Universality in Three-Frequency Resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems

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

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

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