Study On The Gravitational Dim Effect Of A Baroclinic Rotating Star

Rotation is one of the important factors that affect the structure and evolution of stars. In recent years, a large number of observations have shown that the rotation of stars causes the angular momentum and the transfer of elements in the stellar interior,and it has an important influence on the structure and evolution of stars. The observations show that Achernar is a star close to the critical rotation Based on the observational data of Achernar. We have given the distributions of the physical quantities on the isobaric surface and these distributions are derived from Legendre series expansions. We have found the relationship between all levels of perturbation potential functions including rotational and tidal distortions and the distributions of density and pressure under the condition of the inclined pressure structure. In particular, the gravitational darkening with the models including the effects of rotation and tide are investigated. We have found that the critical ratio of equatorial radius to the polar one can be more consistent with the observations in rotating binaries than the one in single rotating model. The reason is that the tidal force can shorten the polar radius because the tidal force exerts an inward force at two polar points.However, the theoretical angular velocity in binaries is smaller than the one in observations. It is also shown that the positive shear enhances the centrifugal force and decreases the mean effective gravitational acceleration and effective temperature whereas negative shears plays an role in strengthening the effective gravitational acceleration. Moreover, solid body rotation has not been supported inside Achernar because magnetic fields have not been detected in observations. Furthermore, the theoretical angular velocity in rigid rotation is higher than angular velocity in observations. It is shown that the star with the initial big angular velocity has big radius and central density at the beginning and middle of the main sequence, and it has small radius and central density due to the large loss of spin angular momentum.Also, we find that rotation can make the star more centrally condensed and large in size, decreasing the quadrupolar momentum, the gyration radius, central temperature,and the rate of the hydrogen production energy in the stellar core. The star shifts towards low temperature and luminosity in the HR diagram in rotating model.Compared the theoretical results with observations, It is illustrated that when the theoretical spin angular velocity of Achernar is151065.4--? s and the positive shearss?? /are 0.7851, the temperature of the polar points is 16041 K and the temperature of equatorial sphere is 12073 K. Relative errors between the theoretical values and observations are less than 3% and are listed in Table 1. This model is the best and most possible one for Achernar.