132 research outputs found
Tests of Gaussianity
We review two powerful methods to test the Gaussianity of the cosmic
microwave background (CMB): one based on the distribution of spherical wavelet
coefficients and the other on smooth tests of goodness-of-fit. The spherical
wavelet families proposed to analyse the CMB are the Haar and the Mexican Hat
ones. The latter is preferred for detecting non-Gaussian homogeneous and
isotropic primordial models containing some amount of skewness or kurtosis.
Smooth tests of goodness-of-fit have recently been introduced in the field
showing some interesting properties. We will discuss the smooth tests of
goodness-of-fit developed by Rayner and Best for the univariate as well as for
the multivariate analysis.Comment: Proceedings of "The Cosmic Microwave Background and its
Polarization", New Astronomy Reviews, (eds. S. Hanany and K.A. Olive), in
pres
Variograms of the Cosmic Microwave Background Temperature Fluctuations: Confirmation of Deviations from Statistical Isotropy
The Standard Inflationary model predicts an isotropic distribution of the
Cosmic Microwave Background temperature fluctuations. Detection of deviations
from statistical isotropy would call for a revision of the physics of the early
universe. This paper introduces the variogram as a powerful tool to detect and
characterize deviations from statistical isotropy in Cosmic Microwave
Background maps. Application to the Wilkinson Microwave Anisotropy Probe data
clearly shows differences between the northern and the southern hemispheres.
The sill and range of the northern hemisphere's variogram are lower than those
of the southern hemisphere. Moreover the variogram for the northern hemisphere
lies outside the 99% c.l. for scales above ten degrees. Differences between the
northern and southern hemispheres in the functional dependence of the variogram
with the scale can be used as a validation bench mark for proposed anisotropic
cosmological models.Comment: submitted to MNRA
The performance of spherical wavelets to detect non-Gaussianity in the CMB sky
We investigate the performance of spherical wavelets in discriminating
between standard inflationary models (Gaussian) and non-Gaussian models. For
the later we consider small perturbations of the Gaussian model in which an
artificially specified skewness or kurtosis is introduced through the Edgeworth
expansion. By combining all the information present in all the wavelet scales
with the Fisher discriminant, we find that the spherical Mexican Hat wavelets
are clearly superior to the spherical Haar wavelets. The former can detect
levels of the skewness and kurtosis of ~1% for 33' resolution, an order of
magnitude smaller than the later. Also, as expected, both wavelets are better
for discriminating between the models than the direct consideration of moments
of the temperature maps. The introduction of instrumental white noise in the
maps, S/N=1, does not change the main results of this paper.Comment: 12 pages, 7 figures, accepted by MNRAS with minor change
Predicted Planck Extragalactic Point Source Catalogue
An estimation of the number and amplitude (in flux) of the extragalactic
point sources that will be observed by the Planck Mission is presented in this
paper. The study is based on the Mexican Hat wavelet formalism introduced by
Cayon et al. 2000. Simulations at Planck observing frequencies are analysed,
taking into account all the possible cosmological, Galactic and Extragalactic
emissions together with noise. With the technique used in this work the Planck
Mission will produce a catalogue of extragalactic point sources above fluxes:
1.03 Jy (857 GHz), 0.53 Jy (545 GHz), 0.28 Jy (353 GHz), 0.24 Jy (217 GHz),
0.32 Jy (143 GHz), 0.41 Jy (100 GHz HFI), 0.34 Jy (100 GHz LFI), 0.57 Jy (70
GHz), 0.54 Jy (44 GHz) and 0.54 Jy (30 GHz), which are only slightly model
dependent (see text). Amplitudes of these sources are estimated with errors
below 15%. Moreover, we also provide a complete catalogue (for the point
sources simulation analysed) with errors in the estimation of the amplitude
below 10%. In addition we discuss the possibility of identifying different
point source populations in the Planck catalogue by estimating their spectral
indices.Comment: 13 pages, 2 figures, submitted to MNRA
Lensing effect on polarization in microwave background: extracting convergence power spectrum
Matter inhomogeneities along the line of sight deflect the cosmic microwave
background (CMB) photons originating at the last scattering surface at redshift
. These distortions modify the pattern of CMB polarization. We
identify specific combinations of Stokes and parameters that correspond
to spin 0, variables and can be used to reconstruct the projected matter
density. We compute the expected signal to noise as a function of detector
sensitivity and angular resolution. With Planck satellite the detection would
be at a few level. Several times better detector sensitivity would be
needed to measure the projected dark matter power spectrum over a wider range
of scales, which could provide an independent confirmation of the projected
matter power spectrum as measured from other methods.Comment: 17 pages, 5 figures, accepted for publication in PR
Probing non-Gaussianities in the CMB on an incomplete sky using surrogates
