Astrophysical transient events, particularly Type Ia supernovae (SNe Ia) and tidal disruption events (TDEs), provide critical insights into stellar systems and black hole activity. This thesis studies polarimetry of SNe Ia and TDEs in an attempt to better understand the geometry and physical processes behind these explosive events.
For SN 2019ein, spectropolarimetric data from approximately 11 days before to 10 days after peak brightness revealed a continuum polarization of 0.0--0.3\%. The constant polarization angle indicates axial symmetry in the explosion, consistent across inner and outer ejecta regions. Notably, polarization at the Si II and Ca II lines reached about 1\%, suggesting a largely spherical explosion with localized clumping of intermediate-mass elements. These observations largely disfavor merger-induced models for SN 2019ein. A larger sample of SNe Ia spectropolarimetry observed at Lick Observatory is presented and described.
In the study of the TDE AT\,2019qiz, spectropolarimetry showed negligible continuum polarization at peak brightness, suggesting a nearly spherical, optically thick electron scattering photosphere around the black hole. By day 29, polarization increased to around 1\%, indicating a more aspherical interior as the fallback rate decreased and the photosphere receded. This marks the first detailed spectropolarimetric evolution observed in a TDE, and supports the reprocessing model for the source of optical emission in TDEs. The study of AT\,2019qiz is followed by imaging polarimetry of several TDEs from Keck Observatory in an attempt to build a more comprehensive picture of gas geometry in TDEs.
Additionally, the thesis explores the newly discovered X-ray quasi-periodic eruptions (QPEs), analyzing archival {\it Hubble Space Telescope} images of the QPE source GSN 069. The data revealed a compact [O III] emission region within a 35 pc radius of the nucleus, along with extended emission up to 2 kpc away. Simulations with the photoionization code \textsc{Cloudy} suggest this emission comes from dense gas, likely ionized by X-rays from a young accretion disk, offering a unique glimpse into the dynamic processes at play in the host galaxies of QPEs.