The morphological stability of open clusters: A new 2D perspective

Context . Open clusters (OCs) usually evolve gradually as the number of their members changes, which can be manifested in their morphological characteristics. Therefore, the morphological study of OCs lays the foundation for a better understanding of their formation and evolutionary processes. Aims . We aim to investigate the morphological stability of 1490 OCs and further explore the potential change in the morphological stability of the OCs at different spatial positions, using the OC catalog from the literature. Methods . We delineated the 2D morphology of OCs quantitatively in the projection perpendicular to the Galactic disk plane by the rose diagram and analyzed the slope changes between the morphological stabilities (S core /S outer and N core /N outer ) and the number of members (N) within tidal radii to investigate the influence of the external environment on the OCs at different spatial positions. Results . We defined for the first time a new morphological stability parameter, N core /N outer , a ratio of member numbers between cluster core and outer areas within tidal radii, which has a significant positive correlation against N, with a slope of 1.140 ± 0.039, significantly steeper than the 0.720 ± 0.026 measured for S core /S outer . This demonstrates that the stellar density in the core is a more sensitive tracer for morphological stability than geometry. Spatially, the radial sample OCs have larger slopes of N core /N outer and S core /S outer against N, with 1.083 ± 0.116 and 0.733 ± 0.080, respectively, whereas those in the tangential direction have 1.013 ± 0.110 and 0.529 ± 0.075, respectively, which means that the impact on sample OCs from tidal forces directed toward the Galactic center is possibly stronger than that from the shear force caused by the differential rotation of the Galactic disk. Moreover, the sample OCs within 90° of the Galactic center, closer to the bar, exhibit slopes below 0.6 of S core /S outer against N, indicating heightened external perturbations and diminished stability. But the opposite is true for the side greater than 90°. Thus, this illustrates that the influence of the external environment on our sample OCs is asymmetrical. Besides, the sample OCs younger than 30 Myr display a shallow slope of 0.751 ± 0.166, while those older than 800 Myr displaying a slope of 1.442 ± 0.128, reflecting that young OCs likely endure both internal disruptions, such as early dynamical heating weakening core binding and more severe external disturbances, compared to older OCs. Conclusions . The morphological stability of OCs is not only determined by their gravitational binding, but also strongly modulated by the external environment in which they are located.