The linear polarization of the optical continuum of type II supernovae (SNe), together with its temporal evolution is a promising source of information about the large-scale geometry of their ejecta. To help access this information, we undertook 2D polarized radiative transfer calculations to map the possible landscape of type II SN continuum polarization (Pcont) from 20 to 300 days after explosion. Our simulations were based on crafted 2D axisymmetric ejecta constructed from 1D nonlocal thermodynamic equilibrium time-dependent radiative transfer calculations for the explosion of a red supergiant star. Following the approach used in our previous work on SN 2012aw, we considered a variety of bipolar explosions in which spherical symmetry is broken by material within ~30° of the poles that has a higher kinetic energy (up to a factor of two) and higher 56Ni abundance (up to a factor of about five, allowing for 56Ni at high velocity). Our set of eight 2D ejecta configurations produced considerable diversity in Pcont (λ ~ 7000 Å), although its maximum of 1–4% systematically occurs around the transition to the nebular phase. Before and after this transition, Pcont may be null, constant, rising, or decreasing, which is caused by the complex geometry of the depth-dependent density and ionization and also by optical depth effects. Our modest angle-dependent explosion energy can yield a Pcont of 0.5–1% at early times. Residual optical-depth effects can yield an angle-dependent SN brightness and constant polarization at nebular times. The observed values of Pcont tend to be lower than obtained here. This suggests that more complicated geometries with competing large-scale structures cancel the polarization. Extreme asymmetries seem to be excluded.
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