An application of an optimal statistic for characterising relative orientations

TL;DR

This paper introduces the projected Rayleigh statistic (PRS), a new statistical method for analyzing the relative orientations of pseudo-vector fields, demonstrating its superior efficiency over traditional binning methods in astrophysical data analysis.

Contribution

The paper presents the PRS as an improved statistical tool for characterizing relative orientations, with demonstrated higher power in astrophysical applications.

Findings

PRS outperforms binning methods in statistical power

Higher significance in detecting alignments in Vela C data

Increased detection sensitivity by up to 30%

Abstract

We present the projected Rayleigh statistic (PRS), a modification of the classic Rayleigh statistic, as a test for non-uniform relative orientation between two pseudo-vector fields. In the application here this gives an effective way of investigating whether polarization pseudo-vectors (spin-2 quantities) are preferentially parallel or perpendicular to filaments in the interstellar medium. For example, there are other potential applications in astrophysics, e.g., when comparing small-scale orientations with larger-scale shear patterns. We compare the efficiency of the PRS against histogram binning methods that have previously been used for characterising the relative orientations of gas column density structures with the magnetic field projected on the plane of the sky. We examine data for the Vela C molecular cloud, where the column density is inferred from Herschel submillimetre observations, and the magnetic field from observations by the Balloon-borne Large-Aperture Submillimetre Telescope in the 250-, 350-, and 500-{\mu}m wavelength bands. We find that the PRS has greater statistical power than approaches that bin the relative orientation angles, as it makes more efficient use of the information contained in the data. In particular, the use of the PRS to test for preferential alignment results in a higher statistical significance, in each of the four Vela C regions, with the greatest increase being by a factor 1.3 in the South-Nest region in the 250-{\mu}m band.