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The measurement of non-zero polarization can be used to infer the presence ofdepartures from spherical symmetry in supernovae (SNe). The origin of themajority of the intrinsic polarization observed in SNe is in electronscattering, which induces a wavelength-independent continuum polarization thatis generally observed to be low (<1%) for all SN types. The key indicator ofasymmetry in SNe is the polarization observed across spectral lines, inparticular the characteristic ``inverse P Cygni'' profile. The results of asuite of 900 Monte Carlo radiative transfer simulations are presented here.These simulations cover a range of possible axisymmetric structures (includingunipolar, bipolar and equatorial enhancements) for the line forming region ofthe Ca II infrared triplet. Using a Variational Autoencoder, 7 key latentparameters are learned that describe the relationship between Stokes I andStokes q, under the assumption of an axially symmetric line forming region andresonant scattering. Likelihood-free inference techniques are used to invertthe Stokes I and q line profiles, in the latent space, to derive the underlyinggeometries. For axially symmetric structures, that yield an observable``dominant axis'' on the Stokes $q-u$ plane, we propose the existence of ageometry ``conjugate" (which is indistinguishable under a rotation of $\pi/2$). Using this machine learning infrastructure, we attempt to identifypossible geometries associated with spectropolarimetric observations of theType Ib SN 2017gax.

Exploring the Polarization of Axially Symmetric Supernovae with Unsupervised Deep Learning