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 $unicode{x212B}$). In particular, increasingly fainter and redder spectra are predicted for observer orientations further from the cavity, while a modest polarisation signal $Psim0.2$ 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.
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