The Statistical Analysis Of The Galactic Open Clusters' Structure

TL;DR

The study addresses how the internal dynamical evolution of open clusters (OCs) and their interactions with the Galactic environment shape their structures. It applies the Limepy lowered-isothermal model to a Gaia DR3-based sample of 1,481 OCs, jointly fitting cluster and field-star populations via MCMC to derive the structural parameters $W_0$, $g$, and $R_h$. The analysis reveals a strong anti-correlation between $W_0$ and $g$, a growth of the lower limit of $R_h$ with age, and a dependence of $W_0$ on vertical height $|Z|$, implying mass segregation and tidal stripping as key drivers of structural evolution. The results also show substantial overlap in structural parameter space between OCs and globular clusters, suggesting common dynamical processes despite different masses and environments. These findings advance our understanding of cluster evolution under internal dynamics and Galactic tides, with implications for modeling cluster survival in the Milky Way.

Abstract

We present a systematic investigation of 1,481 Galactic open clusters (OCs) through the application of the Limepy dynamical model, from which we derive the fundamental structural parameters of OCs. We conduct the statistical analyses on the structural parameters with clusters' ages and locations within the Milky Way. Our results reveal the higher concentration in the cluster centeris associated with the sharper truncation at the periphery of cluster, which is consistent with previous findings for globular clusters(GCs). We further find the systematic increase of the lower limit of clusters' half-mass radius (Rh) with age. Our results also show that OCs located at larger vertical distances from the Galactic plane systematically display higher central concentrations. Our findings collectively suggest that the structural characteristics of OCs are shaped by both intrinsic evolutionary processes and interactions with the Galactic environment. During the evolution of star clusters, the combined effects of mass segregation and tidal stripping lead to the systematic pattern between central concentration and outer truncation. Clusters of different ages and locations within the Milky Way undergo different evolutionary histories, resulting in correlations between the Rh and age, as well as between central concentration and galactic location.

Figures (9)

• Figure 1: We take NGC 7789 as an example for our process. (Left-panel) The corner diagram of the MCMC result for four parameters in our model. (Right-panel) The compared results between the model obtained from MCMC and the original data. The histogram is original data which translates into the normalized number density distribution. The blue line is the model with the best-parameters from MCMC. The yellow line and green line represent cluster members and field stars, respectively.
• Figure 2: (Left panel) The relationship between structural parameters $W_0$ and $g$. The color dots represent OCs in Group A, colored with the half-mass radius $R_h$. The grey triple dots show the result for OCs in Group B. The green dots stand for GCs, which are from 2019de-Boer. The OCs in dashed-line box have low values of $W_0$ and $g$, while their $R_h$ are relatively large. (Right panel) The histograms represent the distributions of $W_0$, comparing OCs and GCs 2019de-Boer. The purple line represents OCs in Group A, while the green line represents GCs.
• Figure 3: ((Left panel) $W_0\ vs\ R_h$ between OCs (OCs in Group A for red dots and OCs in Group B for grey triple dots) and GCs (green dots). (Right panel) $g\ vs\ R_h$ between OCs (OCs in Group A for red dots and OCs in Group B for grey triple dots) and GCs (green dots). The red open-circle dots highlight the subset of OCs located within the dashed box in the left panel of Figure \ref{['fig:2']}, which have low values of $W_0$ and $g$.
• Figure 4: The left and right panels of the figure show the relationships between age and the structural parameters $W_0,\ g$, respectively. Blue points represent OCs in Group A, while grey triple dots indicate OCs in Group B, which are not included in the statistical analysis. The green lines stand the mean values of $W_0,\ g$ in different $log(Age)$ bins and the light green regions indicate the range of standard deviations of $W_0,\ g$ binned by $log (Age)$.
• Figure 5: The figure show the relationships between age and the structural parameters $R_h$ in our sample. Blue points represent OCs in Group A, while grey triple dots indicate OCs in Group B, which are not included in the statistical analysis. The green line is the lower limit of the half-mass radius within different age bins.