Effective polytropic characterization of ZAMS stellar models: The role of mass and metallicity

This study systematically investigates the effective polytropic exponent γ and the corresponding polytropic index n for Zero-Age Main-Sequence (ZAMS) stellar models within a mass range of 1–40 Mʘ . Using internal structure profiles generated via the EZ-Web code and solving the Radau differential equation, we characterize each stellar model with a single effective parameter. Our results indicate that γ decreases monotonically as stellar mass increases, approaching the classical 4/3 limit while the polytropic index n increases, signaling more centrally condensed structures. We also find that increased metallicity (Z = 0.0001–0.02) leads to higher n values at a fixed mass. These findings provide a vital bridge between classical polytropic theory and modern numerical stellar evolution.