Probing the Geometry of Type Ia Supernovae with Spectropolarimetry

Because all observed Type Ia supernovae (SNe Ia) are too distant to be resolved at early phases, asymmetries in the supernova ejecta can only be inferred from spectropolarimetric data. To fully interpret these observations, a comparison with theoretical models is required. Here I present results from a 3-dimensional polarized Monte-Carlo radiative transfer code, which has recently been updated to include time-dependence. The code can be used to evaluate the viability of specific hydrodynamic explosion models of SNe Ia, as well as to place direct model-independent constraints on the ejecta geometry from the spectropolarimetric observations. In this talk, I consider examples of SNe Ia asymmetry on both large and small scales, paying specific attention to the observable properties of the gravitationally confined detonation scenario of thermonuclear explosions. On smaller scales, the polarization of spectral line features constrains the distribution of elements within the ejecta -- in particular, observations of a polarized high-velocity calcium feature in SNe Ia implicate inhomogeneities in the outermost layers of ejecta. Studying the properties of these structures can provide important clues as to the underlying explosion mechanism. On larger scales, I consider how global distortions in the supernova density structure affect the supernova light curve and the time-variation of the continuum polarization (the ``polarization curve"). Studying the time dependent effects provides a powerful way to probe the degree of asymmetry at different ejecta depths.