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Context. The statistical analysis of large sample of strong lensing events can be a powerful tool to extract astrophysical or cosmological valuable information. Their selection using submillimetre galaxies has been demonstrated to be very effective with more than ∼200 proposed candidates in the case of Herschel-ATLAS data and several tens in the case of the South Pole Telescope. However, the number of confirmed events is still relatively low, i.e. a few tens, mostly because of the lengthy observational validation process on individual events. Aims. In this work we propose a new methodology with a statistical selection approach to increase by a factor of ∼5 the number of such events within the Herschel-ATLAS data set. Although the methodology can be applied to address several selection problems, it has particular benefits in the case of the identification of strongly lensed galaxies: objectivity, minimal initial constrains in the main parameter space, and preservation of statistical properties. Methods. The proposed methodology is based on the Bhattacharyya distance as a measure of the similarity between probability distributions of properties of two different cross-matched galaxies. The particular implementation for the aim of this work is called SHALOS and it combines the information of four different properties of the pair of galaxies: angular separation, luminosity percentile, redshift, and the ratio of the optical to the submillimetre flux densities. Results. The SHALOS method provides a ranked list of strongly lensed galaxies. The number of candidates within ∼340 deg2 of the Herschel-ATLAS surveyed area for the final associated probability, Ptot >  0.7, is 447 and they have an estimated mean amplification factor of 3.12 for a halo with a typical cluster mass. Additional statistical properties of the SHALOS candidates, as the correlation function or the source number counts, are in agreement with previous results indicating the statistical lensing nature of the selected sample. [ABSTRACT FROM AUTHOR]

We estimate the average fractional polarization at 143, 217 and 353 GHz of a sample of 4697 extragalactic dusty sources by applying stacking technique. The sample is selected from the second version of the Planck Catalogue of Compact Sources at 857 GHz, avoiding the region inside the Planck Galactic mask (fsky ~ 60 per cent). We recover values for the mean fractional polarization at 217 and 353 GHz of (3.10 ± 0.75) per cent and (3.65 ± 0.66) per cent, respectively, whereas at 143 GHz we give a tentative value of (3.52 ± 2.48) per cent. We discuss the possible origin of the measured polarization, comparing our new estimates with those previously obtained from a sample of radio sources. We test different distribution functions and we conclude that the fractional polarization of dusty sources is well described by a log-normal distribution, as determined in the radio band studies. For this distribution we estimate μ217GHz = 0.3 ± 0.5 [that would correspond to a median fractional polarization of Πmed = (1.3 ± 0.7) per cent] and μ353GHz = 0.7 ± 0.4 (Πmed = (2.0 ± 0.8) per cent), σ217GHz =1.3±0.2 and σ353GHz =1.1±0.2.With these values we estimate the source number counts in polarization and the contribution given by these sources to the Cosmic Microwave Background B-mode angular power spectrum at 217, 353, 600 and 800 GHz. We conclude that extragalactic dusty sources might be an important contaminant for the primordial B-mode at frequencies >217 GHz. [ABSTRACT FROM AUTHOR]

The Second Planck Catalogue of Compact Sources is a list of discrete objects detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two subcatalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these (PCCS2) covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The second (PCCS2E) contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven polarization-sensitive Planck channels. The improved data-processing of the full-mission maps and their reduced noise levels allow us to increase the number of objects in the catalogue, improving its completeness for the target 80% reliability as compared with the previous versions, the PCCS and the Early Release Compact Source Catalogue (ERCSC). [ABSTRACT FROM AUTHOR]

In this paper we present forecasts of the contamination on different shapes of the primordial non-Gaussianity fnl parameter – detectable on future cosmic microwave background (CMB) high-resolution anisotropy maps – produced by unresolved extragalactic point sources at frequencies of cosmological interest (45–375 GHz). We consider two scenarios: an ideal (noiseless) mission and a possible future space-borne satellite, with instrumental characteristics similar to the ones proposed for the Cosmic Origins Explorer (COrE). The local, equilateral, orthogonal and flat shapes are considered in both temperature (intensity) and polarized emission data. The angular power spectrum and bispectrum of extragalactic point sources are estimated by state-of-the-art models of source number counts. The impact of all the most relevant (far-infrared and radio selected) source populations on these shapes at COrE frequencies is studied. The results of this analysis show that unresolved extragalactic point sources should not induce a very relevant non-Gaussian signal in the frequency range 100–200 GHz, thus not preventing a correct estimate of the CMB primordial fnl parameter. Polarization information allows one to significantly reduce the error-bars in the fnl parameter and the bias induced by unresolved sources and, hence, to widen the range of frequencies for fnl studies. On the contrary, at ν < 100 GHz or ν > 225 GHz, important non-Gaussian deviations in CMB anisotropy maps are expected due to unresolved extragalactic sources. [ABSTRACT FROM AUTHOR]

