Polarization has been detected at early times for all types of supernovae (SNe), indicating that all such systems result from or quickly develop some form of asymmetry. In addition, the detection of strong line polarization in SNe is suggestive of chemical inhomogeneities ("clumps") in the layers above the photosphere, which may reflect hydrodynamical instabilities during the explosion. We have developed a fast, flexible, approximate semi-analytic code for modeling polarized line radiative transfer within three-dimensional inhomogeneous rapidly expanding atmospheres. Given a range of model parameters, the code generates random sets of clumps in the expanding ejecta and calculates the emergent line profile and Stokes parameters for each configuration. The ensemble of these configurations represents the effects both of various host geometries and of different viewing angles. We present results for the first part of our survey of model geometries, specifically the effects of the number and size of clumps (and the related effect of filling factor) on the emergent spectrum and Stokes parameters. Our simulations show that random clumpiness can produce line polarization in the range observed in SNe Ia, as well as the Q-U loops that are frequently seen in all SNe. We have also developed a method to connect the results of our simulations to robust observational parameters such as maximum polarization and polarized equivalent width in the line. Our models, in connection with spectropolarimetric observations, can constrain the three-dimensional structure of SN ejecta and offer important insight into the SN explosion physics and the nature of their progenitor systems.
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