A new method to suppress the bias in polarised intensity

Abstract

Context. Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. Aims. We aim to develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that closely follows the signal from the source. Methods. We propose a new method to suppress the bias by estimating the polarisation angle of the source signal in a noisy environment with help of a modified median filter. We then determine the polarised intensity, including the noise, by projection of the observed values of Stokes U and Q onto the direction of this polarisation angle. Results. We show that our new method represents the true signal very well. If the noise distribution in the maps of U and Q is Gaussian, then in the corrected map of polarised intensity it is also Gaussian. Smoothing to larger Gaussian beamsizes, to improve the signal-to-noise ratio, can be done directly with our method in the map of the polarised intensity. Our method also works in case of non-Gaussian noise distributions. Conclusions. The maps of the corrected polarised intensities and polarisation angles are reliable even in regions with weak signals and provide integrated flux densities and degrees of polarisation without the cumulative effect of the bias, which especially affects faint sources. Features at low intensity levels like "depolarisation canals" are smoother than in the maps using the previous methods, which has broader implications, for example on the interpretation of interstellar turbulence.

Magnetic fields and cosmic rays in M 31

“…This "basket-weaving" technique reduces the scanning effects in the coverages. It was originally developed by Chris Salter (see Sieber et al 1979 The resulting maps in Q and U were combined into a map of polarized intensity (PI) and polarization angle with the PolInt option that includes a correction for positive bias due to noise and ensures that the PI map has the same (Gaussian) noise statistics as the maps in Q and U (Müller et al 2017b). Hence, we give only the noise values for PI in Table 2.…”

JCMT BISTRO Survey Observations of the Ophiuchus Molecular Cloud: Dust Grain Alignment Properties Inferred Using a Ricean Noise Model

“…This results in a strong positive bias in measured polarization fraction at low total intensities. Several methods of correcting for this bias have been proposed, of varying levels of sophistication (Wardle & Kronberg 1974;Simmons & Stewart 1985;Vaillancourt 2006;Quinn 2012;Montier et al 2015a,b;Vidal et al 2016;Müller et al 2017). These methods are collectively known as (statistical) debiasing.…”

Magnetic fields and cosmic rays in M 31. I. Spectral indices, scale lengths, Faraday rotation, and magnetic field pattern

“…The resulting maps in Q and U were combined into a map of polarized intensity (PI) and polarization angle with the PolInt option that includes a correction for positive bias due to noise and ensures that the PI map has the same (Gaussian) noise statistics as the maps in Q and U (Müller et al 2017a). Hence, we give only the noise values for PI in Table 2.…”