In this work we present a suitable computational tool to deal with large matrices and solve systems of non-linear equations. This technique is applied to a very interesting problem: the detection and flux estimation of point sources in Cosmic Microwave Background (CMB) maps, which allows a good determination of CMB primordial fluctuations and leads to a better knowledge of the chemistry at the early stages of the Universe. The method uses previous information about the statistical properties of the sources, so that this knowledge is incorporated in a Bayesian scheme. Simulations show that our approach allows the detection of more sources than previous non-Bayesian techniques, with a small computation time. [ABSTRACT FROM AUTHOR]

We make use of the Planck all-sky survey to derive number counts and spectral indices of extragalactic sources - infrared and radio sources - from the Planck Early Release Compact Source Catalogue (ERCSC) at 100 to 857 GHz (3mm to 350 μm). Three zones (deep, medium and shallow) of approximately homogeneous coverage are used to permit a clean and controlled correction for incompleteness, which was explicitly not done for the ERCSC, as it was aimed at providing lists of sources to be followed up. Our sample, prior to the 80% completeness cut, contains between 217 sources at 100 GHz and 1058 sources at 857 GHz over about 12 800 to 16 550 deg2 (31 to 40% of the sky). After the 80% completeness cut, between 122 and 452 and sources remain, with flux densities above 0.3 and 1.9 Jy at 100 and 857 GHz. The sample so defined can be used for statistical analysis. Using the multi-frequency coverage of the Planck High Frequency Instrument, all the sources have been classified as either dust-dominated (infrared galaxies) or synchrotron-dominated (radio galaxies) on the basis of their spectral energy distributions (SED). Our sample is thus complete, flux-limited and color-selected to differentiate between the two populations. We find an approximately equal number of synchrotron and dusty sources between 217 and 353 GHz; at 353 GHz or higher (or 217 GHz and lower) frequencies, the number is dominated by dusty (synchrotron) sources, as expected. For most of the sources, the spectral indices are also derived.We provide for the first time counts of bright sources from 353 to 857 GHz and the contributions from dusty and synchrotron sources at all HFI frequencies in the key spectral range where these spectra are crossing. The observed counts are in the Euclidean regime. The number counts are compared to previously published data (from earlier Planck results, Herschel, BLAST, SCUBA, LABOCA, SPT, and ACT) and models taking into account both radio or infrared galaxies, and covering a large range of flux densities. We derive the multi-frequency Euclidean level - the plateau in the normalised differential counts at high flux-density - and compare it to WMAP, Spitzer and IRAS results. The submillimetre number counts are not well reproduced by current evolution models of dusty galaxies, whereas the millimetre part appears reasonably well fitted by the most recent model for synchrotron-dominated sources. Finally we provide estimates of the local luminosity density of dusty galaxies, providing the first such measurements at 545 and 857 GHz. [ABSTRACT FROM AUTHOR]

The Cosmic Microwave Background (CMB) is a diffuse radiation which is contaminated by the radiation emitted by point sources. The precise knowledge of CMB fluctuations can lead to a better knowledge of the chemistry at the early stages of the Universe. In this work, we present an efficient algorithm, with a high degree of parallelism, which can improve, from the computational point of view, the classical approaches for detecting point sources in Cosmic Microwave Background maps. High performance computing libraries and parallel computing techniques have allowed to construct a portable, fast and numerically stable algorithm. To check the performance of the new method, we have carried out several simulations resembling the observational data collected by the Low Frequency Instrument of the Planck satellite. The sources are detected in their real positions. [ABSTRACT FROM AUTHOR]

