Growing evidence suggests that Type Iax supernovae might be the result of thermonuclear deflagrations of Chandrasekhar-mass white dwarfs in binary systems .
We carry out Monte Carlo radiative transfer simulations and predict spectropolarimetric features originating from the supernova explosion and subsequent ejecta interaction with the companion star .
Specifically , we calculate viewing-angle dependent flux and polarisation spectra for a 3D model simulating the deflagration of a Chandrasekhar-mass white dwarf and , for a second model , simulating the ejecta interaction with a main-sequence star .
We find that the intrinsic signal is weakly polarised and only mildly viewing-angle dependent , owing to the overall spherical symmetry of the explosion and the depolarising contribution of iron-group elements dominating the ejecta composition .
The interaction with the companion star carves out a cavity in the ejecta and produces a detectable , but modest signal that is significant only at relatively blue wavelengths ( \lesssim 5000 Å ) .
In particular , increasingly fainter and redder spectra are predicted for observer orientations further from the cavity , while a modest polarisation signal P \sim 0.2 per cent is found at blue wavelengths for orientations 30 ^ { \circ } and 45 ^ { \circ } away from the cavity .
We find a reasonable agreement between the interaction model viewed from these orientations and spectropolarimetric data of SN 2005hk and interpret the maximum-light polarisation signal seen at blue wavelengths for this event as a possible signature of the ejecta–companion interaction .
We encourage further polarimetric observations of SNe Iax to test whether our results can be extended and generalised to the whole SN Iax class .