Search for the possible members of the open cluster NGC 3532 with poor astrometric solutions of Gaia DR3

We performed star counts in the region of the open cluster NGC 3532. The ranges of trigonometric parallaxes and proper motions containing all the stars of the cluster were determined using the stars with 5- and 6-parameter Gaia DR3 solutions. The estimated radius of the cluster was R_c=178+-3 arcminutes and the number of cluster stars was N_c=2200+-40. We estimate the number of stars with poor astrometric solutions that may be members of the cluster. For this purpose, we analyze the surface density distribution of stars with two-parameter Gaia DR3 solutions, stars with the parameter RUWE>1.4, and stars with large relative errors of trigonometric parallaxes in the vicinity of the cluster. We are looking for stars that fall within the area of the color-magnitude diagram occupied by probable members of the NGC 3532 cluster from the Hant&Reffert sample. The radial surface density profile plotted with such stars shows the concentration of stars toward the cluster center. An analysis of the profile yields an estimate of 2150+-230 stars that may be cluster members. Thus, nearly one half of cluster members can be lost when the probable members are selected only by exact astrometric data of Gaia DR3. Among these lost stars, there may be a significant number of unresolved binary and multiple systems.