A novel estimator of the polarization amplitude from normally distributed Stokes parameters

We propose a novel estimator of the polarization amplitude from a single measurement of its normally distributed $(Q,U)$ Stokes components. Based on the properties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), it meets several desirable criteria:(i) its values lie in the whole positive region; (ii) its distribution is continuous; (iii) it transforms smoothly with the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one; (iv) it is unbiased and reaches its components' variance as soon as the SNR exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We also revisit the construction of its associated confidence intervals and show how the Feldman-Cousins prescription efficiently solves the issue of classical intervals lying entirely in the unphysical negative domain. Such intervals can be used to identify statistically significant polarized regions and conversely build masks for polarization data. We then consider the case of a general $[Q,U]$ covariance matrix and perform a generalization of the estimator that preserves its asymptotic properties. We show that its bias does not depend on the true polarization angle, and provide an analytic estimate of its variance. The estimator value, together with its variance, provide a powerful point-estimate of the true polarization amplitude that follows an unbiased Gaussian distribution for a SNR as low as 2. These results can be applied to the much more general case of transforming any normally distributed random variable from Cartesian to polar coordinates.Comment: Accepted by MNRA

The Infrared Luminosity of Galaxy Clusters

The aim of this study is to quantify the infrared luminosity of clusters as a function of redshift and compare this with the X-ray luminosity. This can potentially constrain the origin of the infrared emission to be intracluster dust and/or dust heated by star formation in the cluster galaxies. We perform a statistical analysis of a large sample of galaxy clusters selected from existing databases and catalogues.We coadd the infrared IRAS and X-ray RASS images in the direction of the selected clusters within successive redshift intervals up to z = 1. We find that the total infrared luminosity is very high and on average 20 times higher than the X-ray luminosity. If all the infrared luminosity is to be attributed to emission from diffuse intracluster dust, then the IR to X-ray ratio implies a dust-to-gas mass abundance of 5e-4. However, the infrared luminosity shows a strong enhancement for 0.1 < z < 1, which cannot be attributed to cluster selection effects. We show that this enhancement is compatible with a star formation rate in the member galaxies that is typical of the central Mpc of the Coma cluster at z = 0 and evolves with the redshift as (1+z)^5. It is likely that most of the infrared luminosity that we measure is generated by the ongoing star formation in the member galaxies. From theoretical predictions calibrated on extinction measurements (dust mass abundance equal to 1e-5), we expect only a minor contribution, of a few percent, from intracluster dust.Comment: 9 pages, 7 figures, accepted july 31st 2008 for publication in Astronomy and Astrophysics, language improved for this versio

Polarization measurements analysis II. Best estimators of polarization fraction and angle

With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, it becomes critical to evaluate the performance of estimators for the polarization fraction and angle. These two physical quantities suffer from a well-known bias in the presence of measurement noise, as has been described in part I of this series. In this paper, part II of the series, we explore the extent to which various estimators may correct the bias. Traditional frequentist estimators of the polarization fraction are compared with two recent estimators: one inspired by a Bayesian analysis and a second following an asymptotic method. We investigate the sensitivity of these estimators to the asymmetry of the covariance matrix which may vary over large datasets. We present for the first time a comparison among polarization angle estimators, and evaluate the statistical bias on the angle that appears when the covariance matrix exhibits effective ellipticity. We also address the question of the accuracy of the polarization fraction and angle uncertainty estimators. The methods linked to the credible intervals and to the variance estimates are tested against the robust confidence interval method. From this pool of estimators, we build recipes adapted to different use-cases: build a mask, compute large maps, and deal with low S/N data. More generally, we show that the traditional estimators suffer from discontinuous distributions at low S/N, while the asymptotic and Bayesian methods do not. Attention is given to the shape of the output distribution of the estimators, and is compared with a Gaussian. In this regard, the new asymptotic method presents the best performance, while the Bayesian output distribution is shown to be strongly asymmetric with a sharp cut at low S/N.Finally, we present an optimization of the estimator derived from the Bayesian analysis using adapted priors

