109 research outputs found
Tracing the Dark Matter Sheet in Phase Space
The primordial velocity dispersion of dark matter is small compared to the
velocities attained during structure formation. The initial density
distribution is close to uniform and it occupies an initial sheet in phase
space that is single valued in velocity space. Because of gravitational forces
this three dimensional manifold evolves in phase space without ever tearing,
conserving phase-space volume and preserving the connectivity of nearby points.
N-body simulations already follow the motion of this sheet in phase space. This
fact can be used to extract full fine-grained phase-space-structure information
from existing cosmological N-body simulations. Particles are considered as the
vertices of an unstructured three dimensional mesh, moving in six dimensional
phase-space. On this mesh, mass density and momentum are uniquely defined. We
show how to obtain the space density of the fluid, detect caustics, and count
the number of streams as well as their individual contributions to any point in
configuration-space. We calculate the bulk velocity, local velocity
dispersions, and densities from the sheet - all without averaging over control
volumes. This gives a wealth of new information about dark matter fluid flow
which had previously been thought of as inaccessible to N-body simulations. We
outline how this mapping may be used to create new accurate collisionless fluid
simulation codes that may be able to overcome the sparse sampling and
unphysical two-body effects that plague current N-body techniques.Comment: MNRAS submitted; 17 pages, 19 figures; revised in line with referee's
comments, results unchange
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Numerical Simulations of the Dark Universe: State of the Art and the Next Decade
We present a review of the current state of the art of cosmological dark
matter simulations, with particular emphasis on the implications for dark
matter detection efforts and studies of dark energy. This review is intended
both for particle physicists, who may find the cosmological simulation
literature opaque or confusing, and for astro-physicists, who may not be
familiar with the role of simulations for observational and experimental probes
of dark matter and dark energy. Our work is complementary to the contribution
by M. Baldi in this issue, which focuses on the treatment of dark energy and
cosmic acceleration in dedicated N-body simulations. Truly massive dark
matter-only simulations are being conducted on national supercomputing centers,
employing from several billion to over half a trillion particles to simulate
the formation and evolution of cosmologically representative volumes (cosmic
scale) or to zoom in on individual halos (cluster and galactic scale). These
simulations cost millions of core-hours, require tens to hundreds of terabytes
of memory, and use up to petabytes of disk storage. The field is quite
internationally diverse, with top simulations having been run in China, France,
Germany, Korea, Spain, and the USA. Predictions from such simulations touch on
almost every aspect of dark matter and dark energy studies, and we give a
comprehensive overview of this connection. We also discuss the limitations of
the cold and collisionless DM-only approach, and describe in some detail
efforts to include different particle physics as well as baryonic physics in
cosmological galaxy formation simulations, including a discussion of recent
results highlighting how the distribution of dark matter in halos may be
altered. We end with an outlook for the next decade, presenting our view of how
the field can be expected to progress. (abridged)Comment: 54 pages, 4 figures, 3 tables; invited contribution to the special
issue "The next decade in Dark Matter and Dark Energy" of the new Open Access
journal "Physics of the Dark Universe". Replaced with accepted versio
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress is traced from
the early stage of 1D feasibility studies to 2D axisymmetric codes that
accurately simulate the oscillations and gravitational collapse of relativistic
stars and to current 3D codes that provide pieces of a binary black spacetime.