The detection and flux estimation of point sources in cosmic microwave background (CMB) maps is a very important task in order to clean the maps and also to obtain relevant astrophysical information. In this paper we propose a maximum a posteriori (MAP) approach detection method in a Bayesian scheme which incorporates prior information about the source flux distribution, the locations and the number of sources. We apply this method to CMB simulations with the characteristics of the Planck satellite channels at 30, 44, 70 and 100 GHz. With a similar level of spurious sources, our method yields more complete catalogues than the matched filter with a 5σ threshold. Besides, the new technique allows us to fix the number of detected sources in a non-arbitrary way. [ABSTRACT FROM AUTHOR]

Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localized areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman–Pearson lemma, the Neyman–Pearson filter (NPF), and another based on pre-filtering before fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz Planck channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes Jy for (blind/non-blind) detection and in a low noise zone with fluxes Jy for (blind/non-blind) detection with low errors in the estimated flux and position. [ABSTRACT FROM AUTHOR]

We present results on spectral index distributions, number counts, redshift distribution and other general statistical properties of extragalactic point sources in the New Extragalactic WMAP Point Source5σ (NEWPS) sample. The flux calibrations at all the Wilkinson Microwave Anisotropy Probe channels have been reassessed both by comparison with ground-based observations and through estimates of the effective beam areas. The two methods yield consistent statistical correction factors. A search of the NASA Extragalactic Data base (NED) has yielded optical identifications for ∼89 per cent of sources in the complete subsample of 252 sources with signal-to-noise ratio (S/N) ≥ 5 and S≥ 1.1 Jy at 23 GHz; five sources turned out to be Galactic and were removed. The NED also yielded redshifts for ≃92 per cent of the extragalactic sources at | b| > 10°. Their distribution was compared with model predictions; the agreement is generally good but a possible discrepancy is noted. Using the 5 GHz fluxes from the GB6 or PMN surveys, we find that ∼76 per cent of the 191 extragalactic sources with Jy can be classified as flat-spectrum sources between 5 and 23 GHz. A spectral steepening is observed at higher frequencies: only 59 per cent of our sources are still flat-spectrum sources between 23 and 61 GHz, and the average spectral indexes steepen from to . We think, however, that the difference may be due to a selection effect. The source number counts have a close to Euclidean slope and are in good agreement with the predictions of the cosmological evolution model by De Zotti et al. The observed spectral index distributions were exploited to get model-independent extrapolations of counts to higher frequencies. The risks of such operations are discussed and reasons of discrepancies with other recent estimates are clarified. [ABSTRACT FROM AUTHOR]

Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical foregrounds. The detection of the non-Gaussian signal due to extragalactic point sources and its distinction from the possible intrinsic non-Gaussianity is an issue of great importance in CMB analysis. The Mexican Hat Wavelet Family (MHWF), which has been proved very useful for the detection of extragalactic point sources, is applied here to the study of non-Gaussianity due to point sources in CMB maps. We carry out simulations of CMB maps with the characteristics of the forthcoming Planck mission at 70 and 100 GHz and filter them with the MHWF. By comparing the skewness and kurtosis of simulated maps with and without point sources, we are able to detect clearly the non-Gaussian signal due to point sources for flux limits as low as 0.4 Jy (70 GHz) and 0.3 Jy (100 GHz). The second and third members of the MHWF perform better in this respect than the Mexican Hat Wavelet (MHW1) and much better than the Daubechies 4 wavelet. We have also estimated the third order, K3, and fourth order, K4, cumulants produced by point sources at these Planck channels by means of a fit with the MHWF. The average relative errors with respect to the real values are below 12 per cent for fluxes down to 0.6 Jy (70 GHz) and 0.4 Jy (100 GHz). The values of these cumulants allow us to distinguish between different source counts models. From the estimated cumulants and assuming a power law for the source number counts we are able to obtain the coefficients α and A of the differential number counts, for 70 (100) GHz, assuming a flux limit of 1 Jy. These results are consistent with the values obtained from simulations containing only point sources, which are: for 70 (100) GHz. [ABSTRACT FROM AUTHOR]

