Metallicity Dependence of Internal Structure Coefficients in 1–2 M ⊙ Stars and Application to the Eclipsing Binary BW Aquarii

We investigate how metallicity ( Z = 0.0001–0.03) shapes the internal structure of 1.0–2.0 M ⊙ stars by quantifying the apsidal-motion constant k 2 and the related structural coefficients η 2 and Δ 2 , together with the radial derivative d η 2 /dr (hereafter d η 2 ). Using evolutionary models computed with MESA, we derive these coefficients by solving Radau’s differential equation based on the stellar density profiles. We find that increasing metallicity generally produces more centrally concentrated interiors, with the metallicity dependence approaching saturation at near-solar and metal-rich values ( Z ≥ 0.02). While zero-age main-sequence models show smooth, monotonic behavior in η 2 and d η 2 , evolved models at 3 Gyr develop complex local extrema and core-region undulations, signaling deep structural reorganization with age. To test these trends, we compare our predictions with the eclipsing binary BW Aquarii ( M 1 = 1.365 M ⊙ , M 2 = 1.483 M ⊙ ; age = 3 Gyr). Our near-solar models successfully reproduce the observed apsidal-motion constant (log k 2 , obs = −2.02 ± 0.08). Critically, the d η 2 profiles reveal that even a modest mass difference of ~0.12 M ⊙ leads to radically different internal structures, as evidenced by the emergence of sharp structural peaks and undulations in the secondary component. These results demonstrate that η 2 and d η 2 provide sensitive diagnostics of stellar stratification that are masked by the integrated k 2 constant, emphasizing the necessity of precise mass and metallicity modeling in binary star studies.