91 research outputs found

### 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.Comment: 29 pages of latex, uses aaspp4.sty (AASTeX v4.0), submitted to Ap

### 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.Comment: Revised version, shortened. 15 pages without figures. Accepted for
publication in the Astrophysical Journal. Paper and 11 Figures available as
.ps.gz files by anonymous ftp at ftp://ftp.mpa-garching.mpg.de/pub/bepi/MA

### Velocity Structure of Self-Similar Spherically Collapsed Halos

Using a generalized self-similar secondary infall model, which accounts for
tidal torques acting on the halo, we analyze the velocity profiles of halos in
order to gain intuition for N-body simulation results. We analytically
calculate the asymptotic behavior of the internal radial and tangential kinetic
energy profiles in different radial regimes. We then numerically compute the
velocity anisotropy and pseudo-phase-space density profiles and compare them to
recent N-body simulations. For cosmological initial conditions, we find both
numerically and analytically that the anisotropy profile asymptotes at small
radii to a constant set by model parameters. It rises on intermediate scales as
the velocity dispersion becomes more radially dominated and then drops off at
radii larger than the virial radius where the radial velocity dispersion
vanishes in our model. The pseudo-phase-space density is universal on
intermediate and large scales. However, its asymptotic slope on small scales
depends on the halo mass and on how mass shells are torqued after turnaround.
The results largely confirm N-body simulations but show some differences that
are likely due to our assumption of a one-dimensional phase space manifold.Comment: 11 pages, 4 figures. Accepted by PR

### 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.Comment: 4 pages, 2 figures, to be published in X-Ray Timing 2003: Rossi and
Beyond, ed. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American
Institute of Physics

### Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge

We present a systematic treatment of the linear theory of scalar
gravitational perturbations in the synchronous gauge and the conformal
Newtonian (or longitudinal) gauge. We first derive the transformation law
relating the two gauges. We then write down in parallel in both gauges the
coupled, linearized Boltzmann, Einstein and fluid equations that govern the
evolution of the metric perturbations and the density fluctuations of the
particle species. The particle species considered include cold dark matter
(CDM), baryons, photons, massless neutrinos, and massive neutrinos (a hot dark
matter or HDM candidate), where the CDM and baryon components are treated as
fluids while a detailed phase-space description is given to the photons and
neutrinos. The linear evolution equations presented are applicable to any
$\Omega=1$ model with CDM or a mixture of CDM and HDM. Isentropic initial
conditions on super-horizon scales are derived. The equations are solved
numerically in both gauges for a CDM+HDM model with $\Omega_{\rm cold}=0.65,$
$\Omega_{\rm hot}=0.3$, and $\Omega_{\rm baryon}=0.05$. We discuss the
evolution of the metric and the density perturbations and compare their
different behaviors outside the horizon in the two gauges. In a companion paper
we integrate the geodesic equations for the neutrino particles in the perturbed
conformal Newtonian background metric computed here. The purpose is to obtain
an accurate sampling of the neutrino phase space for the HDM initial conditions
in $N$-body simulations of the CDM+HDM models.Comment: 35 pages, AAS LaTeX v3.0, figures and/or postscript available by
anonymous ftp to arcturus.mit.edu, Caltech GRP-375; MIT-AT-94-01;
IASSNS-AST-94/

### An Extension of the Faddeev-Jackiw Technique to Fields in Curved Spacetimes

The Legendre transformation on singular Lagrangians, e.g. Lagrangians
representing gauge theories, fails due to the presence of constraints. The
Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a
symplectic approach to calculating a Hamiltonian paired with a well-defined
initial value problem when working with a singular Lagrangian. This phase space
coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify
its application. We present an extension of the Faddeev-Jackiw technique for
constraint reduction in gauge field theories and non-gauge field theories that
are coupled to a curved spacetime that is described by General Relativity. A
major difference from previous formulations is that we do not explicitly
construct the symplectic matrix, as that is not necessary. We find that the
technique is a useful tool that avoids some of the subtle complications of the
Dirac approach to constraints. We apply this formulation to the Ginzburg-Landau
action and provide a calculation of its Hamiltonian and Poisson brackets in a
curved spacetime.Comment: 30 pages, updated to reflect published versio

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