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Astron. Astrophys. 317, 121-124 (1997)

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3. The mechanism powering mass ejection

In order to investigate whether the dynamical instability can occur in the regions close to the surfaces of red giants and AGB stars, we perform the evolutionary calculations for the stars of 7 [FORMULA] and 2.8 [FORMULA] from the zero-age main sequence to the AGB stage taking into account of turbulent pressure. The numerical model and the expressions for turbulent pressure,the equation of state and the thermodynamical quantities with the consideration of turbulent pressure are discussed in detail in the first paper of this series (cf.Jiang and Huang 1996). The variations of the density and the function [FORMULA] in the envelope of the star of 7 [FORMULA] during the AGB stage are illustrated in Fig. 1. The solid and the dotted curves in Fig. 1 (also in all the following figures) indicate the cases with or without the contribution of turbulent pressure, respectively. From the solid curves in Fig. 1 we find that in the region where the relative mass [FORMULA] has the values of 0.992-0.993 the value of the function [FORMULA] is positive ( [FORMULA] ) and the desity gradient reverses ( [FORMULA] ). This indicates that this region is dynamically instable when the contribution of turbulent pressure is considered. However, the dotted curves in Fig. 1 show that in the same region the value of the function [FORMULA] is negative. This means that the same region is stable when the contribution of turbulent pressure is neglected. Therefore, the occurrence of dynamical instability in the region with [FORMULA] of the AGB star of 7 [FORMULA] is caused obviously by the effect of turbulent pressure. Furthermore, the solid curves in Fig. 1 show that in the layers outside the instable region the value of the function [FORMULA] is negative. This indicates that these layers are in the hydrostatic equilibrium. As a result of the fact, the gas elements in the instable region move outwards but the gas elements in the layers outside the instable region are quite, a shockwave might occur on the outer border of the instable region.The shockwave finally induces mass ejection of the outer layers. This might be the mechanism powering the superwind of the AGB stars. The variations of the density [FORMULA] and the function [FORMULA] in the envelope of the star of 7 [FORMULA] during the red giant stage are illustrated in Fig. 2, where the curves have the same behaviour as shown in Fig. 1. Thus, we know that the effect of turbulent pressure causes the dynamical instability in the region which has the relative masses of 0.99996-0.99997. As

[FIGURE]Fig. 4. The changes in the density [FORMULA] and the value of [FORMULA] in the envelope of a red giant with 2.8 [FORMULA]. The solid and the dotted curves have the same meaning as in Fig. 1.

a result, a mass ejection occurs at the surface of the red giant of 7 [FORMULA] due to the same mechanism as described above. Comparing the position of the instable region in Fig. 1 to that in Fig. 2, we find that the position of the instable region for the AGB star of 7 [FORMULA] is deeper than that for the red giant of 7 [FORMULA]. This indicates that the rate of mass loss of the AGB star must be greater than that of the red giant with the same initial mass. Figs. 3 and 4 show the variations of the density [FORMULA] and the function [FORMULA] in the envelopes of the star of 2.8 [FORMULA] during the AGB stage and the red giant stage respectively. The curves in Figs. 3 and 4 have the same character as shown in Figs. 1 and 2. Thus, we know that the effect of turbulent pressure also causes the dynamical instability in the regions close to the surfaces of these stars. As a result the mass ejection occurs at the surface of the star of 2.8 [FORMULA] during the AGB stage and the red giant stage.

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