Comparison of Algorithms for Determination of Rotation Measure and Faraday Structure. I. 1100–1400 MHZ

Abstract

Faraday rotation measures (RMs) and more general Faraday structures are key parameters for studying cosmic magnetism and also are sensitive probes of faint ionized thermal gas. There is a need to define what derived quantities are required for various scientific studies, and then to address the challenges in determining Faraday structures. A wide variety of algorithms have been proposed to reconstruct these structures. In preparation for the Polarization Sky Survey of the Universe's Magnetism (POSSUM) to be conducted with the Australian Square Kilometre Array Pathfinder (ASKAP) and the ongoing Galactic Arecibo L-band Feeds Array Continuum Transit Survey (GALFACTS), we run a Faraday structure determination data challenge to benchmark the currently available algorithms including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling and QU -fitting. The input models include sources with one Faraday thin component, two Faraday thin components and one Faraday thick component. The frequency set is similar to POS-SUM/GALFACTS with a 300-MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: a) an average RM weighted by polarized intensity, RM wtd , b) the separation ∆φ of two Faraday components and c) the reduced chi-squared χ 2 r . Based on the current test data of signal to noise ratio of about 32, we find that: (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found; (2) For two Faraday thin components, QU -fitting routines perform the best, with errors close to the theoretical ones for RM wtd , but with significantly higher errors for ∆φ. All other methods including standard Faraday synthesis frequently identify only one component when ∆φ is below or near the width of the Faraday point spread function; (3) No methods, as currently implemented, work well for Faraday thick components due to the narrow bandwidth; (4) There exist combinations of two Faraday components which produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model. Further exploration of all these issues is required before upcoming surveys will be able to provide reliable results on Faraday structures.

A STUDY OF BROADBAND FARADAY ROTATION AND POLARIZATION BEHAVIOR OVER 1.3–10 GHz IN 36 DISCRETE RADIO SOURCES

“…For sources possessing multiple S components, the primary issue for interpretation of the polarization data is degeneracy of the fitted polarization models over narrow bands (O'Sullivan et al 2012;Sun et al 2015). The frequency-dependent instantaneous RM values (i.e., y l ¶ ¶ 2 ) of many of our sources can deviate from the RM value determined from a Faraday simple model fit to low frequency, narrowband data by 10 s-100 s of rad m −2 .…”

“…We point out that our method avoids the deconvolution ambiguities that afflict the so-called open-ended spectropolarimetric analysis algorithms (see Sun et al 2015), while at the same time, it avoids making significant a priori assumptions about the magneto-ionic structure of the source under study. It therefore combines some of the benefits of open-ended methods with those of QU-fitting, however, with the drawback that using Monte Carlo methods (see Section 4.3 below), the fitting process can be quite time-consuming.…”

Study of the Vertical Magnetic Field in Face-on Galaxies Using Faraday Tomography

“…The first requires wide frequency coverage observations of P(λ 2 ), which can be provided by, for instance, the Square Kilometre Array (SKA) and its pathfinders and precursors, such as LOFAR, ASKAP, MeerKAT, MWA, and HERA. Various approaches for it have been suggested (e.g., Sun et al 2015 and references therein). The second requires a successful interpretation of F(f).…”

Broadband Polarimetry with the Square Kilometre Array: A Unique Astrophysical Probe

“…6 resolution) of ≈ 0.1 mJy beam −1 (Rudnick & Owen 2014). The signal-to-noise ratio required for analyses such as that shown in Figure 1 is a topic under active investigation (Sun et al 2014), but preliminary results suggest that a 20σ detection is sufficient. We therefore require an rms sensitivity of 5 µJy beam −1 over the entire bandpass (650-1670 MHz).…”