As is known, resonant scattering can distort the surface-brightness profiles of clusters of galaxies in X-ray lines. We demonstrate that the scattered line emission should be polarized and possibly detectable with near-future X-ray polarimeters. Spectrally-resolved mapping of a galaxy cluster in polarized X-rays could provide valuable independent information on the physical conditions, in particular element abundances and the characteristic velocity of small-scale turbulent motions, in the intracluster gas. The expected degree of polarization is of the order of 10% for richest regular clusters (e.g. Coma) and clusters whose X-ray emission is dominated by a central cooling flow (e.g. Perseus or M87/Virgo).
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