Asteroseismic and membership analysis of the eclipsing binary KIC 9777062 in NGC 6811

ABSTRACT Open clusters serve as natural laboratories for testing stellar evolution theories as their member stars share a common age, distance, and chemical composition. Within these environments, eclipsing binary (EB) systems are particularly valuable because their masses and radii can be determined with high precision, offering stringent benchmarks for stellar interior models. Such systems become even more powerful probes when combined with asteroseismic constraints, enabling simultaneous tests of fundamental parameters and internal structure. We present the first detailed interior models of the EB system KIC 9777062, a confirmed member of the open cluster NGC 6811, computed with the mesa stellar evolution code. The analysis combines binary dynamics with non-adiabatic $\delta$ Sct/$\gamma$ Dor pulsation modelling (via GYRE) and adiabatic solar-like oscillations predictions (via ADIPLS) for two independent opacity prescriptions (OPAL A09 and OPAL MB22). The best-fitting models yield $M_{\rm A} = 1.603 \pm 0.016\, \mathrm{M}_{\odot }$, $R_{\rm A} = 1.744 \pm 0.004\, \mathrm{R}_{\odot }$ and $M_{\rm B} = 1.419 \pm 0.009\, \mathrm{M}_{\odot }$, $R_{\rm B} = 1.544 \pm 0.003\, \mathrm{R}_{\odot }$. The corresponding ages are $t_{\rm A} = 0.932 \pm 0.230$ Gyr and $t_{\rm B} = 1.089 \pm 0.230$ Gyr (A09), and $t_{\rm A} = 0.867 \pm 0.230$ Gyr and $t_{\rm B} = 1.033 \pm 0.230$ Gyr (MB22), consistent with independent asteroseismic estimates for NGC 6811. Although non-adiabatic mode frequencies are only weakly sensitive to the adopted opacity table, large separation ($\Delta \nu$) predictions show a stronger dependence, making them a promising diagnostic for future observations. This study demonstrates the power of combining EB dynamics, open cluster constraints, and pulsation modelling to probe the internal physics of intermediate-mass stars, and underlines the potential of upcoming missions such as PLATO to refine these models.