We study the detection of extragalactic point sources in 2D flat simulations for all the frequencies of the forthcoming ESA's Planck mission. In this work, we have used the most recent available templates of the microwave sky: as for the diffuse Galactic components and the Sunyaev–Zel'dovich clusters we have used the ‘Plank Reference Sky Model’; as for the extragalactic point sources, our simulations – which comprise all the source populations relevant in this frequency interval – are based on up-to-date cosmological evolution models for sources. To consistently compare the capabilities of different filters for the compilation of – hopefully – the most complete blind catalogue of point sources, we have obtained three catalogues by filtering the simulated sky maps with: the matched filter (MF), the Mexican Hat Wavelet (MHW1) and the Mexican Hat Wavelet 2 (MHW2), the first two members of the Mexican Hat Wavelet Family. For the nine Planck frequencies we show the number of real and spurious detections and the percentage of spurious detections at different flux detection limits as well as the completeness level of the catalogues and the average errors in the estimation of the flux density of detected sources. Allowing a 5 per cent of spurious detections, we obtain the following number of detections by filtering with the MHW2 an area equivalent to half of the sky: 580 (30 GHz), 342 (44 GHz), 341 (70 GHz), 730 (100 GHz), 1130 (143 GHz), 1233 (217 GHz), 990 (353 GHz), 1025 (545 GHz) and 3183 (857 GHz). Our current results indicate that the MF and the MHW2 yield similar results, whereas the MHW1 performs worse in some cases and especially at very low fluxes. This is a relevant result, because we are able to obtain comparable results with the well-known MF and with this specific wavelet, the MHW2, which is much easier to implement and use. [ABSTRACT FROM AUTHOR]

We propose a new detection technique in the plane based on an isotropic wavelet family. This family is naturally constructed as an extension of the Gaussian–Mexican hat wavelet pair and for that reason we call it the Mexican hat wavelet family (MHWF). We show the performance of these wavelets when dealing with the detection of extragalactic point sources in cosmic microwave background (CMB) maps: a very important issue within the most general problem of the component separation of the microwave sky. Specifically, flat two-dimensional simulations of the microwave sky comprising all astrophysical components plus instrumental noise have been analysed for the channels at 30, 44 and 70 GHz of the forthcoming ESA Planck mission Low Frequency Instrument (LFI). We adopt up-to-date cosmological evolution models of extragalactic sources able to fit well the new data on high-frequency radio surveys and we discuss our current results on point-source detection by comparing them with those obtained using the Mexican hat wavelet (MHW) technique, which has been already proven a suitable tool for detecting point sources. By assuming a 5 per cent reliability level, the first new members of the MHWF, at their ‘optimal scale’, provide three point-source catalogues on half of the sky (at Galactic latitude ) at 30, 44 and 70 GHz of 639, 387 and 340 extragalactic sources, respectively. The corresponding flux detection limits are 0.38, 0.45 and 0.47 Jy. By using the same simulated sky patches and at the same frequencies as before, the MHW at its optimal scale provides 543, 322 and 311 sources with flux detection limits of 0.44, 0.51 and 0.50 Jy, respectively (5 per cent reliability level). These results show a clear improvement when we use the new members of the MHWF and, in particular, the MHW2 with respect to the MHW. [ABSTRACT FROM AUTHOR]

ABSTRACT Goodness-of-fit tests, including smooth ones, are introduced and applied to detecting non-Gaussianity in cosmic microwave background simulations. We study the power of three different tests: the Shapiro–Francia test, the uncategorized smooth test developed by Rayner & Best and Neyman's smooth goodness-of-fit test for composite hypotheses. The smooth goodness-of-fit tests are designed to be sensitive to the presence of ‘smooth’ deviations from a given distribution. We study the power of these tests based on the discrimination between Gaussian and non-Gaussian simulations. Non-Gaussian cases are simulated using the Edgeworth expansion and assuming pixel-to-pixel independence. Results show that these tests behave similarly and are more powerful than tests directly based on cumulants of order 3, 4, 5 and 6. We have applied these tests to the released MAXIMA data. The applied tests are built to be powerful against detecting deviations from univariate Gaussianity. The Cholesky matrix corresponding to signal (based on an assumed cosmological model) plus noise is used to decorrelate the observations prior to the analysis. Results indicate that the MAXIMA data are compatible with Gaussianity. [ABSTRACT FROM AUTHOR]

