26,099 research outputs found
Cosmological redshift distortion: deceleration, bias and density parameters from future redshift surveys of galaxies
The observed two-point correlation functions of galaxies in redshift space
become anisotropic due to the geometry of the universe as well as due to the
presence of the peculiar velocity field. On the basis of linear perturbation
theory, we expand the induced anisotropies of the correlation functions with
respect to the redshift , and obtain analytic formulae to infer the
deceleration parameter , the density parameter and the
derivative of the bias parameter at in terms of the
observable statistical quantities. The present method does not require any
assumption of the shape and amplitude of the underlying fluctuation spectrum,
and thus can be applied to future redshift surveys of galaxies including the
Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error
in estimating the value of from a galaxy
redshift survey on the basis of a conventional estimator for which
neglects both the geometrical distortion effect and the time evolution of the
parameter . If the magnitude limit of the survey is as faint as 18.5
(in B-band) as in the case of the Sloan Digital Sky Survey, the systematic
error ranges between -20% and 10% depending on the cosmological parameters.
Although such systematic errors are smaller than the statistical errors in the
current surveys, they will dominate the expected statistical error for future
surveys.Comment: 9 pages, 5 figs, aastex, ApJ in press, replaced version includes
minor correction
Wide Angle Redshift Distortions Revisited
We explore linear redshift distortions in wide angle surveys from the point
of view of symmetries. We show that the redshift space two-point correlation
function can be expanded into tripolar spherical harmonics of zero total
angular momentum . The
coefficients of the expansion are analogous to the 's of
the angular power spectrum, and express the anisotropy of the redshift space
correlation function. Moreover, only a handful of are
non-zero: the resulting formulae reveal a hidden simplicity comparable to
distant observer limit. The depend on spherical Bessel
moments of the power spectrum and . In the plane parallel
limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered.
The general formalism is used to derive useful new expressions. We present a
particularly simple trigonometric polynomial expansion, which is arguably the
most compact expression of wide angle redshift distortions. These formulae are
suitable to inversion due to the orthogonality of the basis functions. An
alternative Legendre polynomial expansion was obtained as well. This can be
shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity
of the underlying theory will admit similar calculations for higher order
statistics as well.Comment: 6 pages, 1 figure, ApJL submitte
Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method
We present a method of measuring galaxy power spectrum based on the
multiresolution analysis of the discrete wavelet transformation (DWT). Since
the DWT representation has strong capability of suppressing the off-diagonal
components of the covariance for selfsimilar clustering, the DWT covariance for
popular models of the cold dark matter cosmogony generally is diagonal, or
(scale)-diagonal in the scale range, in which the second scale-scale
correlations are weak. In this range, the DWT covariance gives a lossless
estimation of the power spectrum, which is equal to the corresponding Fourier
power spectrum banded with a logarithmical scaling. In the scale range, in
which the scale-scale correlation is significant, the accuracy of a power
spectrum detection depends on the scale-scale or band-band correlations. This
is, for a precision measurements of the power spectrum, a measurement of the
scale-scale or band-band correlations is needed. We show that the DWT
covariance can be employed to measuring both the band-power spectrum and second
order scale-scale correlation. We also present the DWT algorithm of the binning
and Poisson sampling with real observational data. We show that the alias
effect appeared in usual binning schemes can exactly be eliminated by the DWT
binning. Since Poisson process possesses diagonal covariance in the DWT
representation, the Poisson sampling and selection effects on the power
spectrum and second order scale-scale correlation detection are suppressed into
minimum. Moreover, the effect of the non-Gaussian features of the Poisson
sampling can be calculated in this frame.Comment: AAS Latex file, 44 pages, accepted for publication in Ap
Unusually Large Fluctuations in the Statistics of Galaxy Formation at High Redshift
We show that various milestones of high-redshift galaxy formation, such as
the formation of the first stars or the complete reionization of the
intergalactic medium, occurred at different times in different regions of the
universe. The predicted spread in redshift, caused by large-scale fluctuations
in the number density of galaxies, is at least an order of magnitude larger
than previous expectations that argued for a sharp end to reionization. This
cosmic scatter in the abundance of galaxies introduces new features that affect
the nature of reionization and the expectations for future probes of
reionization, and may help explain the present properties of dwarf galaxies in
different environments. The predictions can be tested by future numerical
simulations and may be verified by upcoming observations. Current simulations,
limited to relatively small volumes and periodic boundary conditions, largely
omit cosmic scatter and its consequences. In particular, they artificially
produce a sudden end to reionization, and they underestimate the number of
galaxies by up to an order of magnitude at redshift 20.Comment: 8 ApJ pages, 4 figures, ApJ. Minor changes in revised version.
