Spectral Consequences of Deviation from Spherical Composition Symmetry in Type Ia Supernovae

We investigate the prospects for constraining the maximum scale of clumping in composition that is consistent with observed Type Ia supernova flux spectra. Synthetic spectra generated without purely spherical composition symmetry indicate that gross asymmetries make prominent changes to absorption features. Motivated by this, we consider the case of a single unblended line forming in an atmosphere with perturbations of different scales and spatial distributions. Perturbations of about 1% of the area of the photodisk simply weaken the absorption feature by the same amount independent of the line of sight. Conversely, perturbations of about 10% of the area of the photodisk introduce variation in the absorption depth which does depend on the line of sight. Thus, 1% photodisk area perturbations may be consistent with observed profile homogeneity but 10% photodisk area perturbations can not. Based on this, we suggest that the absence of significant variation in the depths of Si II 6355 absorption features in normal Type Ia spectra near maximum light indicates that any composition perturbations in these events are quite small. This also constrains future three-dimensional explosion models to produce ejecta profiles with only small scale inhomogeneities.