ABSTRACT Non-linearity introduced in slow-roll inflation will produce weakly non-Gaussian cosmic microwave background (CMB) temperature fluctuations. We have simulated non-Gaussian large-scale CMB maps (including COBE–DMR constraints) introducing an additional quadratic term in the gravitational potential. The amount of non-linearity is controlled by the so-called non-linear coupling parameter f[sub nl] . An analysis based on the Spherical Mexican Hat wavelet was applied to these and to the COBE–DMR maps. Skewness values obtained at several scales were combined into a Fisher discriminant. Comparison of the Fisher discriminant distributions obtained for different non-linear coupling parameters with the COBE–DMR values sets a constraint of |f[sub nl]| < 1100 at the 68 per cent confidence level. This new constraint is tighter than the one previously obtained by using the bispectrum by Komatsu et al. [ABSTRACT FROM AUTHOR]

We investigate the performance of spherical wavelets in discriminating between standard inflationary (Gaussian) and non-Gaussian models. For the latter we consider small perturbations of the Gaussian model in which an artificially specified skewness or kurtosis is introduced through the Edgeworth expansion. By combining all the information present in all the wavelet scales with the Fisher discriminant, we find that the spherical Mexican Hat wavelets are clearly superior to the spherical Haar wavelets. The former can detect levels of skewness and kurtosis of ≈1 per cent for 33-arcmin resolution, an order of magnitude smaller than the latter. Also, as expected, both wavelets are better for discriminating between the models than the direct consideration of moments of the temperature maps. The introduction of instrumental white noise in the maps, S/N = 1, does not change the main results of this paper. [ABSTRACT FROM AUTHOR]

The spherical Mexican hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the cosmic microwave background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE-DMR maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale–scale correlations (for two and three scales) and Kolmogorov–Smirnov tests indicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COBE-DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outside the 95 and 99 per cent limits is consistent with that obtained from Gaussian simulations, at all scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations. [ABSTRACT FROM AUTHOR]

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 cosmic microwave background (CMB) maps. The most suitable 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 frequencies respectively in the Planck channels. We are able to detect bright sources above 1.58 Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100 GHz (100 per cent of all), with errors in the flux estimation below 25 per cent. 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 & Oliveira-Costa. Both methods are compared, producing similar results. [ABSTRACT FROM AUTHOR]

Analysis and denoising of cosmic microwave background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12.8×12.8 deg[sup 2] maps, with the resolution resembling the experimental one expected for future high-resolution space observations. Semi-analytic 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 ratio, SN∼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[sub ℓ]s up to l∼1500 with errors always below 20 per cent in cases with SN&ges;1. [ABSTRACT FROM AUTHOR]

A microscopic technique has been developed to obtain the protein profiles inside calcium alginate gel. To do this, the diffusion of BSA, previously marked with FITC, inside calcium alginate beads was observed using confocal laser microscopy, thus obtaining the spatio-temporal evolution of the protein concentration. The technique, however, presents certain limitations and zones where it is impossible to obtain experimental data. Wavelets analysis, commonly used in signal processing and statistics, was employed to reconstruct and subsequently analyse the experimental results. Once the diffusion model was defined, the substrate profiles obtained were used to calculate a diffusivity value for BSA in alginate gel. [ABSTRACT FROM AUTHOR]

The solution of Einstein’s field equations is studied for a metric written in the form (δ≠γ)ds2=-α2(t,r,θ,φ)dt2 +e2β(t,r) dr2+e2γ(t,r) dθ2 +e2δ(t,r)M2(θ)dφ2. A perfect fluid, which flows orthogonally to the hypersurfaces t=const is considered as matter content. These hypersurfaces admit a translational Killing vector, which will not be, in general, a Killing vector of the whole space-time. All the possible solutions are obtained when α depends on the variable φ. These solutions represent either a perfect fluid without expansion or vacuum with a cosmological constant Λ0. Some particular inhomogeneous solutions are obtained for α independently of φ. These solutions are physical, the fluid obeys an equation of state p=ρ (stiff matter), and the space-time admits, apparently, only a group G2 of isometries. A vacuum family is also obtained in this case. [ABSTRACT FROM AUTHOR]