2025ApJ...994...77H

The post-main-sequence evolution of massive stars is highly sensitive to key stellar model parameters, particularly initial rotational velocity and metallicity. Using the MESA code, we computed stellar models with initial masses of 16-32 M_⊙, metallicities of Z = 0.0047-0.025, and initial rotational velocities of 0.0-400 km s^–1. Our results demonstrate that the evolutionary trajectory toward red or blue supergiants is primarily regulated by the parameter ϵ_grav, which is the rate of generation or absorption of gravitational energy in the energy conservation equation. Three main factors drive the evolution toward lower effective temperatures (to produce the reduced blue-to-red supergiant ratio, B/R) during central helium burning: (1) an increase in helium and CNO abundances in the hydrogen-burning shell, (2) an increase in the core mass ratio, and (3) a decrease in central helium abundance during the latter half of core helium burning. Rotation amplifies the core mass during the core He-burning phase, inducing atmospheric inflation, stronger mass loss, and redward evolution. Consequently, rapid rotation leads to a lower B/R supergiant ratio. A thinner envelope induced by strong winds favors a higher B/R supergiant ratio. The minimum envelope mass required for stars to transition from a red to a blue supergiant decreases with higher metallicity and higher initial rotational velocity. High-metallicity stars undergo an extended blue excursion after the red supergiant phase, increasing the B/R supergiant ratio. A higher B/R supergiant ratio is strongly linked to the presence of an intermediate convective region during the first crossing of the Hertzsprung gap.