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Intermittent magnetic structures are a plausible candidate for explaining cosmic-ray (CR) diffusion rates derived from observed CR energy spectra. Independently, studies of extreme scattering events (ESEs) of radio quasars and pulsar scintillation have hinted that very straight, large-aspect-ratio, magnetic current sheets may be responsible for the localized large scattering of radio waves. The required shortest axis of the typical structures producing ESEs is of the same scale ($\sim$AU) as the gyroradii of $\sim$GeV CRs. In this paper, we propose that the same magnetic/density sheets can produce large scattering of both CRs and radio waves. We demonstrate that the geometry and volume filling factor of the sheets derived from quasar ESEs can explain the observed mean free path of GeV CRs without introducing free parameters. The model places constraints on the sheet geometry, such as straightness and large aspect ratio, and assumes the statistics of the sheets are similar throughout the Galactic volume. We, therefore, discuss observational tests of the sheet model, which includes observations of echoes in pulsars and fast radio bursts, gravitationally lensed quasars, the distribution of ESE durations, and spatial correlations between ESE events and rotation-measure fluctuations. Such tests will be enabled by upcoming wide-field radio instruments, including Canadian Hydrogen Observatory and Radio-transient Detector (CHORD) and Deep Synoptic Array 2000 Antennas (DSA-2000)., Comment: 21 Pages, 9 Figures. Comments welcome

As part of the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) project, we report 41 new Rotation Measures (RMs) from 20 repeating Fast Radio Bursts (FRBs) obtained between 2019 and 2023 for which no previous RM was determined. We also report 22 additional RM measurements for eight further repeating FRBs. We observe temporal RM variations in practically all repeating FRBs. Repeaters appear to be separated into two categories: those with dynamic and those with stable RM environments, differentiated by the ratios of RM standard deviations over the averaged RM magnitudes. Sources from stable RM environments likely have little RM contributions from the interstellar medium (ISM) of their host galaxies, whereas sources from dynamic RM environments share some similarities with Galactic pulsars in eclipsing binaries but appear distinct from Galactic centre solitary pulsars. We observe a new stochastic, secular, and again stochastic trend in the temporal RM variation of FRB 20180916B, which does not support binary orbit modulation being the reason for this RM changes. We highlight two more repeaters that show RM sign change, namely FRBs 20290929C and 20190303A. We perform an updated comparison of polarization properties between repeating and non-repeating FRBs, which show a marginal dichotomy in their distribution of electron-density-weighted parallel-component line-of-sight magnetic fields., Comment: Submitted to ApJ

Fast radio bursts (FRBs) are unique probes of extragalactic ionized baryonic structure as each signal, through its burst properties, holds information about the ionized matter it encounters along its sightline. FRB 20200723B is a burst with a scattering timescale of $\tau_\mathrm{400\,MHz} >$1 second at 400 MHz and a dispersion measure of DM $\sim$ 244 pc cm$^{-3}$. Observed across the entire CHIME/FRB frequency band, it is the single-component burst with the largest scattering timescale yet observed by CHIME/FRB. The combination of its high scattering timescale and relatively low dispersion measure present an uncommon opportunity to use FRB 20200723B to explore the properties of the cosmic web it traversed. With an $\sim$arcminute-scale localization region, we find the most likely host galaxy is NGC 4602 (with PATH probability $P(O|x)=0.985$), which resides $\sim$30 Mpc away within a sheet filamentary structure on the outskirts of the Virgo Cluster. We place an upper limit on the average free electron density of this filamentary structure of $\langle n_e \rangle < 4.6^{+9.6}_{-2.0} \times 10^{-5}$ cm$^{-3}$, broadly consistent with expectations from cosmological simulations. We investigate whether the source of scattering lies within the same galaxy as the FRB, or at a farther distance from an intervening structure along the line of sight. Comparing with Milky Way pulsar observations, we suggest the scattering may originate from within the host galaxy of FRB 20200723B., Comment: 20 pages, 6 figures, submitted. Comments welcome!

The recent discovery of ultra-long wavelength gravitational waves through the advent of pulsar timing arrays (PTA) has opened up new avenues for fundamental science. Here we show that every PTA source will be diffractively lensed by potentially hundreds of galactic disks transverse to its line of sight, leading to modest modulations in the strain, $\Delta h / h \sim 10^{-3} \lambda^{-1}_{1 \rm pc.}$, due to wave lensing effects. The induced interference, or scintillation, pattern will be resolvable by coherent PTAs and may be leveraged, alongside fore-ground redshift information, to make precise measurements of cosmic expansion. If future PTA experiments can achieve enough signal-to-noise to detect these small modulations, hundreds of redshift-distance pairs may be inferred from the diffractive lensing of an individual PTA source.

