19,971 research outputs found
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
Fluctuation properties of laser light after interaction with an atomic system: comparison between two-level and multilevel atomic transitions
The complex internal atomic structure involved in radiative transitions has
an effect on the spectrum of fluctuations (noise) of the transmitted light. A
degenerate transition has different properties in this respect than a pure
two-level transition. We investigate these variations by studying a certain
transition between two degenerate atomic levels for different choices of the
polarization state of the driving laser. For circular polarization,
corresponding to the textbook two-level atom case, the optical spectrum shows
the characteristic Mollow triplet for strong laser drive, while the
corresponding noise spectrum exhibits squeezing in some frequency ranges. For a
linearly polarized drive, corresponding to the case of a multilevel system,
additional features appear in both optical and noise spectra. These differences
are more pronounced in the regime of a weakly driven transition: whereas the
two-level case essentially exhibits elastic scattering, the multilevel case has
extra noise terms related to spontaneous Raman transitions. We also discuss the
possibility to experimentally observe these predicted differences for the
commonly encountered case where the laser drive has excess noise in its phase
quadrature.Comment: New version. Accepted for publication in Physical Review
Incoherent multi-gap optical solitons in nonlinear photonic lattices
We demonstrate numerically that partially incoherent light can be trapped in
the spectral band gaps of a photonic lattice, creating partially incoherent
multi-component spatial optical solitons in a self-defocusing nonlinear
periodic medium. We find numerically such incoherent multi-gap optical solitons
and discuss how to generate them in experiment by interfering incoherent light
beams at the input of a nonlinear periodic medium.Comment: 9 pages, 5 figure
Can We Detect the Anisotropic Shapes of Quasar HII Regions During Reionization Through The Small-Scale Redshifted 21cm Power Spectrum?
Light travel time delays distort the apparent shapes of HII regions
surrounding bright quasars during early stages of cosmic reionization.
Individual HII regions may remain undetectable in forthcoming redshifted 21 cm
experiments. However, the systematic deformation along the line of sight may be
detectable statistically, either by stacking tomographic 21cm images of quasars
identified, for example, by JWST, or as small-scale anisotropy in the
three-dimensional 21cm power spectrum. Here we consider the detectability of
this effect. The anisotropy is largest when HII regions are large and expand
rapidly, and we find that if bright quasars contributed to the early stages of
reionization, then they can produce significant anisotropy, on scales
comparable to the typical sizes of HII regions of the bright quasars (approx.
30 Mpc and below). The effect therefore cannot be ignored when analyzing future
21cm power spectra on small scales. If 10 percent of the volume of the IGM at
redshift z=10 is ionized by quasars with typical ionizing luminosity of S= 5 x
10^{56} photons/second, the distortions can enhance by more than 10 percent the
21cm power spectrum in the radial (redshift) direction, relative to the
transverse directions. The level of this anisotropy exceeds that due to
redshift-space distortion, and has the opposite sign. We show that on-going
experiments such as MWA should be able to detect this effect. A detection would
reveal the presence of bright quasars, and shed light on the ionizing yield and
age of the ionizing sources, and the distribution and small-scale clumping of
neutral intergalactic gas in their vicinity.Comment: Version accepted by ApJ, with new fiducial model and improved
discussio
A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows
An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered
Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator
We present an explicit solution based on the phase-amplitude approximation of
the Fokker-Planck equation associated with the Langevin equation of the
birhythmic modified van der Pol system. The solution enables us to derive
probability distributions analytically as well as the activation energies
associated to switching between the coexisting different attractors that
characterize the birhythmic system. Comparing analytical and numerical results
we find good agreement when the frequencies of both attractors are equal, while
the predictions of the analytic estimates deteriorate when the two frequencies
depart. Under the effect of noise the two states that characterize the
birhythmic system can merge, inasmuch as the parameter plane of the birhythmic
solutions is found to shrink when the noise intensity increases. The solution
of the Fokker-Planck equation shows that in the birhythmic region, the two
attractors are characterized by very different probabilities of finding the
system in such a state. The probability becomes comparable only for a narrow
range of the control parameters, thus the two limit cycles have properties in
close analogy with the thermodynamic phases
Transmission of sound through nonuniform circular ducts with compressible mean flows
An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows
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
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