# Extra-Tidal Members and Dynamics of the Open Cluster NGC 6705
## 1 Introduction  
Open clusters are typical representatives of the thin disk of the galaxy [1]. By studying open clusters, we can gain insights into the dynamical evolution of stellar systems and galaxy structure. Thus, open clusters are very important tracers [2, 3]. NGC 6705 (\(l=27.300^{\circ},b=-2.744^{\circ}\)) is a widely studied open cluster, located approximately 2200 pc from Earth and over 6000 pc from the Galactic Center, with an age of about 300 Myr [4, 5, 6, 7]. It is known to be one of the richest and densest of the open clusters. NGC 6705 is an inner disk cluster of the Milky Way, and inner disk clusters serve as important probes for studying the formation and evolution of the Milky Way, the chemical abundance distribution of the disk, the dynamical properties, and the distribution of dark matter [8, 9, 10]. Through in-depth research on NGC 6705, we can gain a more comprehensive understanding of the Milky Way and its disk. [PERSON] et al. [11] estimated the core radius of NGC 6705 to be 1.23 pc and the tidal radius to be 29 pc, with the cluster's mass estimated to be between 3700 \(M_{\sun}\) and 11,000 \(M_{\sun}\).  
However, the NGC 6705 cluster, located 2200 pc from Earth in the direction of the Galactic Center, is heavily contaminated by field stars; this not only complicates the identification of cluster members but also affects the accuracy of stellar photometry and kinematicdata. This, in turn, makes the analysis of key dynamical characteristics, such as mass distribution, central density, and stellar velocity distribution, more challenging [12]. This complexity significantly limits the ability to gain a deeper understanding of the cluster's dynamical evolution and its trajectory within the Milky Way. If we obtain reliable cluster members, it becomes highly meaningful for studying the extended halo and extra-tidal structures of heavily contaminated clusters [13; 14; 15; 16]. Fortunately, Gaia-DR3 data provide us with high-precision positional measurements, parallaxes, and proper motion data [17; 18], enabling us to obtain reliable members of NGC 6705 within the complex star field background. Based on some previous studies, [PERSON] et al. [4] identified 1409 cluster members, while [PERSON] and [PERSON] [7] identified even more, over 1900 members, 39% of which were located outside the tidal radius. Accurately separating the core-halo components is of great significance for studying the spatial structure of NGC 6705, yet this point has not been specifically emphasized in previous papers. In this context, GMM is an effective tool for distinguishing between these components based on stellar positions and kinematics. GMM allows us to model the spatial distribution of stars in a probabilistic framework, providing insights into the distinct dynamical characteristics of the core and halo regions [16; 19]. By applying the GMM, we better understand the spatial structure and dynamical state of NGC 6705 and further analyze whether it has formed tidal structures. Tidal structures are typically the result of interactions between the cluster and the gravitational field of the Milky Way [20; 21]. By studying these structures, we can better understand the cluster's evolution within the galactic gravitational field and its dynamic history along its orbit. Recently, [PERSON] [22] confirmed the existence of tidal structures of NGC 6705.  
Reliable cluster members are crucial for studying star clusters, especially for highly contaminated inner disk clusters. In this paper, we aim to separate the reliable members of NGC 6705 and investigate its structural and dynamical properties. The remainder of this paper is organized as follows: Section 2 outlines the data and methods employed in this study. In Section 3, we investigate the structural parameters and dynamical state of the cluster using the identified members. Section 4 explores the tidal structures and their associated structural parameters. Finally, Section 5 presents the discussion and conclusions.