We demonstrate the feasibility to generate surrogates by Fourier-based
methods for an incomplete data set. This is performed for the case of a CMB
analysis, where astrophysical foreground emission, mainly present in the
Galactic plane, is a major challenge. The shuffling of the Fourier phases for
generating surrogates is now enabled by transforming the spherical harmonics
into a new set of basis functions that are orthonormal on the cut sky. The
results show that non-Gaussianities and hemispherical asymmetries in the CMB as
identified in several former investigations, can still be detected even when
the complete Galactic plane (|b| < 30{\deg}) is removed. We conclude that the
Galactic plane cannot be the dominant source for these anomalies. The results
point towards a violation of statistical isotropy.Comment: 9 pages, 13 figures, accepted by Physical Review
Goodness-of-fit tests of Gaussianity: constraints on the cumulants of the MAXIMA data
In this work, goodness-of-fit tests are adapted and applied to CMB maps to
detect possible non-Gaussianity. We use Shapiro-Francia test and two Smooth
goodness-of-fit tests: one developed by Rayner and Best and another one
developed by Thomas and Pierce. The Smooth tests test small and smooth
deviations of a prefixed probability function (in our case this is the
univariate Gaussian). Also, the Rayner and Best test informs us of the kind of
non-Gaussianity we have: excess of skewness, of kurtosis, and so on. These
tests are optimal when the data are independent. We simulate and analyse
non-Gaussian signals in order to study the power of these tests. These
non-Gaussian simulations are constructed using the Edgeworth expansion, and
assuming pixel-to-pixel independence. As an application, we test the
Gaussianity of the MAXIMA data. Results indicate that the MAXIMA data are
compatible with Gaussianity. Finally, the values of the skewness and kurtosis
of MAXIMA data are constrained by |S| \le 0.035 and |K| \le 0.036 at the 99%
confidence level.Comment: New Astronomy Reviews, in pres
Filter design for the detection of compact sources based on the Neyman-Pearson detector
This paper considers the problem of compact source detection on a Gaussian
background in 1D. Two aspects of this problem are considered: the design of the
detector and the filtering of the data. Our detection scheme is based on local
maxima and it takes into account not only the amplitude but also the curvature
of the maxima. A Neyman-Pearson test is used to define the region of
acceptance, that is given by a sufficient linear detector that is independent
on the amplitude distribution of the sources. We study how detection can be
enhanced by means of linear filters with a scaling parameter and compare some
of them (the Mexican Hat wavelet, the matched and the scale-adaptive filters).
We introduce a new filter, that depends on two free parameters (biparametric
scale-adaptive filter). The value of these two parameters can be determined,
given the a priori pdf of the amplitudes of the sources, such that the filter
optimizes the performance of the detector in the sense that it gives the
maximum number of real detections once fixed the number density of spurious
sources. The combination of a detection scheme that includes information on the
curvature and a flexible filter that incorporates two free parameters (one of
them a scaling) improves significantly the number of detections in some
interesting cases. In particular, for the case of weak sources embedded in
white noise the improvement with respect to the standard matched filter is of
the order of 40%. Finally, an estimation of the amplitude of the source is
introduced and it is proven that such an estimator is unbiased and it has
maximum efficiency. We perform numerical simulations to test these theoretical
ideas and conclude that the results of the simulations agree with the
analytical ones.Comment: 15 pages, 13 figures, version accepted for publication in MNRAS.
Corrected typos in Tab.
Reconstructing Projected Matter Density from Cosmic Microwave Background
Gravitational lensing distorts the cosmic microwave background (CMB)
anisotropies and imprints a characteristic pattern onto it. The distortions
depend on the projected matter density between today and redshift . In this paper we develop a method for a direct reconstruction of the
projected matter density from the CMB anisotropies. This reconstruction is
obtained by averaging over quadratic combinations of the derivatives of CMB
field. We test the method using simulations and show that it can successfully
recover projected density profile of a cluster of galaxies if there are
measurable anisotropies on scales smaller than the characteristic cluster size.
In the absence of sufficient small scale power the reconstructed maps have low
signal to noise on individual structures, but can give a positive detection of
the power spectrum or when cross correlated with other maps of large scale
structure. We develop an analytic method to reconstruct the power spectrum
including the effects of noise and beam smoothing. Tests with Monte Carlo
simulations show that we can recover the input power spectrum both on large and
small scales, provided that we use maps with sufficiently low noise and high
angular resolution.Comment: 21 pages, 9 figures, submitted to PR
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