Sıfır yaş ana kol (ZAMS) yıldız modellerinin etkin politropik karakterizasyonu: kütle ve metalikliğin rolü

Abstract

Bu çalışma, 1–40 Mʘ kütle aralığındaki Sıfır-Yaş Ana Kol (ZAMS) yıldız modelleri için etkin politropik üs γ ve buna karşılık gelen politropik indis n değerlerini sistematik olarak incelemektedir. EZ-Web kodu aracılığıyla üretilen iç yapı profilleri kullanılarak ve Radau diferansiyel denklemi çözülerek, her bir yıldız modeli tek bir etkin parametre ile karakterize edilmiştir. Sonuçlarımız, yıldız kütlesi arttıkça γ değerinin monotonik olarak azaldığını ve klasik 4/3 sınırına yaklaştığını; politropik indis n'in ise artarak daha yüksek merkezi yoğunlaşmaya sahip yapılara işaret ettiğini göstermektedir. Ayrıca, artan metal bolluğunun (Z = 0.0001–0.02), sabit bir kütlede daha yüksek n değerlerine yol açtığı saptanmıştır. Bu bulgular, klasik politropik teori ile modern sayısal yıldız evrimi arasında önemli bir köprü kurmaktadır

Keywords

• Polytropik yıldız modelleri
• Radau integrasyon yöntemi
• ZAMS kütle–metaliklik ilişkisi
• yıldız iç yapısı

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

Abstract

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.

Keywords

• Polytropic stellar models
• Radau integration method
• ZAMS mass-metallicity relation
• Stellar internal structure.

References

1. Chandrasekhar, S., An Introduction to the Study of Stellar Structure. Chicago, University of Chicago Press, (1939).
2. Brooker, R. A. ve Olle, T. W., Apsidal-Motion Constants for Polytropic Models, Monthly Notices of the Royal Astronomical Society, 115, 101–106, (1955).
3. Wei, X., Construct a realistic stellar model with polytropic relation, Astronomy and Computing, 41, 100650, 1–3, (2022).
4. Dewberry, J. W., Tidally Driven Inertial Waves Enhance Eccentricity Damping and Spin Evolution in Planets and Stars, The Astrophysical Journal, 997, 27, 1–15, (2026).
5. Ijaz, S. ve Bhatti, M. Z., Investigating compact stars in f(Q) gravity: Analytical models and physical viability, Nuclear Physics B, 1022, 117243, 1–20, (2026).
6. Afzal, W. A. ve Feroze, T., A generalized polytropic equation of state stellar model with anisotropic charged fluid, Astrophysics and Space Science, 369, 11, 1–17, (2024).
7. Lai, X. Y. ve Xu, R. X., A polytropic model of quark stars, Astroparticle Physics, 31, 128–134, (2009).
8. Lindblom, L. ve Masood-ul-Alam, A. K. M., Limits on the adiabatic index in static stellar models, Physical Review D, 49, 172–181, (1993).

9. Paxton, B., Bildsten, L., Dotter, A., et al., Modules for Experiments in Stellar Astrophysics (MESA), The Astrophysical Journal Supplement Series, 192, 1–35, (2011).
10. Paxton, B., Cantiello, M., Arras, P., et al., Modules for Experiments in Stellar Astrophysics (MESA): Planets, oscillations, rotation, and massive stars, The Astrophysical Journal Supplement Series, 208, 1–43, (2013).
11. Paxton, B., Marchant, P., Schwab, J., et al., Modules for Experiments in Stellar Astrophysics (MESA): Binaries, pulsations, and explosions, The Astrophysical Journal Supplement Series, 220, 1–44, (2015).
12. Paxton, B., Schwab, J., Bauer, E. B., et al., Modules for Experiments in Stellar Astrophysics (MESA): Convective boundaries, element diffusion, and massive star explosions, The Astrophysical Journal Supplement Series, 234, 1–50, (2018).
13. Paxton, B., Smolec, R., Schwab, J., et al., Modules for Experiments in Stellar Astrophysics (MESA): Pulsating variable stars, rotation, convective boundaries, and energy conservation, The Astrophysical Journal Supplement Series, 243, 1–44, (2019).
14. Kopal, Z., Close Binary Systems. Chapman & Hall, London, (1959).
15. Andronopoulos, A. ve Gourgouliatos, K. N., Equation of State of Highly Asymmetric Neutron Star Matter from Liquid Drop Model and Meson Polytropes, Symmetry, 18, 225, 1–18, (2026).