Structure and Evolution of Rotating Stars

The star rotation is a difficult problem in the theory of the stellar structure and evolution. Recent observational data, especially observational data for the early type stars have indicated that some efficient mixing processes might be induced by the rotation. Thus, the study of the evolution of rotating stars has attracted more and more attention in the last decades. The stellar structure and evolution model will be two dimensional due to the effects of the rotation. Many scientists have tried to simplify the two dimensional stellar structure and evolution model to one dimensional. Their ways of dealing this problem are reviewed, and a relative simple way is proposed based on the following assumption: physical quantities such as the temperature, density, pressure, luminosities, chemical composition and angular velocities are nearly the same on the equipotential surfaces, and they are equal to their counterparts on the equivalent sphere. We have derived the new structure and evolution equations for rotating stars by using the quantities of an point on the equivalent sphere, and construced a new model. Comparing with the non-rotating model, it has the following changes: the change in the hydrostatic equation; the change in the radiation temperature gradient and the criterion of the convection, and the enhancement of the stellar wind and angular momentum loss. As the application of our new rotating model,we have studied the main factors which affect the formation and extension of the blue loops for the middle and low mass stars. It is interesting to notice that although the rotation and overshooting can both affect the length of the blue loops, their effects are appreciably different. Hence, a comparison of the differences in the inner structure of a star affected by the rotation and overshooting can isolate those factors, which play a primary role in the formation and extension of the blue loops. We have found that the feature of the blue loops is correlated to the variation of the total energy production rate of the star during the core He-burning. When the variation of the total energy production rate is contributed mainly by the H-burning shell, the formation and extension of the blue loops is dependent on the temperature and the hydrogen profile in the μ-gradient region and the inward penetration of the outer convective zone. When the variation of the total energy production rate is contributed by both of the H-burning shell and the core He-burning, the formation and extension of the blue loops is dependent not only on the properties of the μ-gradient region, but also on both of the size of the He core and the temperature in the region of the He core. In the present paper, some physical effects of the star rotation are discussed.