3,767 research outputs found
Geometrical estimators as a test of Gaussianity in the CMB
We investigate the power of geometrical estimators on detecting
non-Gaussianity in the cosmic microwave background. In particular the number,
eccentricity and Gaussian curvature of excursion sets above (and below) a
threshold are studied. We compare their different performance when applied to
non-Gaussian simulated maps of small patches of the sky, which take into
account the angular resolution and instrumental noise of the Planck satellite.
These non-Gaussian simulations are obtained as perturbations of a Gaussian
field in two different ways which introduce a small level of skewness or
kurtosis in the distribution. A comparison with a classical estimator, the
genus, is also shown. We find that the Gaussian curvature is the best of our
estimators in all the considered cases. Therefore we propose the use of this
quantity as a particularly useful test to look for non-Gaussianity in the CMB.Comment: 9 pages, 6 postscript figures, submitted to MNRA
Wavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising
Analysis and denoising of Cosmic Microwave Background (CMB) maps are
performed using wavelet multiresolution techniques. The method is tested on
maps with resolution resembling the
experimental one expected for future high resolution space observations.
Semianalytic formulae of the variance of wavelet coefficients are given for the
Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold
Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal
of wavelet coefficients dominated by instrumental noise. CMB maps with a
signal-to-noise, , are denoised with an error improvement factor
between 3 and 5. Moreover we have also tested how well the CMB temperature
power spectrum is recovered after denoising. We are able to reconstruct the
's up to with errors always below in cases with
.Comment: latex file 9 pages + 5 postscript figures + 1 gif figure (figure 6),
to be published in MNRA
Filtering techniques for the detection of Sunyaev-Zel'dovich clusters in multifrequency CMB maps
The problem of detecting Sunyaev-Zel'dovich (SZ) clusters in multifrequency
CMB observations is investigated using a number of filtering techniques. A
multifilter approach is introduced, which optimizes the detection of SZ
clusters on microwave maps. An alternative method is also investigated, in
which maps at different frequencies are combined in an optimal manner so that
existing filtering techniques can be applied to the single combined map. The SZ
profiles are approximated by the circularly-symmetric template , with and , where the core radius and the overall amplitude of the effect
are not fixed a priori, but are determined from the data. The background
emission is modelled by a homogeneous and isotropic random field, characterized
by a cross-power spectrum with . The
filtering methods are illustrated by application to simulated Planck
observations of a patch of sky in 10 frequency
channels. Our simulations suggest that the Planck instrument should detect
SZ clusters in 2/3 of the sky. Moreover, we find the catalogue
to be complete for fluxes mJy at 300 GHz.Comment: 12 pages, 7 figures; Corrected figures. Submitted to MNRA
Comparing filters for the detection of point sources
This paper considers filters (the Mexican hat wavelet, the matched and the
scale-adaptive filters) that optimize the detection/separation of point sources
on a background. We make a one-dimensional treatment, we assume that the
sources have a Gaussian profile, i. e. , and a
background modelled by an homogeneous and isotropic Gaussian random field,
characterised by a power spectrum .
Local peak detection is used after filtering. Then, the Neyman-Pearson
criterion is used to define the confidence level for detections and a
comparison of filters is done based on the number of spurious and true
detections. We have performed numerical simulations to test theoretical ideas
and conclude that the results of the simulations agree with the analytical
results.Comment: 17 pages, 17 figures, accepted for publication in MNRA
Correlation of Excursion Sets for Non-Gaussian CMB Temperature Distributions
We present a method, based on the correlation function of excursion sets
above a given threshold, to test the Gaussianity of the CMB temperature
fluctuations in the sky. In particular, this method can be applied to
discriminate between standard inflationary scenarios and those producing
non-Gaussianity such as topological defects. We have obtained the normalized
correlation of excursion sets, including different levels of noise, for 2-point
probability density functions constructed from the Gaussian, \chi_n^2 and
Laplace 1-point probability density functions in two different ways.
