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 f
rom 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.
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.
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 desira
ble 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.
We present a possible identification strategy for first hydrostatic core (FHSC) candidates and make predictions of ALMA dust continuum emission maps from these objects. We analyze the results given by the different bands and array configurations and
identify which combinations of the two represent our best chance of solving the fragmentation issue in these objects. If the magnetic field is playing a role, the emission pattern will show evidence of a pseudo-disk and even of a magnetically driven outflow, which pure hydrodynamical calculations cannot reproduce.
The S3-Tools are a set of Python-based routines and interfaces whose purpose is to provide user-friendly access to the SKA Simulated Skies (S3) set of simulations, an effort led by the University of Oxford in the framework of the European Unions SKAD
S program (http://www.skads-eu.org). The databases built from the S3 simulations are hosted by the Oxford e-Research Center (OeRC), and can be accessed through a web portal at http://s-cubed.physics.ox.ac.uk. This paper focuses on the practical steps involved to make radio images from the S3-SEX and S3-SAX simulations using the S3-Map tool and should be taken as a broad overview. For a more complete description, the interested reader should look up the users guide. The output images can then be used as input to instrument simulators, e.g. to assess technical designs and observational strategies for the SKA and SKA pathfinders.
We investigate the case of CII 158 micron observations for SPICA/SAFARI using a three-dimensional magnetohydrodynamical (MHD) simulation of the diffuse interstellar medium (ISM) and the Meudon PDR code. The MHD simulation consists of two converging f
lows of warm gas (10,000 K) within a cubic box 50 pc in length. The interplay of thermal instability, magnetic field and self-gravity leads to the formation of cold, dense clumps within a warm, turbulent interclump medium. We sample several clumps along a line of sight through the simulated cube and use them as input density profiles in the Meudon PDR code. This allows us to derive intensity predictions for the CII 158 micron line and provide time estimates for the mapping of a given sky area.
Fourier phases contain a vast amount of information about structure in direct space, that most statistical tools never tap into. We address ALMAs ability to detect and recover this information, using the probability distribution function (PDF) of pha
se increments, and the related concepts of phase entropy and phase structure quantity. We show that ALMA, with its high dynamical range, is definitely needed to achieve significant detection of phase structure, and that it will do so even in the presence of a fair amount of atmospheric phase noise. We also show that ALMA should be able to recover the actual amount of phase structure in the noise-free case, if multiple configurations are used.
