  The study of spiral structures in protoplanetary disks is of great importance
for understanding of processes in the disks, including planet formation. Bright
spiral arms were detected in the disk of young star CQ Tau by Uyama et al.
(2020) in H and L bands. The spiral arms are located inside the gap in
millimeter size dust, recovered earlier using ALMA observations (Ubeira
Gabellini et al. 2019). To explain the gap, Ubeira Gabellini et al. (2019)
proposed the existence of a planet with the semimajor axis of 20 AU. We
obtained multiepoch observations of a spiral feature in the circumstellar
envelope of CQ Tau in Ic band using a novel technique of differential speckle
polarimetry. The observations covering period from 2015 to 2021 allow us to
estimate the pattern speed of spiral: $-0.2\pm1.1^{\circ}$/yr (68% credible
interval, positive value indicates counter-clockwise rotation), assuming
face-on orientation of the disk. This speed is significantly smaller than
expected for a companion-induced spiral, if the perturbing body has the
semimajor axis of 20 AU. We emphasize that the morphology of the spiral
structure is likely to be strongly affected by shadows of a misaligned inner
disk detected by Eisner et al. (2004).
