Measurement of the cylindrical rotation of the south-east side of M 31 according to the method by Molaeinezhad et al. (2016). Top: stellar line-of-sight velocity parallel to the major axis of galaxies at different heights from the disk plane. Bottom: line-of-sight velocity gradient parallel to the minor axis at different distances from the minor axis. Profiles are color-coded according to the distance from the minor axis. The solid black profile represents the average value m_avg . The cylindrical rotation is then m_cyl =m_avg + 1 as a quantity to express the level of cylindrical rotation.