# Extra-Tidal Members and Dynamics of the Open Cluster NGC 6705
## 5 Discussion and Conclusions  
In this paper, we conducted a comprehensive investigation into the structural parameters, dynamical state, and extra-tidal members of the open cluster NGC 6705, employing Gaia-DR3 astrometric data combined with DBSCAN clustering algorithms. Through the identification of 1969 reliable cluster members, we successfully characterized the core and halo components of the cluster, revealing a tight structure. By fitting the RDP to the King  
Figure 17: Parallax (\(\varpi\)) of 3D cluster members as a function of radial distance (R), where red dots are extra-tidal 3D members and gray dots are intra-tidal 3D members.  
Figure 18: PM-VPDs for extra-tidal members (red dots) and intra-tidal members (blue dots) of 3D clusters. Gray dots represent field stars.  
model, we estimated the core radius (\(R_{c}\)) to be 3.11 \(\pm\) 0.21 arcmin (\(\sim\)2.02 pc) and the tidal radius (\(R_{t}\)) to be 20.02 \(\pm\) 0.71 arcmin (\(\sim\)13.00 pc). These results indicate that NGC 6705 exhibits a tighter core and a larger tidal extent compared to previous studies, such as the work of [PERSON] and [PERSON] [7], where a smaller core and tidal radii were reported. The high central density of NGC 6705, as reflected by the concentration parameter (C\(\sim\)0.81), suggests that the cluster's internal gravitational interactions have led to the formation of a tightly bound core, which may be a result of ongoing dynamical relaxation. The GMM analysis allowed us to distinguish between the core and halo components of the cluster. PCA further reveals that the core has a semi-major axis of \(\sim\)7\({}^{\prime}\) (\(\sim\)4.5 pc) and an ellipticity (\(e\)\(\sim\)0.89), indicating a nearly circular core with minimal tidal distortion. In contrast, the halo exhibits a more elongated structure with a semi-major axis of \(\sim\) 21\({}^{\prime}\) (\(\sim\)13.6 pc) and a lower ellipticity (\(e\)\(\sim\)0.80), suggesting that the outer regions of the cluster are significantly influenced by external tidal forces, likely from the galactic potential. Based on these results, we detected a significant mass segregation effect, indicating that brighter stars tend to concentrate in the core, while fainter stars are distributed in the halo. Additionally, in contrast to earlier findings [22], no clear tidal tail structures could be detected around the cluster. However, we identified 72 extra-tidal members, implying that NGC 6705 is losing its members. These extra-tidal members have a wide range of magnitudes (star masses), which is comparable to that of the intra-tidal members. Our study contributes to understanding the dynamical evolution of NGC 6705, particularly in the context of mass segregation and tidal stripping. The detection of extra-tidal stars highlights the cluster's interaction with the galactic tidal field, which may have profound implications for its long-term dynamical evolution. Future studies utilizing higher precision astrometric data can further explore the extent of tidal features and provide deeper insights into the processes driving star loss in open clusters located in the inner Galactic disk.  
Conceptualization, C.Z. and X.G.; methodology, C.Z. and X.G.; formal analysis, C.Z. and X.G.; writing--original draft preparation, C.Z. and X.G.; writing--review and editing, C.Z. and X.G. All authors have read and agreed to the published version of the manuscript. This work was supported by the Foundation of Changzhou University (Grant Nos. KYP2202231C, KYP2402265C). Not applicable. Not applicable.  
The authors declare no conflicts of interest.