Originally first submitted for publication on Aug. 29, 200
Instanton Theory of Burgers Shocks and Intermittency
A lagrangian approach to Burgers turbulence is carried out along the lines of
the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics.
We derive, from an analysis based on the hypothesis of unbroken galilean
invariance, the asymptotic form of the probability distribution function of
negative velocity-differences. The origin of Burgers intermittency is found to
rely on the dynamical coupling between shocks, identified to instantons, and
non-coherent background fluctuations, which, then, cannot be discarded in a
consistent statistical description of the flow.Comment: 7 pages; LaTe
An Inversion Method for Measuring Beta in Large Redshift Surveys
A precision method for determining the value of Beta= Omega_m^{0.6}/b, where
b is the galaxy bias parameter, is presented. In contrast to other existing
techniques that focus on estimating this quantity by measuring distortions in
the redshift space galaxy-galaxy correlation function or power spectrum, this
method removes the distortions by reconstructing the real space density field
and determining the value of Beta that results in a symmetric signal. To remove
the distortions, the method modifies the amplitudes of a Fourier plane-wave
expansion of the survey data parameterized by Beta. This technique is not
dependent on the small-angle/plane-parallel approximation and can make full use
of large redshift survey data. It has been tested using simulations with four
different cosmologies and returns the value of Beta to +/- 0.031, over a factor
of two improvement over existing techniques.Comment: 16 pages including 6 figures Submitted to The Astrophysical Journa
Observation of non-Markovian micro-mechanical Brownian motion
All physical systems are to some extent open and interacting with their
environment. This insight, basic as it may seem, gives rise to the necessity of
protecting quantum systems from decoherence in quantum technologies and is at
the heart of the emergence of classical properties in quantum physics. The
precise decoherence mechanisms, however, are often unknown for a given system.
In this work, we make use of an opto-mechanical resonator to obtain key
information about spectral densities of its condensed-matter heat bath. In
sharp contrast to what is commonly assumed in high-temperature quantum Brownian
motion describing the dynamics of the mechanical degree of freedom, based on a
statistical analysis of the emitted light, it is shown that this spectral
density is highly non-Ohmic, reflected by non-Markovian dynamics, which we
quantify. We conclude by elaborating on further applications of opto-mechanical
systems in open system identification.Comment: 5+6 pages, 3 figures. Replaced by final versio
Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales
If one wants to represent the galaxy number density at some point in terms of
only the mass density at the same point, there appears the stochasticity in
such a relation, which is referred to as ``stochastic bias''. The stochasticity
is there because the galaxy number density is not merely a local function of a
mass density field, but it is a nonlocal functional, instead. Thus, the
phenomenological stochasticity of the bias should be accounted for by nonlocal
features of galaxy formation processes. Based on mathematical arguments, we
show that there are simple relations between biasing and nonlocality on linear
scales of density fluctuations, and that the stochasticity in Fourier space
does not exist on linear scales under a certain condition, even if the galaxy
formation itself is a complex nonlinear and nonlocal precess. The stochasticity
in real space, however, arise from the scale-dependence of bias parameter, .
As examples, we derive the stochastic bias parameters of simple nonlocal models
of galaxy formation, i.e., the local Lagrangian bias models, the cooperative
model, and the peak model. We show that the stochasticity in real space is also
weak, except on the scales of nonlocality of the galaxy formation. Therefore,
we do not have to worry too much about the stochasticity on linear scales,
especially in Fourier space, even if we do not know the details of galaxy
formation process.Comment: 24 pages, latex, including 2 figures, ApJ, in pres
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