Stellar Models with Convection and with Discontinuity of the Mean Molecular Weight

In this paper the effect of a discontinuity in the mean molecular weight, µ, in stellar models is examined. The case when such a discontinuity occurs in the envelope (r/R<1/2 and m[r] - M) is first considered. And it is shown that, in general, a discontinuity in µ produces convective instability in a small zone past the place where the discontinuity occurs. The resulting turbulence will cause mixing, and the star will rapidly adjust itself to a neighboring stable state, in which the interior region of higher µ and the exterior region of lower µ are separated by a transition region in which µ varies according to the law µ ∝ P^7/5 It is further shown that the time required for such a readjustment is very small, compared to the time in which a discontinuity in µ can be established. The case in which the discontinuity in µ occurs in the deep interior is next examined. It appears that, even here, a pure discontinuity of µ will, in general, be smoothed out and a transition zone of variable µ established. The law of variation of µ in this transition zone follows the law µ ∝ m(r)P^7/5. Owing to the presence of the factor m(r), the importance of the transition zone is greater when the change in µ occurs in the deep interior. Finally, stellar models are constructed which consist of convective cores and radiative envelopes with assigned mean molecular weights µ_i and µ_e, respectively, separated by transition zones of variable µ (also in radiative equilibrium). It is shown that these models satisfy all the conditions of the problem and, further, that they do not differ greatly in their physical properties from models constructed with point-source envelopes fitted directly to convective cores without regard to the continuity of the luminosity at the interface. However, up to a certain point their interpretation as a sequence of evolution is easier.