Time-Series Photometric Detection and Physical Characterization of Variable Stars in Four Intermediate- to Old-Age Galactic Open Clusters
We present a ground-based time-series photometric study of stellar variability in four intermediate- to old-age open clusters NGC 2192, NGC 2266, NGC 2509, and IC 1369 based on high-cadence Cousins R-band observations obtained with the 0.6 m VASISTHA telescope at the IERCOO observatory. The monitoring campaign comprises more than 34 h of time-series data, providing sensitivity to short-period variability on timescales of 0.02-2 d. We identified between 190 and 290 probable members in each cluster using a Gaussian Mixture Model. Structural parameters were derived from radial density profiles fitted with King models. Fundamental parameters were further constrained using color-magnitude diagram analysis with PARSEC isochrones, yielding ages of 0.3-1.6 Gyr and distances of 2.5-3.9 kpc. From the time-series photometry, we identify four new variable stars and seven previously uncharacterized periodic variables, including δ Scuti and γ Doradus pulsators, as well as rotational variables. The detected variables exhibit periods between 0.12-0.90 d, with R-band amplitudes ranging from 0.01 to 0.20 mag. Periods were determined using Lomb-Scargle analysis of calibrated light curves. For a subset of variables, spectral energy distribution fitting was performed to derive effective temperatures (4300-10 000 K), radii (1.3-46 R_{\odot}), and luminosities (2-100 L_{\odot}), enabling reliable placement on the Hertzsprung-Russell diagram. We present PHOEBE light-curve modelling of the W UMa-type eclipsing binary Gaia DR3 2164531610149292288 in IC 1369, deriving its physical parameters and providing the first detailed characterization beyond its previously reported variability. These results demonstrate that combining dense-cadence ground-based observations with Gaia astrometry provides a reliable approach for identifying and characterizing variable stars in OCs.