Analytical modeling of polarization signals arising from confined circumstellar material in Type II supernovae

Recent observations of Type II supernovae (SNe) have brought a challenge in our understanding on the final evolutionary stage of massive stars. The early-time spectra and light curves of Type II SNe suggest that a majority of them have dense circumstellar material (CSM) in their vicinity, the so-called confined CSM. However, the mechanism of these extensive mass loss has not yet been understood. For addressing this problem, we aim to study the spatial distribution of the confined CSM, which has important information on the mechanism. We analytically calculate the polarization signals created by electron scatterings within disk-like confined CSM, and apply the results to the case of SN 2023ixf. The calculated polarization angle remains fixed at the angle aligned with the CSM disk axis, and is insensitive to the disk parameters. The calculated polarization degree evolves over a timescale of < 10 days, depending on the disk parameters: it stays constant or increases slightly while the unshocked CSM is optically thick, peaks as it becomes optically thin, and drops to zero when the shock reaches the disk's outer edge. We also find that the time evolution of the polarization in Type II SNe with confined CSM can be used for estimating the CSM parameters. In particular, the maximum degree and the rise time are strongly connected to the values of the viewing angle and the opening angle of the CSM disk, while the duration and the decline time are sensitive to the values of the mass and extension of the CSM disk. We demonstrate that the time evolution of the polarization of SN 2023ixf can be explained with a disk-like CSM. This information of the CSM is a strong constraint on the mechanism to create the confined CSM.