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Torques acting on galaxies lead to physical alignments, but the resultingellipticity correlations are difficult to predict. As they constitute a majorcontaminant for cosmic shear studies, it is important to constrain theintrinsic alignment signal observationally. We measured the alignments ofsatellite galaxies within 90 massive galaxy clusters in the redshift range0.05<z<0.55 and quantified their impact on the cosmic shear signal. We combineda sample of 38,104 galaxies with spectroscopic redshifts with high-quality datafrom the Canada-France-Hawaii Telescope. We used phase-space information toselect 14,576 cluster members, 14,250 of which have shape measurements andmeasured three different types of alignment: the radial alignment of satellitegalaxies toward the brightest cluster galaxies (BCGs), the common orientationsof satellite galaxies and BCGs, and the radial alignments of satellites witheach other. Residual systematic effects are much smaller than the statisticaluncertainties. We detect no galaxy alignment of any kind out to at least 3r200. The signal is consistent with zero for both blue and red galaxies, brightand faint ones, and also for subsamples of clusters based on redshift,dynamical mass, and dynamical state. These conclusions are unchanged if weexpand the sample with bright cluster members from the red sequence. We augmentour constraints with those from the literature to estimate the importance ofthe intrinsic alignments of satellites compared to those of central galaxies,for which the alignments are described by the linear alignment model.Comparison of the alignment signals to the expected uncertainties of currentsurveys such as the Kilo-Degree Survey suggests that the linear alignment modelis an adequate treatment of intrinsic alignments, but it is not clear whetherthis will be the case for larger surveys.

Constraints on the Alignment of Galaxies in Galaxy Clusters from $\sim$14,000 Spectroscopic Members