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

Simulated CII observations for SPICA/SAFARI

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 flows 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.Comment: 4 pages, 5 figures, to appear in the proceedings of the workshop "The Space Infrared Telescope for Cosmology & Astrophysics: Revealing the Origins of Planets and Galaxies" (July 2009, Oxford, United Kingdom

SKA HI end2end simulation

The current status of the HI simulation efforts is presented, in which a self consistent simulation path is described and basic equations to calculate array sensitivities are given. There is a summary of the SKA Design Study (SKADS) sky simulation and a method for implementing it into the array simulator is presented. A short overview of HI sensitivity requirements is discussed and expected results for a simulated HI survey are presented.Comment: 7 pages, 6 figues, need skads2009.cls file to late

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

Magnetic field morphology in nearby molecular clouds as revealed by starlight and submillimetre polarization

Within four nearby (d < 160 pc) molecular clouds, we statistically evaluate the structure of the interstellar magnetic field, projected on the plane of the sky and integrated along the line of sight, as inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz and from the optical and NIR polarization of background starlight. We compare the dispersion of the field orientation directly in vicinities with an area equivalent to that subtended by the Planck effective beam at 353 GHz (10') and using the second-order structure functions of the field orientation angles. We find that the average dispersion of the starlight-inferred field orientations within 10'-diameter vicinities is less than 20 deg, and that at these scales the mean field orientation is on average within 5 deg of that inferred from the submillimetre polarization observations in the considered regions. We also find that the dispersion of starlight polarization orientations and the polarization fractions within these vicinities are well reproduced by a Gaussian model of the turbulent structure of the magnetic field, in agreement with the findings reported by the Planck collaboration at scales greater than 10' and for comparable column densities. At scales greater than 10', we find differences of up to 14.7 deg between the second-order structure functions obtained from starlight and submillimetre polarization observations in the same positions in the plane of the sky, but comparison with a Gaussian model of the turbulent structure of the magnetic field indicates that these differences are small and are consistent with the difference in angular resolution between both techniques.Comment: 15 pages, 10 figures, submitted to A&

First detection of [N II] 205 micrometer absorption in interstellar gas

We present high resolution [NII] 205 micrometer ^3P_1-^3P_0 spectra obtained with Herschel-HIFI towards a small sample of far-infrared bright star forming regions in the Galactic plane: W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. All sources display an emission line profile associated directly with the HII regions themselves. For the first time we also detect absorption of the [NII] 205 micrometer line by extended low-density foreground material towards W31C and W49N over a wide range of velocities. We attribute this absorption to the warm ionised medium (WIM) and find N(N^+)\approx 1.5x10^17 cm^-2 towards both sources. This is in agreement with recent Herschel-HIFI observations of [CII] 158 micrometer, also observed in absorption in the same sight-lines, if \approx7-10 % of all C^+ ions exist in the WIM on average. Using an abundance ratio of [N]/[H] = 6.76x10^-5 in the gas phase we find that the mean electron and proton volume densities are ~0.1-0.3 cm^-3 assuming a WIM volume filling fraction of 0.1-0.4 with a corresponding line-of-sight filling fraction of 0.46-0.74. A low density and a high WIM filling fraction are also supported by RADEX modelling of the [NII] 205 micrometer absorption and emission together with visible emission lines attributed mainly to the WIM. The detection of the 205 micrometer line in absorption emphasises the importance of a high spectral resolution, and also offers a new tool for investigation of the WIM.Comment: 7 pages, 4 figures, accepted for publication in Astronomy & Astrophysics, 11 June 201

On the use of fractional Brownian motion simulations to determine the 3D statistical properties of interstellar gas

Based on fractional Brownian motion (fBm) simulations of 3D gas density and velocity fields, we present a study of the statistical properties of spectro-imagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index gamma_W of the integrated emission is identified with that of the 3D density field (gamma_n) provided the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index gamma_C as that of the velocity field (gamma_v). Further tests with non-fBm density and velocity fields show that this last result holds, and is not modified either by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan (2000).Comment: 28 pages, 14 figures, accepted for publication in ApJ. For preprint with higher-resolution figures, see http://www.cita.utoronto.ca/~mamd/miville_fbm2003.pd

A Virtual Sky with Extragalactic HI and CO Lines for the SKA and ALMA

We present a sky simulation of the atomic HI emission line and the first ten CO rotational emission lines of molecular gas in galaxies beyond the Milky Way. The simulated sky field has a comoving diameter of 500/h Mpc, hence the actual field-of-view depends on the (user-defined) maximal redshift zmax; e.g. for zmax=10, the field of view yields ~4x4 sqdeg. For all galaxies, we estimate the line fluxes, line profiles, and angular sizes of the HI and CO emission lines. The galaxy sample is complete for galaxies with cold hydrogen masses above 10^8 Msun. This sky simulation builds on a semi-analytic model of the cosmic evolution of galaxies in a Lambda-cold dark matter (LCDM) cosmology. The evolving CDM-distribution was adopted from the Millennium Simulation, an N-body CDM-simulation in a cubic box with a side length of 500/h Mpc. This side length limits the coherence scale of our sky simulation: it is long enough to allow the extraction of the baryon acoustic oscillations (BAOs) in the galaxy power spectrum, yet the position and amplitude of the first acoustic peak will be imperfectly defined. This sky simulation is a tangible aid to the design and operation of future telescopes, such the SKA, the LMT, and ALMA. The results presented in this paper have been restricted to a graphical representation of the simulated sky and fundamental dN/dz-analyzes for peak flux density limited and total flux limited surveys of HI and CO. A key prediction is that HI will be harder to detect at redshifts z>2 than predicted by a no-evolution model. The future verification or falsification of this prediction will allow us to qualify the semi-analytic models.Comment: 16 pages, 9 figures, 1 tabl