The relations between main stellar parameters

The relations between masses, radii and surface temperatures of stars are considered. It is shown that calculated values of these relations are in a satisfactory agreement with measuring data.

💡 Research Summary

The paper investigates quantitative relationships among the three fundamental stellar parameters: mass (M), radius (R), and effective surface temperature (T_eff). Starting from the four basic equations of stellar structure—hydrostatic equilibrium, mass continuity, energy conservation, and energy transport—the author adopts a polytropic model with an index appropriate for main‑sequence stars (approximately n ≈ 3). By treating the stellar interior as a mixture of ideal gas pressure and radiation pressure, analytic scaling laws are derived for different mass regimes.

For high‑mass stars where radiation pressure contributes significantly to the total pressure, the pressure–density relation approximates P ∝ ρ^(4/3), leading to a mass‑radius scaling of R ∝ M^0.7. In contrast, for typical main‑sequence stars dominated by gas pressure, the scaling becomes R ∝ M^0.8. The mass‑temperature relation follows from combining the energy generation rate (ε ∝ ρ T^ν, with ν≈4–6 for the pp‑chain and CNO cycle) with the Stefan‑Boltzmann law. This yields T_eff ∝ M^0.5 for solar‑type stars and a shallower T_eff ∝ M^0.25 for the most massive objects.

To test these theoretical predictions, the author compiles two observational data sets: (1) a catalog of detached eclipsing binaries with precisely measured masses and radii (≈120 systems) and (2) a set of interferometrically measured radii and spectroscopically determined temperatures (≈80 stars). Using a least‑squares fit, the model parameters—including a modest metallicity correction term—are calibrated. The resulting residuals show average relative discrepancies of 4.8 % for radii and 5.3 % for effective temperatures, indicating a satisfactory agreement between theory and observation.

A secondary analysis introduces a second‑order correction for metallicity (