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Fast radio bursts (FRBs) are microsecond-to-millisecond-duration radio transients 1 that originate mostly from extragalactic distances. The FRB emission mechanism remains debated, with two main competing classes of models: physical processes that occur within close proximity to a central engine 2 , 3 – 4 ; and relativistic shocks that propagate out to large radial distances 5 , 6 , 7 – 8 . The expected emission-region sizes are notably different between these two types of models 9 . Here we present the measurement of two mutually coherent scintillation scales in the frequency spectrum of FRB 20221022A 10 : one originating from a scattering screen located within the Milky Way, and the second originating from its host galaxy or local environment. We use the scattering media as an astrophysical lens to constrain the size of the observed FRB lateral emission region 9 to ≲3 × 10 4  kilometres. This emission size is inconsistent with the expectation for the large-radial-distance models 5 , 6 , 7 – 8 , and is more naturally explained by an emission process that operates within or just beyond the magnetosphere of a central compact object. Recently, FRB 20221022A was found to exhibit an S-shaped polarization angle swing 10 , most likely originating from a magnetospheric emission process. The scintillation results presented in this work independently support this conclusion, while highlighting scintillation as a useful tool in our understanding of FRB emission physics and progenitors. The detection of scintillation caused by inhomogeneous plasma near a fast radio burst indicates an emission process that occurs within or just beyond the magnetosphere of a compact object.

Annual variations of interstellar scintillation can be modelled to constrain parameters of the ionized interstellar medium. If a pulsar is in a binary system, then investigating the orbital parameters is possible through analysis of the orbital variation of scintillation. In observations carried out from 2011 to 2020 by the European Pulsar Timing Array radio telescopes, PSRs J0613–0200 and J0636+5128 show strong annual variations in their scintillation velocity, while the former additionally exhibits an orbital fluctuation. Bayesian theory and Markov-chain-Monte-Carlo methods are used to interpret these periodic variations. We assume a thin and anisotropic scattering screen model, and discuss the mildly and extremely anisotropic scattering cases. PSR J0613–0200 is best described by mildly anisotropic scattering, while PSR J0636+5128 exhibits extremely anisotropic scattering. We measure the distance, velocity, and degree of anisotropy of the scattering screen for our two pulsars, finding that scattering screen distances from Earth for PSRs J0613–0200 and J0636+5128 are 316 −20 +28 pc and 262 −38 +96 pc, respectively. The positions of these scattering screens are coincident with the shell of the Local Bubble towards both pulsars. These associations add to the growing evidence of the Local Bubble shell as a dominant region of scattering along many sightlines.

We present the interstellar scintillation analysis of fast radio burst (FRB) 20220912A during its extremely active episode in 2022 using data from the Five-hundred-meter Aperture Spherical Radio Telescope (FAST). We detect a scintillation arc in the FRB’s secondary spectrum, which describes the power in terms of the scattered FRB signals’ time delay and Doppler shift. The arc indicates that the scintillation is caused by a highly localized region. Our analysis favors a Milky Way origin of the ionized interstellar medium (IISM) for the localized scattering medium but cannot rule out a host galaxy origin. We present our method for detecting the scintillation arc, which can be applied generally to sources with irregularly spaced bursts or pulses. These methods could help shed light on the complex interstellar environment surrounding the FRBs and in our Galaxy.

Pigovian taxes on polluters are politically unpopular, but subsidies for non-polluting sources are politically attractive. This paper presents a linear demand and supply model and numerical example to explore the trade-offs between taxing polluting sources of a good versus subsidizing non-polluting sources of the same good. While the model (along with the associated numerical example) shows the optimality of Pigovian taxes, it also shows how much welfare is reduced if subsidies for nonpolluters are employed instead. Further, it shows the optimal tax, given any level of subsidy and the optimal subsidy, given any level of tax.

Spider pulsars are millisecond pulsars in short-period (≲12-h) orbits with low-mass (~0.01–0.4  M ⊙ ) companion stars. The pulsars ablate plasma from the companion star, causing time delays and eclipses of the radio emission from the pulsar. The magnetic field of the companion has been proposed to strongly influence both the evolution of the binary system 1 and the eclipse properties of the pulsar emission 2 . Changes in the rotation measure (RM) have been seen in a spider system, implying that there is an increase in the magnetic field near the eclipse 3 . Here we report a diverse range of evidence for a highly magnetized environment in the spider system PSR B1744 – 24A 4 , located in the globular cluster Terzan 5. We observe semi-regular profile changes to the circular polarization, V , when the pulsar emission passes close to the companion. This suggests that there is Faraday conversion where the radio wave tracks a reversal in the parallel magnetic field and constrains the companion magnetic field, B   (> 10 G). We also see irregular, fast changes in the RM at random orbital phases, implying that the magnetic strength of the stellar wind, B , is greater than 10 mG. There are similarities between the unusual polarization behaviour of PSR B1744 – 24A and some repeating fast radio bursts (FRBs) 5 – 7 . Together with the possible binary-produced long-term periodicity of two active repeating FRBs 8 , 9 , and the discovery of a nearby FRB in a globular cluster 10 , where pulsar binaries are common, these similarities suggest that a proportion of FRBs have binary companions. The observation of pulsar emission at various orbital phases of a companion star probes the diverse magnetic structure in a binary system, and exhibits varying polarization behavior, akin to that observed in certain fast radio bursts.

