Occultation polarimetry as a probe of unresolved polarization

Abstract

Context: Low polarization in an unresolved source may reflect weak local polarization or spatial cancellation between strongly polarized regions. An occultation can break this spatial degeneracy by differentially sampling the source as the occulting boundary moves. Aims: We develop a general theoretical framework for occultation polarimetry and determine what information can be inferred directly from unresolved full Stokes light curves, without reconstructing a polarization image or prescribing a source model. Methods: For a stationary, spatially incoherent source undergoing monotonic occultation, we relate Stokes variations to the polarization sampled by an arbitrarily curved occulting boundary and derive an exact variance decomposition of the normalized Stokes vector. Results: The polarization deficit decomposes exactly into three non-negative contributions: local polarization deficit, mixing within limb samples, and mixing between their mean polarization states. The last is directly measurable and provides a sharp, model-independent lower bound on total spatial mixing. The associated covariance tensor further characterizes the direction and correlations of the resolved polarization variations, including those between linear and circular polarization. Finite sampling preserves the bound, which can be strengthened through complementary occultation trajectories. Conclusions: Occultation polarimetry provides a powerful observational technique for extracting quantitative, model independent constraints on spatial polarization mixing directly from unresolved Stokes light curves. It offers a means to reveal both the extent and the form of polarization structure otherwise inaccessible at the available angular resolution.