Towards precision astrometry of scattered images of compact radio sources: scintillometry theory and prospects

Abstract: Compact radio sources such as pulsars and FRBs undergo scintillation in the interstellar medium (ISM) when scattered images interfere at the observer. ``Scintillometry'' refers to the range of techniques to extract astrometric information -- such as the angular positions of the images and distances to the scattering screen and source -- from scintillation observations. Pulsar scintillometry has proven to be a powerful technique, revealing rich and unexpected scattering phenomenology in the ISM and also shedding light on the emission physics of pulsars. FRB scintillometry stands to be a similarly powerful probe of FRB emission, as well as structure on tiny scales in ionized media beyond our galaxy, such as the circumgalactic medium (CGM). However, nascent FRB scintillation studies are far from the sophisticated lensing geometry reconstructions that have been performed for scintillating pulsars. In this paper, we introduce a novel theoretical framework for scintillometry, demonstrating that the full astrometric content of scintillation observations is contained within a single underlying observable: the instantaneous spatial wavefield. We relate the instantaneous spatial wavefield to more familiar concepts from the pulsar scintillometry literature, such as the dynamic spectrum. Using this framework, we discuss prospects and limitations for FRB scintillometry, towards the goal of full astrometric reconstructions of FRB lensing geometries. We show how key degeneracies in two-screen scattering measurements can be ameliorated. In addition, we discuss the possibility of inferring dispersion measure gradients across scintillation screens, which may shed light on the highly unconstrained physics of the cool CGM phase on tiny ($\sim 100\,{\rm au}$) scales.