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Register a new userPolarization measurements analysis II. Best estimators of polarization fraction and angle
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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.
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With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, the metrology of polarization needs to improve. In particular, it is crucial to take into account full knowledge of the noise properties when estimating polarization fraction and angle, which suffer from well-known biases. While strong simplifying assumptions have usually been made in polarization analysis, we present a method for including the full covariance matrix of the Stokes parameters in estimates for the distributions of the polarization fraction and angle. We thereby quantify the impact of the noise properties on the biases in the observational quantities. We derive analytical expressions for the pdf of these quantities, taking into account the full complexity of the covariance matrix, including the Stokes I intensity components. We perform simulations to explore the impact of the noise properties on the statistical variance and bias of the polarization fraction and angle. We show that for low variations of the effective ellipticity between the Q and U components around the symmetrical case the covariance matrix may be simplified as is usually done, with negligible impact on the bias. For S/N on intensity lower than 10 the uncertainty on the total intensity is shown to drastically increase the uncertainty of the polarization fraction but not the relative bias, while a 10% correlation between the intensity and the polarized components does not significantly affect the bias of the polarization fraction. We compare estimates of the uncertainties affecting polarization measurements, addressing limitations of estimates of the S/N, and we show how to build conservative confidence intervals for polarization fraction and angle simultaneously. This study is the first of a set of papers dedicated to the analysis of polarization measurements.
High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence of measurement noise. It is critical to take into account all the information available in the data in order to accurately derive these parameters. The goal of this paper is to characterize the bias on the polarization angle dispersion function that is used to study the spatial coherence of the polarization angle. We characterize, for the first time, the bias on the conventional estimator of the polarization angle dispersion function (S hereafter) and show that it can be positive or negative depending on the true value. Monte Carlo simulations are performed in order to explore the impact of the noise properties of the polarization data, as well as the impact of the distribution of the true polarization angles on the bias. We show that in the case where the ellipticity of the noise in (Q, U) varies by less than 10 percent, one can use simplified, diagonal approximation of the noise covariance matrix. In other cases, the shape of the noise covariance matrix should be taken into account in the estimation of S. We also study new estimators such as the dichotomic and the polynomial estimators. Though the dichotomic estimator cannot be directly used to estimate S, we show that, on the one hand, it can serve as an indicator of the accuracy of the conventional estimator and, on the other hand, it can be used for deriving the polynomial estimator. We propose a method for determining the upper limit of the bias on the conventional estimator of S. The method is applicable to any linear polarization data set for which the noise covariance matrices are known.
Since more than a century astronomers measure the position angle of the major axis of the polarization ellipse starting from the North direction and increasing counter-clockwise, when looking at the source. This convention has been enforced by the IAU with a Resolution in 1973. Much later the WMAP satellite, which has observed the polarization of the cosmic microwave background, has unfortunately adopted the opposite convention: the polarization position angle is measured starting from the South and increasing clockwise, when looking at the source. This opposite convention has been followed by most cosmic microwave background polarization experiments and is causing obvious problems and misunderstandings. The attempts and prospects to enforce the official IAU convention are described.
We sketch the proposal for a PVLAS-Phase II experiment. The main physics goal is to achieve the first direct observation of non-linear effects in electromagnetism predicted by QED and the measurement of the photon-photon scattering cross section at low energies (1-2 eV). Physical processes such as ALP and MCP production in a magnetic field could also be accessible if sensitive enough operation is reached. The short term experimental strategy is to compact as much as possible the dimensions of the apparatus in order to bring noise sources under control and to attain a sufficient sensitivity. We will also briefly mention future pespectives, such as a scheme to implement the resonant regeneration principle for the detection of ALPs.
We present results for Vela C obtained during the 2012 flight of the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol). We mapped polarized intensity across almost the entire extent of this giant molecular cloud, in bands centered at 250, 350, and 500 {mu}m. In this initial paper, we show our 500 {mu}m data smoothed to a resolution of 2.5 arcminutes (approximately 0.5 pc). We show that the mean level of the fractional polarization p and most of its spatial variations can be accounted for using an empirical three-parameter power-law fit, p = p_0 N^(-0.4) S^(-0.6), where N is the hydrogen column density and S is the polarization-angle dispersion on 0.5 pc scales. The decrease of p with increasing S is expected because changes in the magnetic field direction within the cloud volume sampled by each measurement will lead to cancellation of polarization signals. The decrease of p with increasing N might be caused by the same effect, if magnetic field disorder increases for high column density sightlines. Alternatively, the intrinsic polarization efficiency of the dust grain population might be lower for material along higher density sightlines. We find no significant correlation between N and S. Comparison of observed submillimeter polarization maps with synthetic polarization maps derived from numerical simulations provides a promising method for testing star formation theories. Realistic simulations should allow for the possibility of variable intrinsic polarization efficiency. The measured levels of correlation among p, N, and S provide points of comparison between observations and simulations.
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