Constraining inhomogeneities and asymmetries in SNe, FBOTs, and other high-energy transients from unresolved radio observations
Synchrotron emission in high-energy transients is produced by relativistic electrons accelerated by shocks. As high-energy transients are often unresolved even on angular scales probed by very long baseline interferometry, it is difficult to obtain a full picture of the ejecta and circumstellar medium (CSM) properties that are probed by the radio synchrotron emission. Radio spectra of high-energy transients frequently show optically thick slopes shallower than the standard $F_ν\propto ν^{5/2}$ expected from synchrotron self-absorption (SSA) models, or broader spectra near the self-absorption frequency. Such deviations are often interpreted phenomenologically, without providing clear insights into the structure of the emitting region. We show how information on the homogeneity and symmetry of the emitting region can be directly inferred from SSA spectra, even when the source is unresolved. We discuss the circumstances under which inhomogeneities in the emitting region can change the spectrum below the self-absorption frequency, causing it to follow a different slope. We examine which parameters can be constrained from observations and which remain degenerate. We apply this method to the stripped-envelope supernova (SN) 2016coi and to the fast blue optical transient (FBOT) AT2018cow, showing that SSA spectra constrain the degree of inhomogeneity in these systems, providing strong evidence for inhomogeneities in the emitting region in the SN 2016coi, and asymmetry in the case of AT2018cow, and we infer the characteristics of the emitting region. When well sampled spectra are available, our method can be applied as a general, model-independent, inference method. This approach can be used to constrain inhomogeneities in a variety of unresolved high-energy astrophysical transients, including SNe, FBOTs, tidal disruption events and gamma-ray bursts.