Multi-wavelength characterisation of z~2 clustered, dusty star forming galaxies discovered by Planck

(abridged) We report the discovery of PHz G95.5-61.6, a complex structure detected in emission in the Planck all-sky survey that corresponds to two over-densities of high-redshift galaxies. This is the first source from the Planck catalogue of high-z candidates that has been completely characterised with follow-up observations from the optical to the sub-millimetre domain. Herschel/SPIRE observations at 250, 350 and 500 microns reveal the existence of five sources producing a 500 microns emission excess that spatially corresponds to the candidate proto-clusters discovered by Planck. Further observations at CFHT in the optical bands (g and i) and in the near infrared (J, H and K_s), plus mid infrared observations with IRAC/Spitzer (at 3.6 and 4.5 microns) confirm that the sub-mm red excess is associated with an over-density of colour-selected galaxies. Follow-up spectroscopy of 13 galaxies with VLT/X-Shooter establishes the existence of two high-z structures: one at z~1.7 (three confirmed member galaxies), the other at z~2.0 (six confirmed members). This double structure is also seen in the photometric redshift analysis of a sample of 127 galaxies located inside a circular region of 1'-radius containing the five Herschel/SPIRE sources, where we found a double-peaked excess of galaxies at z~1.7 and z~2.0 with respect to the surrounding region. These results suggest that PHz G95.5-61.6 corresponds to two accreting nodes, not physically linked to one another, embedded in the large scale structure of the Universe at z~2 and along the same line-of-sight. In conclusion, the data, methods and results illustrated in this pilot project confirm that Planck data can be used to detect the emission from clustered, dusty star forming galaxies at high-z, and, thus, to pierce through the early growth of cluster-scale structures.Comment: 15 pages, 13 figures. Accepted for publication in Astronomy and Astrophysic

Infrared properties of the SDSS-maxBCG galaxy clusters

The physics of galaxy clusters has proven to be influenced by several processes connected with their galactic component which pollutes the ICM with metals, stars and dust. However, it is not clear whether the presence of diffuse dust can play a role in clusters physics since a characterisation of the IR properties of galaxy clusters is yet to be completely achieved. We focus on the recent work of Giard et al. (2008) who performed a stacking analysis of the IRAS data in the direction of several thousands of galaxy clusters, providing a statistical characterisation of their IR luminosity and redshift evolution. We model the IR properties of the galactic population of the SDSS-maxBCG clusters (0.1<z<0.3) in order to check if it accounts for the entire observed signal and to constrain the possible presence of other components, like dust in the ICM. Starting from the optical properties of the galaxy members, we estimate their emission in the 60 and 100 micron IRAS bands making use of modeled SEDs of different spectral types (E/S0, Sa, Sb, Sc and starburst). We also consider the evolution of the galactic population/luminosity with redshift. Our results indicate that the galactic emission, which is dominated by the contribution of star-forming galaxies, is consistent with the observed signal. In fact, our model slightly overestimates the observed fluxes, with the excess being concentrated in low-redshift clusters (z <~ 0.17). This indicates that, if present, the IR emission from intracluster dust must be very small. We obtain an upper limit on the dust-to-gas mass ratio in the ICM of Z_d <~ 5 10^-5. The excess in luminosity obtained at low redshift constitutes an indication that the cluster environment is driving a process of star-formation quenching in its galaxy members.Comment: 12 pages, 6 figures, 2 tables. Accepted for publication in A&

Variations of the spectral index of dust emissivity from Hi-GAL observations of the Galactic plane

