We consider a simple dynamical and relativistic model to explain the spectro-temporal structure often displayed by repeating fast radio bursts (FRBs). We show how this model can account for the downward frequency drift in a sequence of sub-bursts of increasing arrival time (the “sad trombone” effect) and their tendency for exhibiting a reduced pulse width with increasing frequency of observation. Most importantly, this model also predicts a systematic inverse relationship between the (steeper) slope of the frequency drift observed within a single sub-burst and its temporal duration. Using already published data for FRB 121102 we find and verify the relationship predicted by this model. We therefore argue that the overall behaviour observed for this object as a function of frequency is consistent with an underlying narrow-band emission process, where the wide-band nature of the measured FRB spectrum is due to relativistic motions. Although this scenario and the simple dynamics we consider could be applied to other theories, they are well-suited for a model based upon Dicke’s superradiance as the physical process responsible for FRB radiation in this and similar sources.

We study the spectro-temporal characteristics of two repeating fast radio bursts (FRBs), namely, FRB 20180916B and FRB 20180814A , and combine the results with those from our earlier analysis on FRB 20121102A. The relationship between the frequency drift rate, or slope, of individual sub-bursts and their temporal duration is investigated. We consider a broad sample of possible dispersion measure (DM) values for each source to understand the range of valid sub-burst slope and duration measurements for all bursts and to constrain our results. We find good agreement with an inverse scaling law between the two parameters previously predicted using a simple dynamical relativistic model. The remarkably similar behaviour observed in all sources provides strong evidence that a single and common underlying physical phenomenon is responsible for the emission of signals from these three FRBs, despite their associations with different types of host galaxies at various redshifts. It also opens up the possibility that this sub-burst slope law may be a universal property among repeating FRBs, or indicates a distinct subclass among them.

We investigate the application of the conventional quasi-steady state maser modelling algorithm of Menegozzi & Lamb (ML) to the high field transient regime of the one-dimensional Maxwell-Bloch (MB) equations for a velocity distribution of atoms or molecules. We quantify the performance of a first order perturbation approximation available within the ML framework when modelling regions of increasing electric field strength, and we show that the ML algorithm is unable to accurately describe the key transient features of R. H. Dicke’s superradiance (SR). We extend the existing approximation to one of variable fidelity, and we derive a generalisation of the ML algorithm convergent in the transient SR regime by performing an integration on the MB equations prior to their Fourier representation. We obtain a manifestly unique integral Fourier representation of the MB equations which is $\mathcal {O}\left(N\right)$ complex in the number of velocity channels N and which is capable of simulating transient SR processes at varying degrees of fidelity. As a proof of operation, we demonstrate our algorithm’s accuracy against reference time domain simulations of the MB equations for transient SR responses to the sudden inversion of a sample possessing a velocity distribution of moderate width. We investigate the performance of our algorithm at varying degrees of approximation fidelity, and we prescribe fidelity requirements for future work simulating SR processes across wider velocity distributions.

Accurately measuring the magnetic field in the ISM is essential for understanding star-formation processes. We searched archival data of the Submillimeter Array (SMA) for evidence of circular polarization in common molecular tracers, most notably CO. This circular polarization possibly arises from anisotropic resonant scattering, which would imply that some background linearly polarized radiation is being converted to circular polarization. We find circular polarization in the star-forming regions NGC7538 (in CO) and Orion KL (in CO and SiO), as well as in the carbon star IRC+10216 (in CS, SiS, H 13 CN and CO) at high enough levels to suggest that the presence of circular polarization in these spectral lines is common for such objects. This implies that measuring circular polarization is important when studying magnetic fields through the linear polarization of molecular spectral lines in the interstellar medium. We also provide a simple Python wrapper for the Miriad data reduction package.

We discuss the existence of elliptical polarisation in rotational spectral lines of CO and other molecules within the context of the Anisotropic Resonant Scattering (ARS) model. We show that the effect of ARS on the radiation field can lead to not only the previously predicted transformation of background linear polarisation into circular polarisation (i.e. Faraday conversion), but also the occurrence of Faraday rotation and the generation of elliptically polarised signals in an otherwise initially unpolarised radiation field. This is due to a collective behaviour between the large number of molecules acting as a diffraction ensemble that strongly favours forward scattering over any other mode. Our application to astronomical data demonstrates the dependency of the Stokes parameters on the strength and orientation of the ambient magnetic field, and suggests that ARS will manifest itself for a wide range of molecular species and transitions.