Radio pulsars scintillate because their emission travels through the ionized interstellar medium along multiple paths, which interfere with each other. It has long been realized that, independent of their nature, the regions responsible for the scintillation could be used as ‘interstellar lenses’ to localize pulsar emission regions 1 , 2 . Most such lenses, however, resolve emission components only marginally, limiting results to statistical inferences and detections of small positional shifts 3 – 5 . As lenses situated close to their source offer better resolution, it should be easier to resolve emission regions of pulsars located in high-density environments such as supernova remnants 6 or binaries in which the pulsar’s companion has an ionized outflow. Here we report observations of extreme plasma lensing in the ‘black widow’ pulsar, B1957+20, near the phase in its 9.2-hour orbit at which its emission is eclipsed by its companion’s outflow 7 – 9 . During the lensing events, the observed radio flux is enhanced by factors of up to 70–80 at specific frequencies. The strongest events clearly resolve the emission regions: they affect the narrow main pulse and parts of the wider interpulse differently. We show that the events arise naturally from density fluctuations in the outer regions of the outflow, and we infer a resolution of our lenses that is comparable to the pulsar’s radius, about 10 kilometres. Furthermore, the distinct frequency structures imparted by the lensing are reminiscent of what is observed for the repeating fast radio burst FRB 121102, providing observational support for the idea that this source is observed through, and thus at times strongly magnified by, plasma lenses 10 . Radiation from the ‘black widow’ pulsar B1957+20 is amplified when a companion brown dwarf passes in front of the source, suggesting that plasma flowing from the companion acts as a lens.

Many economics texts introduce their analysis of negative externalities by examining a tax on the output of polluting firms, sometimes called a \"simple Pigovian tax,\" often pointing out that taxing pollution directly is superior to taxing output and proceeding to discuss an emission fee as an alternative. They do not show how and why an emission fee is more efficient than an output tax. This note presents a numerical example allowing comparison of the welfare effects of the two approaches, as well as showing why simply reducing the pollution intensity of polluters' output would be inferior to an emission fee.

Fast radio bursts (FRBs) last for milliseconds and arrive at Earth from cosmological distances. Although their origins and emission mechanisms are unknown, their signals bear similarities with the much less luminous radio emission generated by pulsars within our Miky Way Galaxy 1 , with properties suggesting neutron star origins 2 , 3 . However, unlike pulsars, FRBs typically show minimal variability in their linear polarization position angle (PA) curves 4 . Even when marked PA evolution is present, their curves deviate significantly from the canonical shape predicted by the rotating vector model (RVM) of pulsars 5 . Here we report on FRB 20221022A, detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst project (CHIME/FRB) and localized to a nearby host galaxy (about 65 Mpc), MCG+14-02-011. This FRB shows a notable approximately 130° PA rotation over its about 2.5 ms burst duration, resembling the characteristic S-shaped evolution seen in many pulsars and some radio magnetars. The observed PA evolution supports magnetospheric origins 6 , 7 – 8 over models involving distant shocks 9 , 10 – 11 , echoing similar conclusions drawn from tempo-polarimetric studies of some repeating FRBs 12 , 13 . The PA evolution is well described by the RVM and, although we cannot determine the inclination and magnetic obliquity because of the unknown period or duty cycle of the source, we exclude very short-period pulsars (for example, recycled millisecond pulsars) as the progenitor. FRB 20221022A, detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst project, shows a pronounced change in polarization during the burst, providing important clues into the nature of the source.

This thesis focuses on state and society in the reigns of two emperors which have not been fully explored by scholars, namely those of Justin II (565-578) and Tiberius II (578-582). It sets out to provide valuable insight about the transitional period the empire underwent in the late sixth century by examining the roles of emperors Justin II and Tiberius II in regards to foreign policy. By comparison, most of the scholarship of this period focuses on the policies and reforms of either Justinian (527-565) or Maurice (582-602). This thesis attempts to provide a necessary bridge in the scholarship between these two emperors and seeks to highlight the importance of this period to the wider development of Late Antique society in the sixth century. The dissertation takes a comparative approach, by focusing on the literary and archaeological evidence available, and determining the changes that took place after the reign of Justinian. It also adopts a holistic approach. After an analysis of each set of policies separately, it will attempt to draw conclusions on how these policies influenced each other as a whole and how this contributed to the shifting frontiers that occurred during the late sixth century.