finite photon mean free path. The resulting diffusive corrections smear the sharp features in the photon and baryon density Green's functions over the scale of Silk damping.

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arXiv2001

Position-Space Description of the Cosmic Microwave Background and Its Temperature Correlation Function

We suggest that the cosmic microwave background (CMB) temperature correlation function C(theta) as a function of angle provides a direct connection between experimental data and the fundamental cosmological quantities. The evolution of inhomogeneities in the prerecombination universe is studied using their Green's functions in position space. We find that a primordial adiabatic point perturbation propagates as a sharp-edged spherical acoustic wave. Density singularities at its wavefronts create a feature in the CMB correlation function distinguished by a dip at theta ~ 1.2 deg. Characteristics of the feature are sensitive to the values of cosmological parameters, in particular to the total and the baryon densities.

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arXiv2001

Multiscale Gaussian Random Fields for Cosmological Simulations

This paper describes the generation of initial conditions for numerical simulations in cosmology with multiple levels of resolution, or multiscale simulations. We present the theory of adaptive mesh refinement of Gaussian random fields followed by the implementation and testing of a computer code package performing this refinement called GRAFIC2. This package is available to the computational cosmology community at http://arcturus.mit.edu/grafic/ or by email from the author.

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arXiv2000

Cosmological Perturbation Theory and Structure Formation

These lecture notes discuss several topics in the physics of cosmic structure formation starting from the evolution of small-amplitude fluctuations in the radiation-dominated era. The topics include relativistic cosmological perturbation theory with the scalar-vector-tensor decomposition, the evolution of adiabatic and isentropic initial fluctuations, microwave background anisotropy, spatial and angular power spectra, the cold dark matter linear transfer function, Press-Schechter theory, and a brief introduction to numerical simulation methods.

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arXiv1998

Self-Similar Evolution of Gravitational Clustering: N-Body Simulations of the n=-2 Spectrum

The power spectrum P(k)\propto k^n with n=-2 is close to the shape of the measured galaxy spectrum on small scales. Unfortunately this spectrum has proven rather difficult to simulate. Further, 2-dimensional simulations have suggested a breakdown of self-similar scaling for spectra with n<-1 due to divergent contributions from the coupling of long wave modes. This paper is the second (numerical) part of our investigation into the nonlinear gravitational clustering of scale-free spectra. Using high-resolution N-body simulations we find that the n=-2 power spectrum, as well as trajectories of the amplitude and phase of Fourier modes, display self-similar scaling. The evolution of the phase shift does show a different scaling at late times, but this was shown analytically to arise from the purely kinematical effect of bulk flows. Thus our analytical and N-body results verify that self-similarity in gravitational clustering holds for -3<n<1. The N-body spectrum is also compared with analytic fitting formulae, which are found to slightly underestimate the power in the nonlinear regime. The asymptotic shape of the spectrum at high-k is a power law with the same slope as predicted by the stable clustering hypothesis.

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arXiv1997

Integral Solution for the Microwave Background Anisotropies in Non-fl at Universes

We present an efficient method to compute CMB anisotropies in non-flat universes. First we derive the Boltzmann equation for cosmic microwave background temperature and polarization fluctuations produced by scalar perturbations in a general Robertson-Walker universe. We then apply the integral method to solve this equation, writing temperature and polarization anisotropies as a time integral over a geometrical term and a source term. The geometrical terms can be written using ultra-spherical Bessel functions, which depend on curvature. These cannot be precomputed in advance as in flat space. Instead we solve directly their differential equation for selected values of the multipoles. The resulting computational time is comparable to the flat space case and improves over previous methods by 2-3 orders of magnitude. This allows one to compute highly accurate CMB temperature and polarization spectra, matter transfer functions and their CMB normalizations for any cosmological model, thereby avoiding the need to use various approximate fitting formulae that exist in the literature.

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arXiv1997

Cosmological Constraints from High-Redshift Damped Lyman-Alpha Systems

Any viable cosmological model must produce enough structure at early epochs to explain the amount of gas associated with high-redshift damped Ly$α$ systems. We study the evolution of damped Ly$α$ systems at redshifts $z\ge 2$ in cold dark matter (CDM) and cold+hot dark matter (CDM+HDM) models using both N-body and hydrodynamic simulations. Our approach incorporates the effects of gas dynamics, and we find that all earlier estimates which assumed that all the baryons in dark matter halos would contribute to damped Ly$α$ absorption have overestimated the column density distribution $f(N)$ and the fraction of neutral dense gas $Ω_g$ in damped Ly$α$ systems. The differences are driven by ionization of hydrogen in the outskirts of galactic halos and by gaseous dissipation near the halo centers, and they tend to exacerbate the problem of late galaxy formation in CDM+HDM models. We only include systems up to the highest observed column density $N\sim 10^{21.8}$ cm$^{-2}$ in the estimation of $Ω_g$ for a fair comparison with data. If the observed $f(N)$ and $Ω_g$ inferred from a small number of confirmed and candidate absorbers are robust, the amount of gas in damped Ly$α$ systems at high redshifts in the $Ω_ν=0.2$ CDM+HDM model falls well below the observations.