Considering subdegree angular scales, we find that this method can distinguish
between different distributions even if the corresponding marginal probability
density functions and/or the radiation power spectra are the same.Comment: 7 pages latex file using mn.sty + 4 postscript figures, to appear in
MNRA
Isotropic Wavelets: a Powerful Tool to Extract Point Sources from CMB Maps
It is the aim of this paper to introduce the use of isotropic wavelets to
detect and determine the flux of point sources appearing in CMB maps. The most
suited wavelet to detect point sources filtered with a Gaussian beam is the
Mexican Hat. An analytical expression of the wavelet coefficient obtained in
the presence of a point source is provided and used in the detection and flux
estimation methods presented. For illustration the method is applied to two
simulations (assuming Planck Mission characteristics) dominated by CMB (100
GHz) and dust (857 GHz) as these will be the two signals dominating at low and
high frequency respectively in the Planck channels. We are able to detect
bright sources above 1.58 Jy at 857 GHz (82% of all sources) and above 0.36 Jy
at 100 GHz (100% of all) with errors in the flux estimation below 25%. The main
advantage of this method is that nothing has to be assumed about the underlying
field, i.e. about the nature and properties of the signal plus noise present in
the maps. This is not the case in the detection method presented by Tegmark and
Oliveira-Costa 1998. Both methods are compared producing similar results.Comment: 6 pages. Accepted for publication in MNRA
Analysis of CMB maps with 2D wavelets
We consider the 2D wavelet transform with two scales to study sky maps of
temperature anisotropies in the cosmic microwave background radiation (CMB). We
apply this technique to simulated maps of small sky patches of size 12.8 \times
12.8 square degrees and 1.5' \times 1.5' pixels. The relation to the standard
approach, based on the cl's is established through the introduction of the
scalogram. We consider temperature fluctuations derived from standard, open and
flat-Lambda CDM models. We analyze CMB anisotropies maps plus uncorrelated
Gaussian noise (uniform and non-uniform) at idfferent S/N levels. We explore in
detail the denoising of such maps and compare the results with other techniques
already proposed in the literature. Wavelet methods provide a good
reconstruction of the image and power spectrum. Moreover, they are faster than
previously proposed methods.Comment: latex file 7 pages + 5 postscript files + 1 gif file; accepted for
publication in A&A
Cosmological applications of a wavelet analysis on the sphere
The cosmic microwave background (CMB) is a relic radiation of the Big Bang
and as such it contains a wealth of cosmological information. Statistical
analyses of the CMB, in conjunction with other cosmological observables,
represent some of the most powerful techniques available to cosmologists for
placing strong constraints on the cosmological parameters that describe the
origin, content and evolution of the Universe. The last decade has witnessed
the introduction of wavelet analyses in cosmology and, in particular, their
application to the CMB. We review here spherical wavelet analyses of the CMB
that test the standard cosmological concordance model. The assumption that the
temperature anisotropies of the CMB are a realisation of a statistically
isotropic Gaussian random field on the sphere is questioned. Deviations from
both statistical isotropy and Gaussianity are detected in the reviewed works,
suggesting more exotic cosmological models may be required to explain our
Universe. We also review spherical wavelet analyses that independently provide
evidence for dark energy, an exotic component of our Universe of which we know
very little currently. The effectiveness of accounting correctly for the
geometry of the sphere in the wavelet analysis of full-sky CMB data is
demonstrated by the highly significant detections of physical processes and
effects that are made in these reviewed works.Comment: 17 pages, 8 figures; JFAA invited review, in pres
Peaks in the Cosmic Microwave Background: flat versus open models
We present properties of the peaks (maxima) of the CMB anisotropies expected
in flat and open CDM models. We obtain analytical expressions of several
topological descriptors: mean number of maxima and the probability distribution
of the gaussian curvature and the eccentricity of the peaks. These quantities
are calculated as functions of the radiation power spectrum, assuming a
gaussian distribution of temperature anisotropies. We present results for
angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are
relevant for the MAP and COBRAS/SAMBA space missions and the ground-based
interferometer experiments. Our analysis also includes the effects of noise. We
find that the number of peaks can discriminate between standard CDM models, and
that the gaussian curvature distribution provides a useful test for these
various models, whereas the eccentricity distribution can not distinguish
between them.Comment: 13 pages latex file using aasms4.sty + 3 tables + 2 postscript
figures, to appear in ApJ (March 1997
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