Abstract: One of the most interesting explanations for the non-Gaussian cold spot detected in the Wilkinson Microwave Anisotropy Probe (WMAP) data by Vielva et al. is that it arises from the interaction of the cosmic microwave background radiation with a cosmic texture. In this case, a lack of polarization is expected in the region of the spot, as compared to the typical values associated to large fluctuations of a Gaussian and isotropic random field. In addition, other physical processes related to a non-linear evolution of the gravitational field could lead to a similar scenario. However, some of these alternative scenarios (e.g. a large void in the large-scale structure) have been shown to be very unlikely. In this work we characterize the polarization properties of the cold spot under both hypotheses: a large Gaussian fluctuation and an anomalous feature generated, for instance, by a cosmic texture. We also propose a methodology to distinguish between them, and we discuss its discrimination power as a function of the instrumental noise level. In particular, we address the cases of current experiments, like WMAP and Planck, and others in development as the Q, U and I Joint Tenerife Experiment (QUIJOTE). We find that for an ideal experiment with a high-polarization sensitivity, the Gaussian hypothesis could be rejected at a significance level better than 0.8 per cent. While WMAP is far from providing useful information in this respect, we find that Planck will be able to reach a significance level of around 7 per cent; in addition, we show that the ground-based experiment QUIJOTE could provide a significance level of around 1 per cent, close to the ideal case. If these results are combined with the significance level found for the cold spot in temperature, the capability of QUIJOTE and Planck to reject the alternative hypothesis becomes 0.025 and 0.124 per cent, respectively.

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