A prime application of characteristic evolution is to compute waveforms via
Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1
Cluster Lenses
Clusters of galaxies are the most recently assembled, massive, bound
structures in the Universe. As predicted by General Relativity, given their
masses, clusters strongly deform space-time in their vicinity. Clusters act as
some of the most powerful gravitational lenses in the Universe. Light rays
traversing through clusters from distant sources are hence deflected, and the
resulting images of these distant objects therefore appear distorted and
magnified. Lensing by clusters occurs in two regimes, each with unique
observational signatures. The strong lensing regime is characterized by effects
readily seen by eye, namely, the production of giant arcs, multiple-images, and
arclets. The weak lensing regime is characterized by small deformations in the
shapes of background galaxies only detectable statistically. Cluster lenses
have been exploited successfully to address several important current questions
in cosmology: (i) the study of the lens(es) - understanding cluster mass
distributions and issues pertaining to cluster formation and evolution, as well
as constraining the nature of dark matter; (ii) the study of the lensed objects
- probing the properties of the background lensed galaxy population - which is
statistically at higher redshifts and of lower intrinsic luminosity thus
enabling the probing of galaxy formation at the earliest times right up to the
Dark Ages; and (iii) the study of the geometry of the Universe - as the
strength of lensing depends on the ratios of angular diameter distances between
the lens, source and observer, lens deflections are sensitive to the value of
cosmological parameters and offer a powerful geometric tool to probe Dark
Energy. In this review, we present the basics of cluster lensing and provide a
current status report of the field.Comment: About 120 pages - Published in Open Access at:
http://www.springerlink.com/content/j183018170485723/ . arXiv admin note:
text overlap with arXiv:astro-ph/0504478 and arXiv:1003.3674 by other author
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed
Nonlinear localized dissipative structures for long-time solution of wave equation
In this dissertation, a new numerical method, Wave Confinement (WC), is developed to efficiently solve the linear wave equation. This is similar to the originally developed Vorticity Confinement method for fluid mechanics problems. It involves modification of the discrete wave equation by adding an extra nonlinear term that can accurately propagate the pulses for long distances without numerical dispersion/diffusion. These pulses are propagated as stable codimension-one surfaces and do not suffer phase shift or amplitude exchange in spite of nonlinearity. The pulses remain thin unlike conventional higher order numerical schemes, which only converge as N (number of grid cells across the pulse) becomes large. The additional term does not interfere with conservation of the important integral quantities such as total amplitude, centroid. Also, properties like varying index of refraction, diffraction, multiple reflections are included and tested.The generated short pulses can be best described as solitary waves, which can recover the shape after a collision due to nondestructive interaction between the pulses. Within the pulse, the dissipative effects due to the numerical errors are balanced with those of nonlinearity and the pulse will its their original form and speed even after many collisions. The pulse is also used as a carrier wave to propagate other properties such as direction. Wave equation solutions in the high frequency approximation can be generated using the carrier wave approach. WC, together with Keller\u27s Approximation is then used to capture diffraction effects from a straight edge. Scattering over complex bodies can be modeled with no use of complicated adaptive grid generation schemes around the bodies. The confinement term smoothens the boundary and prevents stair casing effects but the boundary remains thin.Validation studies have been performed for a number of real flow models and compared to the exact solutions. It is observed that the solutions match quite well with the exact solution. A new approximation for long range propagation of high frequency waves, the Local Parabolic Method , is introduced. There is a wide range of applications such as radio wave propagation, cell phone communications, target detection, etc. This approximation has a number of advantages over the existing paraxial approximation used to simulate radio wave propagation
The density and peculiar velocity fields of nearby galaxies
We review the quantitative science that can be and has been done with
redshift and peculiar velocity surveys of galaxies in the nearby universe.
After a brief background setting the cosmological context for this work, the
first part of this review focuses on redshift surveys. The practical issues of
how redshift surveys are carried out, and how one turns a distribution of
galaxies into a smoothed density field, are discussed. Then follows a
description of major redshift surveys that have been done, and the local
cosmography out to 8,000 km/s that they have mapped. We then discuss in some
detail the various quantitative cosmological tests that can be carried out with
redshift data. The second half of this review concentrates on peculiar velocity
studies, beginning with a thorough review of existing techniques. After
discussing the various biases which plague peculiar velocity work, we survey
quantitative analyses done with peculiar velocity surveys alone, and finally
with the combination of data from both redshift and peculiar velocity surveys.
The data presented rule out the standard Cold Dark Matter model, although
several variants of Cold Dark Matter with more power on large scales fare
better. All the data are consistent with the hypothesis that the initial
density field had a Gaussian distribution, although one cannot rule out broad
classes of non-Gaussian models. Comparison of the peculiar velocity and density
fields constrains the Cosmological Density Parameter. The results here are
consistent with a flat universe with mild biasing of the galaxies relative to
dark matter, although open universe models are by no means ruled out.Comment: In press, Physics Reports. 153 pages. gzip'ed postscript of text plus
20 embedded figures. Also available via anonymous ftp at
ftp://eku.ias.edu/pub/strauss/review/physrep.p
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