Fractality of open clusters in singles, pairs, and groups

Abstract

In this work, we investigate the global structural properties and fractality of 1,876 open clusters (OCs) in different environments, including 1,145 singles, 392 pairs, and 339 groups. We analyze cluster mass, age, size, concentration, and fractal structure using the Q parameter and the fractal dimension fdim, and examine their correlations with key physical parameters. Our results reveal systematic environmental trends: clusters in groups are generally younger, less massive, slightly larger, and less centrally concentrated than those in pairs or singles. Fractality is more pronounced in clusters within pairs and groups, with 44% of group clusters exhibiting fractal substructure compared to 38.5% for pairs and 33.2% for singles. Similarly, median fdim values increase from singles (1.13) to pairs (1.16) to groups (1.25), reflecting greater substructure in denser environments. These findings indicate that both intrinsic cluster properties and environmental context significantly influence cluster evolution. More massive clusters tend to evolve toward centrally concentrated, radially symmetric configurations, while less massive clusters retain fractal features for longer periods. Overall, our study demonstrates that open clusters do not evolve in isolation: interactions with the environment play a critical role in shaping their structural evolution and dynamical state.

Figures (7)

• Figure 1: Box-counting $\log_e N(L)$ vs. $-\log_e L$ for the NGC 3532 cluster. The red solid line represent the best-fit robust linear regression, with its slope corresponding to the estimated fractal dimension $f_\mathrm{dim}$. The vertical dashed lines mark the fitting range of $[-\log_e 2, \log_e 2]$. The horizontal dashed lines indicate the natural logarithm of the total number of member stars in the cluster.
• Figure 2: Global properties of the OCs sample. Singles are shown in blue, pairs in green, and groups in red.
• Figure 3: Median values of global parameters (from left to right: age, concentration and distance) as a function of cluster mass for our sample of OCs. Shaded areas indicate uncertainties estimated using the bootstrap method. Singles are shown in blue, pairs in green, and groups in red.
• Figure 4: Histogram of the $Q$ parameter. Singles are shown in blue, pairs in green, and groups in red. The vertical grey dashed line marks $Q=0.8$, which serves as the threshold distinguishing fractal substructure from radial density profiles.
• Figure 5: $Q$ parameter as a function of various global cluster parameters, including mass, age, concentration, and cluster size. Singles are shown in blue, pairs in green, and groups in red. Shaded areas indicate uncertainties estimated using the bootstrap method. The Spearman correlation coefficient for each panel is indicated in the lower-right corner, with colors corresponding to the cluster types. Positive values of $s$ indicate a positive correlation, with a maximum of 1 representing a perfect positive correlation. Negative values indicate a negative correlation, while 0 corresponds to no correlation. The horizontal grey dashed lines marks $Q=0.8$, which serves as the threshold distinguishing fractal substructure from radial density profiles.