Line Polarization of Si II $\lambda$6355 \AA\ in Type Ia Supernovae: A New Statistical Approach to Probe the Explosion Physics and Diversity

Abstract

Spectropolarimetry provides a unique probe of ejecta asphericities, offering direct insights into the underlying explosion physics of Type Ia supernovae (SNe Ia). We analyze the statistical properties of pre-maximum spectropolarimetric data for 24 SNe Ia observed with VLT/FORS, focusing on the Si II $\lambda$6355 \AA line. Previous studies have revealed a correlation between the peak Si II polarization degree and the expansion velocity. Here, we combine these observations with multi-dimensional non-LTE radiative transfer simulations. We consider two asphericity classes: (i) lopsided abundance distributions produced by off-center delayed-detonation transitions in near-$M_{Ch}$ white dwarfs or, for example, WD collisions (Class I), and (ii) global, axisymmetric density asphericities such as those arising from explosions of rapidly rotating WDs or mergers (Class II). Our model grid spans normal to subluminous SNe Ia and successfully reproduces the observed Si II velocity-polarization trend, with higher velocities associated with stronger asphericities. Consistent with observations, transitional SNe Ia and the faint end of the normal SNe Ia population show the highest Si II polarization and are best explained by Class I scenarios. In contrast, subluminous SNe Ia are dominated by Class II asphericities, characterized by lower Si II polarization but significant continuum polarization. The observed distribution of Si II polarization depends on both the observer's viewing angle $\theta$ and the intrinsic asphericity. Statistical analysis of these spectropolarimetric snapshots enables the separation of Class I and Class II contributions and highlights the intrinsic diversity among SNe Ia. Our results imply viewing-angle-dependent luminosities in our local sample, which may have implications when using high-redshift SNe Ia as evidence for the need of non-standard cosmology.