A Deep Look into the Intermediate-Age Open Cluster NGC 2506: What Binary Systems Reveal About Cluster Distance and Age

Using high-precision observations from the space-based \textit{Gaia} and \textit{TESS} missions, complemented by ground-based spectroscopic data and multi-band photometric surveys, we perform a detailed investigation of the Galactic open cluster NGC~2506. We present a new analysis of the intermediate-age open cluster NGC~2506, using joint fits to the radial velocities (RVs) and spectral energy distributions (SEDs) of five double-lined binary systems, including two eclipsing binaries. The analysis yields self-consistent estimates of the cluster's age, distance, and extinction, based on 18 free parameters: 10 stellar masses, 5 orbital inclinations, and common values for age, distance, and $A_V$. The SED fitting incorporates stellar isochrones, and the resulting parameters are examined through HR diagrams (R--$T_{\rm eff}$, R--M, and M--$T_{\rm eff}$) to assess evolutionary consistency. The age we derive for the cluster is $1.94 \pm 0.03$ Gyr for an assumed [Fe/H] = -0.30, and a fitting formula is given for extrapolation to other metallicities. The distance we find from the SED fitting is $3189 \pm 53$ pc, and this is to be compared with our own inference from the Gaia data which is $3105 \pm 75$ pc, based on 919 stars identified as cluster members. Our results demonstrate the power of binary systems in tightly constraining cluster-wide age and distance at this evolutionary stage. This approach represents one of the most accurate characterizations of an intermediate-age open cluster using multiple binary systems.