Higher Criticism Statistic: Detecting and Identifying Non-Gaussianity in the WMAP First Year Data

Higher Criticism is a recently developed statistic for non-Gaussian detection, proposed in Donoho & Jin 2004. We find that Higher Criticism is useful for two purposes. First, Higher Criticism has competitive detection power, and non-Gaussianity is detected at the level 99% in the first year WMAP data. We find that the Higher Criticism value of WMAP is outside the 99% confidence region at a wavelet scale of 5 degrees (99.46% of Higher Criticism values based on simulated maps are below the values for WMAP). Second, Higher Criticism offers a way to locate a small portion of data that accounts for the non-Gaussianity. Using Higher Criticism, we have successfully identified a ring of pixels centered at (l\approx 209 deg, b\approx -57 deg), which seems to account for the observed detection of non-Gaussianity at the wavelet scale of 5 degrees. Note that the detection is achieved in wavelet space first. Second, it is always possible that a fraction of pixels within the ring might deviate from Gaussianity even if they do not appear to be above the 99% confidence level in wavelet space. The location of the ring coincides with the cold spot detected in Vielva et al. 2004 and Cruz et al. 2005.Comment: submitted to MNRA

Genus and spot density in the COBE DMR first year anisotropy maps

A statistical analysis of texture on the {\it COBE}-DMR first year sky maps based on the genus and spot number is presented. A generalized $\chi^2$ statistic is defined in terms of ``observable'' quantities: the genus and spot density that would be measured by different cosmic observers. This strategy together with the use of Monte Carlo simulations of the temperature fluctuations, including all the relevant experimental parameters, represent the main difference with previous analyses. Based on the genus analysis we find a strong anticorrelation between the quadrupole amplitude $Q_{rms-PS}$ and the spectral index $n$ of the density fluctuation power spectrum at recombination of the form $Q_{rms-PS}= 22.2 \pm 1.7 - (4.7 \pm 1.3) \times n\ \mu$K for fixed $n$, consistent with previous works. The result obtained based on the spot density is consistent with this $Q_{rms-PS} (n)$ relation. In addition to the previous results we have determined, using Monte Carlo simulations, the minimum uncertainty due to cosmic variance for the determination of the spectral index with the genus analysis. This uncertainty is $\delta n\approx 0.2$.Comment: 5 pages, uuencode file containing text and 1 figure. MNRAS in press

Constraining our Universe with X-ray & Optical Cluster Data

We have used recent X-ray and optical data in order to impose some constraints on the cosmology and cluster scaling relations. Generically two kind of hypotheses define our model. First we consider that the cluster population is well described by the standard Press-Schechter (PS) formalism, and second, these clusters are supposed to follow scaling relations with mass: Temperature-Mass (T-M) and X-ray Luminosity-Mass (L_x - M). As a difference with many other authors we do not assume specific scaling relations to model cluster properties such as the usual $T-M$ virial relation or one observational determination of the $L_x-T$ relation. Instead we consider general free parameter scaling relations. With the previous model (PS plus scalings) we fit our free parameters to several X-ray and optical data with the advantage over many other works that we consider all the data sets at the same time. This prevents us from being inconsistent with some of the available observations. Among other interesting conclusions, we find that only low-density universes are compatible with all the data considered and that the degeneracy between $\Omega_m$ and $\sigma_8$ is broken. Also we obtain interesting limits on the parameters characterizing the scaling relations.Comment: 11 pages, 7 figures. MNRAS accepted versio

R-Band Imaging of Fields Around 1<z<2 Radiogalaxies

We have taken deep $R$-band images of fields around five radiogalaxies: 0956+47, 1217+36, 3C256, 3C324 and 3C294 with $1<z<2$ . 0956+47 is found to show a double nucleus. Our data on 1217+36 suggest the revision of its classification as a radiogalaxy. We found a statistically significant excess of bright ($19.5<R<22$) galaxies on scales of 2 arcmin around the radiogalaxies (which have $R \approx 21.4$) in our sample. The excess has been determined empirically to be at $\gtrsim 99.5\%$ level. It is remarkable that this excess is not present for $22<R<23.75$ galaxies within the same area, suggesting that the excess is not physically associated to the galaxies but due to intervening groups and then related to gravitational lensing.Comment: 20 pages, uuencoded compressed PostScript including tables. Figures available upon request. To appear in the March 1995 issue of The Astronomical Journa

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 $12^{\circ}.8\times 12^{\circ}.8$ 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, $S/N \sim 1$, 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 $C_{\ell}$'s up to $l\sim 1500$ with errors always below $20$ in cases with $S/N \ge 1$.Comment: latex file 9 pages + 5 postscript figures + 1 gif figure (figure 6), to be published in MNRA

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

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

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