The vertex coordinates of the Galaxy's stellar systems according to the Gaia DR3 catalogue

We present the results of determining the coordinates of the vertices of various stellar systems, the centroids of which are located in the Galactic plane. To do this, the positions, parallaxes, proper motions, and radial velocities of red giants and subgiants contained in the $Gaia$~DR3 catalogue have been used. When determining the components of the deformation velocity tensors in local coordinate systems, we found the coordinates of the vertices of the stellar systems under study. It turned out that there is a complex dependence of vertex deviations $l_{xy}$ in Galactocentric cylindrical ($R, \theta$) and Galactic rectangular ($X,Y$) coordinates. Based on the approach proposed in this paper, heliocentric distances to vertices have been determined for the first time. The results obtained show that in addition to the fact that the angular coordinates of the Galactic center and the vertices of stellar systems do not coincide, their heliocentric distances do not coincide as well. This presumably indicates that there are structures in the Galaxy that noticeably affect its axisymmetry.