The search for extratidal star candidates around Galactic globular clusters NGC 2808, NGC 6266, and NGC 6397 with {\textit{Gaia}} DR2 astrometry

Context. Extratidal stars are stellar bodies that end up outside the tidal radius of a cluster as a result of internal processes or external forces acting upon it. The presence and spatial distribution of these stars can give us insights into the past evolution of a cluster inside our Galaxy. Aims. Previous works suggest that globular clusters, when explored in detail, show evidence of extratidal stars. We aim to search for possible extratidal stars in the Galactic globular clusters NGC 6397, NGC 2808, and NGC 6266 using the photometry and proper motion measurements from Gaia DR2 database (Gaia Collaboration et al. 2018). Results. Finally, 120, 126, and 107 extratidal candidate stars were found lying outside the tidal radius of the globular clusters NGC 6397, NGC 2808, and NGC 6266, respectively. 70%, 25.4%, and 72.9% of the extratidal stars found are located outside the Jacobi radius of NGC 6397, NGC 2808, and NGC 6266, respectively. The spatial distribution of the extratidal stars belonging to NGC 6397 appears S-like, extending along the curved leading and trailing arms. NGC 2808 has an overdensity of stars in the trailing part of the cluster and NGC 6266 seems to have overdensities of extratidal stars in its eastern and northern sides. Conclusions. Proper motions and color-magnitude diagrams can be used to identify extratidal candidate stars around GCs. Nonetheless, depending on how different the kinematics and stellar populations of a cluster are compared to the Milky Way field, the fraction of contamination can be larger. All three clusters are found to have extratidal stars outside their tidal radii. For NGC 6397 and NGC 2808, these stars may be the result of a combined effect of the disc shocks and tidal disruptions. For NGC 6266, the distribution of extratidal stars is symmetrical around it, most likely indicating that the cluster has an extended stellar envelope.