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

Quasar-galaxy associations revisited

Gravitational lensing predicts an enhancement of the density of bright, distant QSOs around foreground galaxies. We measure this QSO-galaxy correlation w_qg for two complete samples of radio-loud quasars, the southern 1Jy and Half-Jansky samples. The existence of a positive correlation between z~1 quasars and z~0.15 galaxies is confirmed at a p=99.0% significance level (>99.9%) if previous measurements on the northern hemisphere are included). A comparison with the results obtained for incomplete quasar catalogs (e.g. the Veron-Cetty and Veron compilation) suggests the existence of an `identification bias', which spuriously increases the estimated amplitude of the quasar-galaxy correlation for incomplete samples. This effect may explain many of the surprisingly strong quasar-galaxy associations found in the literature. Nevertheless, the value of w_qg that we measure in our complete catalogs is still considerably higher than the predictions from weak lensing. We consider two effects which could help to explain this discrepancy: galactic dust extinction and strong lensing.Comment: 9 pages, 6 figures, MNRAS accepte

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

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

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 $\tau (x) = [1 +(x/r_c)^2]^{-\lambda}$, with $\lambda \simeq \tfrac{1}{2}$ and $x\equiv |\vec{x}|$, where the core radius $r_c$ 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 $P_{\nu_1 \nu_2}(q)$ with $q\equiv |\vec{q}|$. The filtering methods are illustrated by application to simulated Planck observations of a $12.8^\circ \times 12.8^\circ$ patch of sky in 10 frequency channels. Our simulations suggest that the Planck instrument should detect $\approx 10000$ SZ clusters in 2/3 of the sky. Moreover, we find the catalogue to be complete for fluxes $S > 170$ mJy at 300 GHz.Comment: 12 pages, 7 figures; Corrected figures. Submitted to MNRA