Original article can be found at: http://www.aanda.org/ Copyright The European Southern ObservatoryContext. Variations in the dust emissivity are critical for gas mass determinations derived from far-infrared observations, but also for separating dust foreground emission from the Cosmic Microwave Background (CMB). Hi-GAL observations allow us for the first time to study the dust emissivity variations in the inner regions of the Galactic plane at resolution below 1°. Aims. We present maps of the emissivity spectral index derived from the combined Herschel PACS 160 μm, SPIRE 250 μm, 350 μm, and 500 μm data, and the IRIS 100 μm data, and we analyze the spatial variations of the spectral index as a function of dust temperature and wavelength in the two science demonstration phase Hi-GAL fields, centered at l = 30° and l = 59°. Methods. Applying two different methods, we determine both dust temperature and emissivity spectral index between 100 and 500 μm, at an angular resolution (θ) of 4'. Results. Combining both fields, the results show variations of the emissivity spectral index in the range 1.8–2.6 for temperatures between 14 and 23 K. The median values of the spectral index are similar in both fields, i.e. 2.3 in the range 100–500 μm, while the median dust temperatures are equal to 19.1 K and 16.0 K in the l = 30° and l = 59° field, respectively. Statistically, we do not see any significant deviations in the spectra from a power law emissivity between 100 and 500 μm. We confirm the existence of an inverse correlation between the emissivity spectral index and dust temperature, found in previous analyses.Peer reviewe

Model Order Reduction applied to a linear Finite Element model of a squirrel cage induction machine based on POD approach

The Proper Orthogonal Decomposition (POD) approach is applied to a linear Finite Element (FE) model of a squirrel cage induction machine. In order to obtain a reduced model valid on the whole operating range, snapshots are extracted from the simulation of typical tests such as at locked rotor and at the synchronous speed. Then, the reduced model of the induction machine is used to simulate different operating points with variable rotation speed and the results are compared to the full FE model to show the effectiveness of the proposed approach

The Good, the Bad, and the Ugly: Statistical quality assessment of SZ detections

International audienceWe examine three approaches to the problem of source classification in catalogues. Our goal is to determine the confidence withwhich the elements in these catalogues can be distinguished in populations on the basis of their spectral energy distribution (SED).Our analysis is based on the projection of the measurements onto a comprehensive SED model of the main signals in the consideredrange of frequencies. We first consider likelihood analysis, which is halfway between supervised and unsupervised methods. Next, weinvestigate an unsupervised clustering technique. Finally, we consider a supervised classifier based on artificial neural networks. Weillustrate the approach and results using catalogues from various surveys, such as X-rays (MCXC), optical (SDSS), and millimetric(Planck Sunyaev-Zeldovich (SZ)). We show that the results from the statistical classifications of the three methods are in very goodagreement with each other, although the supervised neural network-based classification shows better performance allowing the bestseparation into populations of reliable and unreliable sources in catalogues. The latest method was applied to the SZ sources detectedby the Planck satellite. It led to a classification assessing and thereby agreeing with the reliability assessment published in the PlanckSZ catalogue. Our method could easily be applied to catalogues from future large surveys such as SRG/eROSITA and Euclid

The good, the bad, and the ugly: Statistical quality assessment of SZ detections

We examine three approaches to the problem of source classification in catalogues. Our goal is to determine the confidence with which the elements in these catalogues can be distinguished in populations on the basis of their spectral energy distribution (SED). Our analysis is based on the projection of the measurements onto a comprehensive SED model of the main signals in the considered range of frequencies. We first consider likelihood analysis, which is halfway between supervised and unsupervised methods. Next, we investigate an unsupervised clustering technique. Finally, we consider a supervised classifier based on artificial neural networks. We illustrate the approach and results using catalogues from various surveys, such as X-rays (MCXC), optical (SDSS), and millimetric (Planck Sunyaev-Zeldovich (SZ)). We show that the results from the statistical classifications of the three methods are in very good agreement with each other, although the supervised neural network-based classification shows better performance allowing the best separation into populations of reliable and unreliable sources in catalogues. The latest method was applied to the SZ sources detected by the Planck satellite. It led to a classification assessing and thereby agreeing with the reliability assessment published in the Planck SZ catalogue. Our method could easily be applied to catalogues from future large surveys such as SRG/eROSITA and Euclid.We acknowledge the support of the French Agence Nationale de la Recherche under grant ANR-11-BD56-015. The development of Planck has been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN and JA (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU).Peer Reviewe