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 Cayón et al. 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 the following flux values: 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, high-frequency instrument), 0.34 Jy (100 GHz, low-frequency instrument), 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 per cent. Moreover, we also provide a complete catalogue (for the point-source simulations analysed) with errors in the estimation of the amplitude below ∼10 per cent. In addition we discuss the possibility of identifying different point-source populations in the Planck catalogue by estimating their spectral indices.     

Wavelet analysis and the detection of non-Gaussianity in the cosmic microwave background

We investigate the use of wavelet transforms in detecting and characterizing non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the KaiserStebbins effect resulting from cosmic strings, on to which Gaussian signals of varying amplitudes are superposed. We find that the method significantly outperforms standard techniques based on measuring the moments of the pixel temperature distribution. We also compare the results with those obtained using techniques based on Minkowski functionals, and we again find the wavelet method to be superior. In particular, using the wavelet technique, we find that it is possible to detect non-Gaussianity even in the presence of a superposed Gaussian signal with 3 times the rms amplitude of the original cosmic string map. We also find that the wavelet technique is useful in characterizing the angular scales at which the non-Gaussian signal occurs.     

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background

An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background. A Bayesian approach is taken, based on modelling the string signal in the wavelet domain with generalized Gaussian distributions. Good performance of the algorithm is demonstrated by simulated experiments at arcminute resolution under noise conditions including primary and secondary cosmic microwave background anisotropies, as well as instrumental noise.     

Excess B‐modes extracted from the Planck polarization maps

One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Foreground removal from Planck Sky Model temperature maps using a MLP neural network

Unfortunately, the Cosmic Microwave Background (CMB) radiation is contaminated by emission originating in the Milky Way (synchrotron, free‐free and dust emission). Since the cosmological information is statistically in nature, it is essential to remove this foreground emission and leave the CMB with no systematic errors. To demonstrate the feasibility of a simple multilayer perceptron (MLP) neural network for extracting the CMB temperature signal, we have analyzed a specific data set, namely the Planck Sky Model maps, developed for evaluation of different component separation methods before including them in the Planck data analysis pipeline. It is found that a MLP neural network can provide a CMB map of about 80 % of the sky to a very high degree uncorrelated with the foreground components. Also the derived power spectrum shows little evidence for systematic errors (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel multifrequency technique for the detection of point sources in cosmic microwave background maps

In this work we address the problem of simultaneous multifrequency detection of extragalactic point sources in the maps of the cosmic microwave background. We apply a new linear filtering technique, the 'matched matrix filters', that incorporates full spatial information, including the cross-correlation among channels, without making any a priori assumption about the spectral behaviour of the sources. A substantial reduction of the background is achieved thanks to the optimal combination of filtered maps. We describe the new technique in detail and apply it to the detection of radio sources and estimation of their parameters in realistic all-sky Planck simulations at 30, 44, 70 and 100 GHz. Then, we compare the results with the single-frequency approach based on the standard matched filter, in terms of reliability, completeness and flux accuracy of the resulting point source catalogues. The new filters outperform the standard matched filters for all these indexes at 30, 44 and 70 GHz, whereas at 100 GHz both kinds of filters have a similar performance. We find a notable increment of the number of true detections for a fixed reliability level. In particular, for a 95 per cent reliability we practically double the number of detections at 30, 44 and 70 GHz.     

Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.     

Foreground separation methods for satellite observations of the cosmic microwave background

A maximum entropy method (MEM) is presented for separating the emission resulting from different foreground components from simulated satellite observations of the cosmic microwave background radiation (CMBR). In particular, the method is applied to simulated observations by the proposed Planck Surveyor satellite. The simulations, performed by Bouchet &38; Gispert, include emission from the CMBR and the kinetic and thermal Sunyaev–Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free–free and synchrotron emission. We find that the MEM technique performs well and produces faithful reconstructions of the main input components. The method is also compared with traditional Wiener filtering and is shown to produce consistently better results, particularly in the recovery of the thermal SZ effect.     

Estimating the spectral indices of correlated astrophysical foregrounds by a second-order statistical approach

We present the first tests of a new method, the correlated component analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parametrized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free–free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the Planck satellite, and realistic foreground emissions, with a position-dependent synchrotron spectral index. We work with two sets of Planck frequency channels: the low-frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high-frequency set, from 217 to 545 GHz. The concentration of intense free–free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of Planck , especially at low frequencies. A cut of a narrow strip around the Galactic equator  (| b | < 3°)  , however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.     

The observability of topological defects with ground-based interferometers

Topological defect theories lead to non-Gaussian features on maps of fluctuations of the cosmic microwave background radiation (CMBR), which enable us to distinguish them from maps predicted by standard inflationary models. We have recently presented a maximum entropy method (MEM) which simultaneously deconvolves interferometer maps of CMBR fluctuations, and separates out foreground contaminants. By applying this method to simulated observations using a realistic ground-based interferometer, we demonstrate that it is possible to recover the prominent hotspots in the CMBR maps which delineate individual defects, even in the presence of a significant Galactic foreground.