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arXiv1996

Adding Long Wavelength Modes to an $N$-Body Simulation

We present a new method to add long wavelength power to an evolved $N$-body simulation, making use of the Zel'dovich (1970) approximation to change positions and velocities of particles. We describe the theoretical framework of our technique and apply it to a P$^3$M cosmological simulation performed on a cube of $100$ Mpc on a side, obtaining a new ``simulation'' of $800$ Mpc on a side. We study the effect of the power added by long waves by mean of several statistics of the density and velocity field, and suggest possible applications of our method to the study of the large-scale structure of the universe.

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arXiv1996

The Peculiar Motions of Elliptical Galaxies in Two Distant Regions - I. Cluster and Galaxy Selection

The EFAR project is a study of 736 candidate elliptical galaxies in 84 clusters lying in two regions towards Hercules-Corona Borealis and Perseus-Pisces-Cetus at distances cz = 6000-15000 km/s. In this paper (the first of a series) we present an introduction to the EFAR project and describe in detail the selection of the clusters and galaxies in our sample. Fundamental data for the galaxies and clusters are given, including accurate new positions for each galaxy and redshifts for each cluster. The galaxy selection functions are determined using diameters measured from Schmidt sky survey images for 2185 galaxies in the cluster fields. Future papers in this series will present the spectroscopic and photometric observations of this sample, investigate the properties of the fundamental plane for ellipticals, and determine the large-scale peculiar velocity fields in these two regions of the universe.

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arXiv1996

Building a Cosmological Hydrodynamic Code: Consistency Condition, Moving Mesh Gravity and SLH-P3M

Building a self-gravitating hydrodynamic code as a combination of a hydrodynamic solver and a gravity solver is discussed. We show that straightforward combining those two solvers generally leads to a code that does not conserve energy locally, and instead a special Consistency Condition ought to be satisfied. A particular example of combining Softened Lagrangian Hydrodynamics (SLH) with a P3M gravity solver is used to demonstrate the effect of the Consistency Condition for a self-gravitating hydrodynamic code. The need to supplement the SLH method with the P3M gravity solver arose because the Moving Mesh Gravity solver, used in conjunction with the SLH method previously, was found to produce inaccurated results. We also show that most existing cosmological hydrodynamic codes implicitly satisfy the Consistency Condition.

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arXiv1995

Local Approximations to the Gravitational Collapse of Cold Matter

We investigate three different local approximations for nonlinear gravitational instability in the framework of cosmological Lagrangian fluid dynamics of cold dust. They include the Zel'dovich approximation (ZA), the ``non-magnetic'' approximation of Bertschinger \& Jain (1994, NMA), and a new ``local tidal'' approximation (LTA). The LTA is exact for any perturbations whose gravitational and velocity equipotentials have the same constant shape with time, including spherical, cylindrical, and plane-parallel perturbations. We tested all three local approximations with the collapse of a homogeneous triaxial ellipsoid, for which an exact solution exists for an ellipsoid embedded in empty space and an excellent approximation is known in the cosmological context. We find that the LTA is significantly more accurate in general than the ZA and the NMA. Like the ZA, but unlike the NMA, the LTA generically leads to pancake collapse. For a randomly chosen mass element in an Einstein-de Sitter universe, assuming a Gaussian random field of initial density fluctuations, the LTA predicts that at least 78\% of initially underdense regions collapse owing to nonlinear effects of shear and tides.

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arXiv1995

Constraining Peaks in Gaussian Primordial Density Fields: an Application of the Hoffman-Ribak Method

We develop an algorithm for setting up initial Gaussian random density and velocity fields containing one or more peaks or dips, in an arbitrary cosmological scenario. The intention is to generate appropriate initial conditions for cosmological N-body simulations that focus on the evolution of the progenitors of the present-day galaxies and clusters. The procedure is an application of the direct and accurate prescription of Hoffman & Ribak (1991) for generating constrained random fields. For each peak a total of 21 physical characteristics can be specified, including its scale, position, density Hessian, velocity, and velocity gradient. The velocity (or, equivalently, gravity) field constrants are based on a generalization of the formalism developed by Bardeen et al. (1986). The resulting density field is sculpted such that it induces the desired amount of net gravitational and tidal forces. We provide a detailed mathematical presentation of the formalism. Afterwards we provide analytical estimates of the likelihood of the imposed constraints. Amongst others, it is shown that the tidal field has a strong tendency to align itself along the principal axes of the mass tensor. The method is illustrated by means of some concrete examples. In addition to the illustration of constraint-field correlation functions and how they add up to the mean fields, followed by illustrations of the variance characteristics of field realizations, we concentrate in particular on the consequences of imposing gravitational field constraints (or, equivalent in the linear regime for growing mode fluctuations, peculiar velocity field constraints).

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