We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value problem. We show that the behavior is universal and central to the problem of quantum tunneling. These analytically continued complex classical paths enrich the study of real-time Feynman path integrals.

The real-time propagator of the symmetric Rosen-Morse, also known as the symmetric modified P\"oschl-Teller, barrier is expressed in the Picard-Lefschetz path integral formalism using real and complex classical paths. We explain how the interference pattern in the real-time propagator and energy propagator is organized by caustics and Stoke's phenomena, and list the relevant real and complex classical paths as a function of the initial and final position. We discover the occurrence of singularity crossings, where the analytic continuation of the complex classical path no longer satisfies the boundary value problem and needs to be analytically continued. Moreover, we demonstrate how these singularity crossings play a central role in the real-time description of quantum tunneling.

We consider the refractive lensing effects of ionized cool ($T \sim 10^4\,{\rm K}$) gas cloudlets in the circumgalactic medium (CGM) of galaxies. In particular, we discuss the combined effects of lensing from these cloudlets and scintillation from plasma screens in the Milky Way interstellar medium (ISM). We show that, if the CGM comprises a mist of sub-parsec cloudlets with column densities of order $10^{17}\,{\rm cm}^{-2}$ (as predicted by McCourt et al. 2018), then FRBs whose sightlines pass within a virial radius of a CGM halo will may be lensed into tens of refractive images with a $\sim 10\,{\rm ms}$ scattering timescale. When these images are formed, they will be resolved by scintillating screens in the Milky Way ISM, and will suppress the observed scintillation. We illustrate this effect in refractive lensing and argue that positive detections of FRB scintillation may constrain the properties of these cool-gas cloudlets, with current scintillation observation weakly disfavouring the cloudlet model. We propose that sheet-like geometries for the cool gas in the CGM can reconcile quasar absorption measurements (from which we infer the presence of the cool gas with structure on sub-parsec scales) and the unexpected lack of lensing signals from this gas thus far observed.

We propose a novel means of directly measuring cosmological distances using scintillated microlensing of fast radio bursts (FRBs). In standard strong lensing measurements of cosmic expansion, the main source of systematic uncertainty lies in modeling the mass profile of galactic halos. Using extra-galactic stellar microlensing to measure the Hubble constant avoids this systematic uncertainty as the lens potential of microlenses depends only on a single parameter: the mass of the lens. FRBs, which may achieve nanosecond precision on lensing time delays, are well-suited to precision measurements of stellar microlensing, for which the time delays are on the order of milliseconds. However, typical angular separations between the microlensed images on the order of microarcseconds make the individual images impossible to spatially resolve with ground-based telescopes. We propose leveraging scintillation in the ISM to resolve the microlensed images, effectively turning the ISM into an astrophysical-scale interferometer. Using this technique, we estimate a 6\% uncertainty on $H_0$ from a single observed scintillated microlensing event, with a sub-percent uncertainty on $H_0$ achievable with only 30 such events. With an optical depth for stellar microlensing of $10^{-3}$, this may be achievable in the near future with upcoming FRB telescopes.

Wave-mechanical effects in gravitational lensing have long been predicted, and with the discovery of populations of compact transients such as gravitational wave events and fast radio bursts, may soon be observed. We present an observer's review of the relevant theory underlying wave-mechanical effects in gravitational lensing. Starting from the curved-spacetime scalar wave equation, we derive the Fresnel-Kirchoff diffraction integral, and analyze it in the eikonal and wave optics regimes. We answer the question of what makes interference effects observable in some systems but not in others, and how interference effects allow for complementary information to be extracted from lensing systems as compared to traditional measurements. We end by discussing how diffraction effects affect optical depth forecasts and lensing near caustics, and how compact, low-frequency transients like gravitational waves and fast radio bursts provide promising paths to open up the frontier of interferometric gravitational lensing., Comment: Comments and suggestions for additional references welcome

