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

Abstract

Open clusters (OCs) usually evolve gradually as the number of their members changes, which can be manifested in their morphological characteristics. We aim to investigate the morphological stability of 1,490 OCs and further explore the potential change of morphological stability of the OCs at different spatial positions, using the OC catalog from the literature. We define for the first time a new morphological stability parameter Ncore/Nouter, 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$\pm$0.039, significantly steeper than the 0.720$\pm$0.026 measured for Score/Souter. This demonstrates that the stellar density in the core is a more sensitive tracer for morphological stability than geometry. Spatially, the radial sample OCs have larger slopes of Ncore/Nouter and Score/Souter against N, with 1.083$\pm$0.116 and 0.733$\pm$0.080, respectively, whereas those in the tangential direction 1.013$\pm$0.110 and 0.529$\pm$0.075, respectively, which means that the impact on sample OCs from tidal forces directed toward the Galactic center is possibly stronger than that from the shear force caused by the differential rotation of the Galactic disk. Besides, the sample OCs younger than 30 Myr display a shallow slope of 0.751$\pm$0.166, with those older than 800 Myr (1.442$\pm$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.

Figures (23)

• Figure 1: Distribution of NGC_6791 in the Galactic coordinate system (left panel) and its flattened projection distribution (right panel). The blue scattered points in each panel represent the member stars of the OC, with the gray bars being the errors of the position coordinates of its members. The orange circles correspond to the tidal radii obtained from 100 Monte Carlo sampling runs. The black dashed circle represents the mean value of the 100 results.
• Figure 2: Rose diagram of the NGC_6791 on the 2D corrected projection, derived from one of ten samplings. The rose-colored sectors represent the normalized directional radial radius values obtained by the Rose diagram method. Each sector spans 30$^{\degree}$, with the first sector starting at 0$^{\degree}$ corresponding to the horizontal line on the right of this diagram. The second sector begins at a position 30$^{\degree}$ counterclockwise from the first sector, and subsequent sectors follow this pattern. The gray semi-transparent sectors are the average extension levels in each direction, with the green scattered points indicating the member stars.
• Figure 3: Map of the sample OCs in the Galactic coordinate system. The size of each circle color-filled is proportional to the number of members of each OC, with its color being coded by the morphological stability parameter I.
• Figure 4: Histogram of the areas of the core ($\mathrm{S}_{\mathrm{core}}$, blue) and the outer ($\mathrm{S}_{\mathrm{outer}}$, red) of our sample OCs. Each set of data was fitted with a normal distribution (colored solid lines), with the mean positions being marked with vertical dashed lines.
• Figure 5: Relationships between the morphological stability parameters ($\mathrm{S}_{\mathrm{core}}$/$\mathrm{S}_{\mathrm{outer}}$: the first two panels from left to right; N$_{\mathrm{core}}$/$\mathrm{N}_{\mathrm{outer}}$: the last two panels) and the number of members (N). For ease of visualization, a logarithmic scale was adopted. Blue scatters in linear fitting panels represent our sample OCs, with the gray bars denoting their parameter errors. The faint gray lines show 1000 MCMC samples, with the thick red lines (the median values) and the yellow shaded bands ($1\sigma$) corresponding to our best parameter estimates. The two corner plots display the marginal posterior distributions (diagonal) and the 2-D joint posterior contours (below diagonal) of the fitted parameters ($m$, $b$, $\sigma$). Contours enclose the $1\sigma$ and $2\sigma$ confidence regions, and the median together with the 16th and 84th percentiles are quoted in each panel.