# Extra-Tidal Members and Dynamics of the Open Cluster NGC 6705
## 4 Extra-Tidal Members  
In this study, after identifying reliable 5D \((l,b,\alpha,\mu_{a}cos\delta,\mu_{\delta})\) cluster members, we conducted clustering analysis using 3D \((l,b,\alpha)\) data, focusing on kinematic parameters to further identify members located outside the tidal radius. In the clustering analysis based on 3D data, position parameters are removed, but the kinematic parameters (self and parallax) are retained. This means that we now pay more attention to stars that may have changed in position but are still kinematically aligned with the cluster [37]. Because of tidal forces, these stars may have deviated from their original positional characteristics outside the tidal radius, but their kinematics may still be consistent with the cluster members. Therefore, clustering analysis based on 3D data can help us identify these extra-tidal stars that are still kinematically part of the cluster. Figure 14 indicates that \(P_{3D}=0.907\) is a safe threshold, and after performing clustering analysis using 3D data, we obtain 571 members (\(P_{3D}>0.907\)) extended up to \(\sim\)30 arcmin (\(\sim\)19 pc) from the cluster center (see Figure 14). In the 3D parametric space, field star contamination is more significant, leading to more than 1000 5D members being identified as field stars. Based on the 3D members, we find that NGC 6705 has formed an extremely extended halo, and 72 members may have escaped from the cluster and become extra-tidal members (\(>\)20.02 arcmin, see Figure 15). Previous work by [PERSON] [22] showed the detection of the tidal tail of NGC 6705 (length \(\sim\)3259 pc) with fewer member stars than ours However, in our work, no clear tidal tails can be detected around the cluster. This may be due to the different methods and data used. Figure 15 illustrates the distribution \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Component** & **Stars** & **Central Positions** & \(\mathbf{\sigma_{II}}\) & \(\mathbf{\sigma_{bb}}\) & **pmRA** & **pmDEC** & \(\mathbf{\sigma_{1}}\) & \(\mathbf{\sigma_{2}}\) & \(\mathbf{e}\) \\ \hline Core & 1279 & \((l,b)=(27.2987^{\circ},-2.7702^{\circ})\) & \(2.2^{\prime}\) & \(2.4^{\prime}\) & \(-1.543\) & \(-4.167\) & \(2.4^{\prime}\) & \(2.2^{\prime}\) & 0.89 \\ Halo & 690 & \((l,b)=(27.4815^{\circ},-2.6402^{\circ})\) & \(7.0^{\prime}\) & \(5.6^{\prime}\) & \(-1.539\) & \(-4.163\) & \(7.0^{\prime}\) & \(5.6^{\prime}\) & 0.80 \\ \hline \end{tabular}
\end{table} 
Table 2: Fundamental parameters of the core and halo components based on GMM and PCA. Figure 13: Cumulative G magnitude distribution of core and halo members. of the positions of 3D members. Intra-tidal members show a denser structure, whereas extra-tidal members are more scattered. Extra-tidal members indicated by the red dots are part of the tidal structure; these stars are located further away from the cluster center in space, but they may still remain kinematically associated with the cluster. Figure 14: \(P_{3D}\) of member stars as a function of radial distance to the cluster center. The red line indicates the threshold probability (\(P_{3D}\) = 0.907) used to select reliable cluster members. The blue dots represent individual member stars, with their corresponding membership probabilities. Figure 15: Two-dimensional spatial distribution of 3D members with field stars (gray dots) and cluster members (colored dots). Intra-tidal 3D members (<20.02 arcmin) are shown as blue dots, while extra-tidal 3D members (>20.02 arcmin) are shown as red dots. The green dashed circle represents the tidal radius of the cluster (20.02 arcmin). The CMDs of the intra-tidal and extra-tidal 3D members are shown in Figure 16. We find that the extra-tidal members cover a wide range of magnitudes (G\(\sim\)13-20 mag), and some extra-tidal members are located on the upper MS (G\(\sim\)15-17 mag). This indicates that some extra-tidal members have relatively high masses. [PERSON] et al. [16] found that star evaporation may be more efficient than mass segregation in open clusters.