Study of Open Star Clusters Using the Gaia DR3: I- Poorly Studied King 2 and King 5

In this study, we utilize photometric and kinematic data from \textit{Gaia} DR3 and the {\sc ASteCA} package to analyze the sparsely studied open clusters, King 2 and King 5. For King 2, we identify 340 probable members with membership probabilities exceeding 50\%. Its mean proper motion components are determined as $(\mu_\alpha\cos\delta,~\mu_\delta) = (-1.407 \pm 0.008, -0.863 \pm 0.012)$ mas yr$^{-1}$, and its limiting radius is derived as $6.94_{-1.06}^{+0.22}$ arcminutes based on radial density profiles. The cluster has an estimated age of $4.80 \pm 0.30$ Gyr, a distance of $6586 \pm 164$ pc, and a metallicity of $\text{[Fe/H]} = -0.25$ dex ($z = 0.0088$). We detect 17 blue straggler stars (BSSs) concentrated in its core, and its total mass is estimated to be $356 \pm 19~M_{\odot}$. The computed apex motion is $(A_o,~D_o) = (-142^\circ.61 \pm 0^\circ.08, -63^\circ.58 \pm 0^\circ.13)$. Similarly, King 5 consists of 403 probable members with mean proper motion components $(\mu_\alpha\cos\delta,~\mu_\delta) = (-0.291 \pm 0.005, -1.256 \pm 0.005)$ mas yr$^{-1}$ and a limiting radius of $11.33_{-2.16}^{+5.45}$ arcminutes. The cluster's age is determined as $1.45 \pm 0.10$ Gyr, with a distance of $2220 \pm 40$ pc and a metallicity of $\text{[Fe/H]} = -0.15$ dex ($z = 0.0109$). We identify 4 centrally concentrated BSSs, and the total mass is estimated as $484 \pm 22~M_{\odot}$. The apex motion is calculated as $(A_o,~D_o) = (-115^\circ.10 \pm 0^\circ.09, -73^\circ.16 \pm 0^\circ.12)$. The orbital analysis of King 2 and King 5 indicates nearly circular orbits, characterized by low eccentricities and minimal variation in their apogalactic and perigalactic distances. King 2 and King 5 reach maximum heights of $499 \pm 25$ pc and $177 \pm 2$ pc from the Galactic plane, respectively, confirming their classification as young stellar disc population.