We present the projected Rayleigh statistic (PRS), a modification of the classic Rayleigh statistic, as a test for non-uniform relative orientation between two pseudovector 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 largerscale 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-µm 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-µm band.

Wave effects are often neglected in microlensing studies; however, for coherent point-like sources, such as pulsars and fast radio bursts (FRBs), wave effects will become important in their gravitational lensing. In this paper, we describe the wave-optics formalism, its various limits, and the conditions for which these limits hold. Using the simple point lens as an example, we show that the frequency dependence of wave effects breaks degeneracies that are present in the usual geometric optics limit, and constructive interference results in larger magnifications further from the lens. This latter fact leads to a generic increase in cross-section for microlensing events in the wave-optics regime compared to the geometric optics regime. For realistic per cent-level spectral sensitivities, this leads to a relative boost in lensing cross-section of more than an order of magnitude. We apply the point-lens model to the lensing of FRBs and pulsars and find that these radio sources will be lensed in the full wave-optics regime by isolated masses in the range of $0.1\!-\!100\,{\rm M}_\oplus$, which includes free-floating planets (FFPs), whose Einstein radius is smaller than the Fresnel scale. More generally, the interference pattern allows an instantaneous determination of lens masses, unlike traditional microlensing techniques that only yield a mass inference from the event time-scale.

We investigate recent claims for a detection of "Hawking points" (positions on the sky with unusually large temperature gradients between rings) in the cosmic microwave background (CMB) temperature maps at the 99.98 % confidence level. We find that, after marginalization over the size of the rings, an excess is detected in Planck satellite maps at only an 87 % confidence level (i.e., little more than 1 σ). Therefore, we conclude that there is no statistically significant evidence for the presence of Hawking points in the CMB.

The study of astrophysical plasma lensing, such as in the case of extreme scattering events, has typically been conducted using the geometric limit of optics, neglecting wave effects. However, for the lensing of coherent sources such as pulsars and fast radio bursts (FRBs), wave effects can play an important role. Asymptotic methods, such as the so-called Eikonal limit, also known as the stationary phase approximation, have been used to include first-order wave effects; however, these methods are discontinuous at Stokes lines. Stokes lines are generic features of a variety of lens models, and are regions in parameter space where imaginary images begin to contribute to the overall intensity modulation of lensed sources. Using the mathematical framework of Picard-Lefschetz theory to compute diffraction integrals, we argue that these imaginary images contain as much information as their geometric counterparts, and may potentially be observable in data. Thus, weak-lensing events where these imaginary images are present can be as useful for inferring lens parameters as strong-lensing events in which multiple geometric images are present.