The scattering structures in the ISM responsible for so-called ``extreme scattering events" (ESEs), observed in quasars and pulsars, remain enigmatic. Current models struggle to explain the high-frequency light curves of ESEs, and a recent analysis of a double lensing event in PSR\,B0834+06 reveals features of ESEs that may also be challenging to accommodate via existing models. We propose that these features arise naturally when the lens has a cusp-like profile, described by the elementary $A_3$ cusp catastrophe. This is an extension of previous work describing pulsar scintillation as arising from $A_2$ fold catastrophes in thin, corrugated plasma sheets along the line of sight. We call this framework of describing the lens potentials via elementary catastrophes ``doubly catastrophic lensing", as catastrophes (e.g. folds and cusps) have long been used to describe universal features in the light curves of lensing events that generically manifest, regardless of the precise details of the lens. Here, we argue that the lenses themselves may be described by these same elementary structures. If correct, the doubly catastrophic lensing framework would provide a unified description of scintillation and ESEs, where the lenses responsible for these scattering phenomena are universal and can be fully described by a small number of unfolding parameters. This could enable their application as giant cosmic lenses for precision measurements of coherent sources, including FRBs and pulsars., Comment: 10 pages, 10 figures

Recently, several eclipsing millisecond pulsars have been shown to experience strong and apparent weak lensing from the outflow of their ionized companions. Lensing can be a powerful probe of the ionized plasma, with the strongest lenses potentially resolving emission regions of pulsars. Understanding lensing in the `laboratory-like' conditions of an eclipsing pulsar may be analogously applied to fast radio bursts, many of which reside in dense, magnetized environments. We examined variable dispersion measure (DM), absorption, scattering, and flux density in the original Black Widow pulsar PSR B1957+20 through an eclipse at the Arecibo Observatory at 327 MHz. We discovered clear evidence of the two regimes of lensing, strong and apparent weak. We show that the flux density variations in the apparently weak lensing regime can be modeled directly from variations of DM, using geometric optics. The mean effective velocities in the ingress, $954\pm 99$ km/s, and egress $604\pm 47$ km/s cannot be explained by orbital motions alone, but are consistent with significant outflow velocity of material from the companion. We also show that geometric optics can predict when and where the lensing regime-change between weak and strong occurs, and argue that the apparent weak lensing is due to averaging many images. Our framework can be applied in any source with variable electron columns, measuring their relative velocities and distances. In other eclipsing pulsars, this provides a unique opportunity to measure companion outflow velocity, predict regions of weak and strong lensing, and in principle independently constrain orbital inclinations., Comment: 15 pages, 9 figures, 1 table, accepted to MNRAS; v3 journal accepted version

Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Diffractive optics is characterized by a perturbative expansion of the Kirchhoff-Fresnel diffraction integral, while refractive optics is characterized by the stationary phase approximation. Previously, it has been assumed that the Fresnel scale, $R_F$ , is the relevant physical scale that separates these two regimes. With the recent introduction of Picard-Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by $R_F / \sqrt{\kappa}$, where $\kappa$ is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive scintillation (DISS)., Comment: 15 pages, 8 figures

Poncelet's theorem states that if there exists an n-sided polygon which is inscribed in a given conic C and circumscribed about another conic D, then there are infinitely many such n-gons. Proofs of this theorem that we are aware of, including Poncelet's original proof and the celebrated modern proof by Griffiths and Harris, assume the two conics to be in general position (that is, not tangent or at least not osculating), or be defined over the field of complex numbers, or both. Here we show that Poncelet's theorem holds for any two conics C and D in the projective plane over an algebraically closed field k of any characteristic other than two. If C and D are osculating and char(k)>2, our result shows that there always exist infinitely many polygons of char(k) sides that are inscribed in C and circumscribed about D. We also describe the situation in characteristic two in the appendix., Comment: 14 pages; minor changes; to appear in Communications in Algebra

Compact radio sources have been observed to undergo large, frequency dependent changes in intensity due to lensing by structures in the interstellar medium, in so-called "extreme scattering events" (ESEs). While the study of astrophysical plasma lensing has primarily focused on the geometric limit of optics, coherent radio sources such as pulsars exhibit wave effects when lensed. The additional phase information provided by interference effects in the wave regime may yield more information about the lens than could be obtained in the geometric regime. In this paper, we show that, using wave effects, one can potentially distinguish a one-dimensional lens (where "one-dimensional" includes both highly elongated lenses, as well as perfectly axisymmetric lenses) from a fully two-dimensional lens, with minimal assumptions on the form of the lensing potential., Comment: 9 pages, 8 figures

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 fail 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.