Comprehensive Analysis of Middle-Aged Open Cluster NGC 6793 in Vulpecula via Gaia DR3 Data

We conducted an in-depth analysis of NGC 6793 open cluster via Gaia DR3 data, including astrometric, spectroscopic, and photometric measurements. Selection of 147 stars, which show membership probabilities $P\geq0.5$ were classified as likely members. The mean trigonometric parallaxes and proper-motion components of the cluster were found to be $\varpi = 1.674 \pm0.045$ mas and ($\mu_{\alpha}\cos \delta$,~$\mu_{\delta}$) =($3.814\pm0.031$,~$3.547\pm0.034$) mas yr$^{-1}$. Fundamental astrophysical parameters of NGC 6793 are derived simultaneously as $t$ = $650 \pm 50$ Myr, $\mu$ = $9.508\pm0.070$ mag, and $E(G_{\rm BP}-G_{\rm RP})$ = $0.361 \pm 0.035$ mag. Additionally, the cluster's luminosity function analysis reveals the $G$-absolute magnitude limit of the most likely stars, indicating a well-defined stellar population. The total mass of the cluster, determined through the mass function (MF) and considering stars with membership probabilities $P \geq 0.5$, was estimated as 139 $\pm$ 12 $M/M_{\odot}$. The slope of the MF was found to be $\Gamma = 1.40 \pm 0.26$, a result consistent with the Salpeter value. The kinematic analyses present velocity ellipsoid parameters as well as the convergent point $(A_{\rm o},~D_{\rm o}) = \left(85^{\circ}.85 \pm 0^{\circ}.11,~3^{\circ}.12 \pm 0^{\circ}.57\right)$. Analyses have shown that it is moving in a box-shaped orbit beyond the Sun's galactic radius and belongs to the thin disk population of the Milky Way. The calculated relaxation time suggests that NGC 6793 has reached a dynamically relaxed state, where the dynamical evolution parameter $\tau$ significantly exceeds one. These results highlight both the cluster's internal stability and its connection to the thin disc population.