Tumbling Dice: Radio Constraints on the Presence of Circumstellar Shells around Type Ia Supernovae with Impact Near Maximum Light

The progenitors of Type Ia supernovae (SNe Ia) are debated, particularly the evolutionary state of the binary companion that donates mass to the exploding carbon-oxygen white dwarf. In previous work, we presented hydrodynamic models and optically thin radio synchrotron light-curves of SNe Ia interacting with detached, confined shells of CSM, representing CSM shaped by novae. In this work, we extend these light-curves to the optically thick regime, considering both synchrotron self-absorption and free-free absorption. We obtain simple formulae to describe the evolution of optical depth seen in the simulations, allowing optically thick light-curves to be approximated for arbitrary shell properties. We then demonstrate the use of this tool by interpreting published radio data. First, we consider the non-detection of PTF11kx - an SN Ia known to have a detached, confined shell - and find that the non-detection is consistent with current models for its CSM, and that observations at a later time would have been useful for this event. Secondly, we statistically analyze an ensemble of radio non-detections for SNe Ia with no signatures of interaction, and find that shells with masses $(10^{-4}-0.3)~M_\odot$ located $(10^{15}-10^{16})$ cm from the progenitor are currently not well constrained by radio datasets, due to their dim, rapidly-evolving light-curves.