Stellar Models with Convection and with Discontinuity of the Mean Molecular

In this paper the effect of a discontinuity in the mean molecular weight, j~, in stellar models is ex- amined. The case when such a discontinuity occurs in the envelope (r/R < ~ and mr - M) is first con- sidered. And it is shown that, in general, a discontinuity in ~ 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 /.L and the exterior region of lower J.L are separated by ~ transition region in which ~ varies according to the law ~ p~/~* It is further shown that the time required for such a readjustment is very small, compared to the time in which a discontinuity in j~ can be established. The case in which the discontinuity in j~ occurs in the deep interior is next examined. It appears that, even here, a pure discontinuity of j~ will, in general, be smoothed out and a transition zone of variable ~ established. The law of variation of JL in this transition zone follows the law ~t ~ mfr)P7/5. Owing to the presence of the factor m(r), the importance of the transition zone is greater when the change in .~ oc- curs in the deep interior. Finally, stellar models are constructed which consist of convective cores and radiative envelopes with assigned mean molecular weights j~ and Pe, respectively, separated by transition zones of variable ~ (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 lumi- nosity at the interface. However, up to a certain point their interpretation as a sequence of evolution is easier