The observational technique of spectropolarimetry has been used to directly measure the asymmetries of Supernovae (SNe), Gamma-Ray Bursts (GRBs) and X-Ray Flashes (XRFs). We wish to determine if non-axial asymmetries are present in SNe that are associated with GRBs and XRFs, given the particular alignment of the jet axis and axis of symmetry with the line of sight in these cases. We performed spectropolarimetry with the Very Large Telescope (VLT) FORS1 instrument of the Type Ic SN 2006aj, associated with the XRF 060218, at V-band maximum at 9.6 rest frame days after the detection of the XRF. Due to observations at only 3 retarder plate angles, the data were reduced assuming that the instrumental signature correction for the $U$ Stokes parameter was identical to the correction measured for $Q$. We find SN 2006aj to be highly polarized at wavelengths corresponding to the absorption minima of certain spectral lines, particularly strong for O I 7774AA and Fe II, observed at 4200AA with a polarization 3%. The value of the Interstellar Polarization is not well constrained by these observations and, considering the low polarization observed between 6000-6500AA, the global asymmetry of the SN is $lesssim 15%$. O I and Fe II lines share a polarization angle that differs from Ca II. SN 2006aj exhibits a higher degree of line polarization than other SNe associated with GRBs and XRFs. The polarization associated with spectral lines implies significant asymmetries of these elements with respect to each other and to the line of sight. This is contrary to the standard picture of SNe associated with GRBs/XRFs, where the axis of symmetry of the SN is aligned with the GRB jet axis and the line of sight.
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