Polarization signatures of the head-on collision model for Type Ia supernovae: How much asymmetry is too much?

In a previous paper, we showed that the asymmetric ejecta produced by (zero impact parameter) head-on collisions of carbon-oxygen white dwarfs allow these progenitor models for Type Ia supernovae (SNe Ia) to cover the observed two-dimensional (2D) distribution of Si II line depths (Branch plot). In this paper, we study the polarization signature associated with the 2D asymmetric ejecta of the collision model and a double-detonation model using similar TARDIS radiative transfer simulations along different lines of sight with a spherical photosphere, combined with a new 3D Monte Carlo polarization code. We show that the polarization $Q$ can be parametrized as a product $Q=Q_{\max}Q_{\rm{x}}$ of a radial structure component $Q_{\max}$ which is insensitive to the model specifics and is shown to be universally around $Q_{\max}\sim 5\%$, and a cancellation component $Q_{\rm{x}}$ which depends on the asymmetry details. The continuum polarization is found to be low for both the collision and double-detonation models with $Q\sim 0.5\%$. However, the irregular Si distribution in the 2D head-on collision model results in Si II line polarization reaching $Q\sim 3\%$ ($Q_{\rm{x}} \lesssim 50\%$) in tension with observations (mostly $\lesssim 1.2\%$). In contrast, we show that the double-detonation model also covers the Branch plot, and yet results in low line polarization $Q\lesssim 0.7\%$ ($Q_{\rm{x}} \sim 10\%$) consistent with previous results and most SNe Ia. These results strengthen the case for asymmetric explosions as progenitors of SNe Ia, emphasizing an additional requirement for large polarization cancellations to account for the low observed line polarizations.