Theoretical space densities and frequency distributions of initial masses of red giants in different evolutionary phases are calculated and compared with observational data on the numbers and masses of peculiar red giants of types Ba, R, S, and N (P giants) in order to obtain constraints on the mixing process. Constraints imposed by luminosities, temperatures, space densities, and masses are combined. It is concluded that: (1) the properties of R stars are consistent with mixing at the helium-core flash; (2) most Ba stars can be identified with the helium-core flash; (3) the helium-core flash cannot be the sole cause of mixing in N and S stars; (4) helium-shell flashes are marginally consistent with observational constraints on cool P stars; and (5) if helium-shell flashes are responsible for the cool P stars, the observed mean masses constrain the mixing process to occur in stars of low initial mass when the core mass is fairly small.
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Scalo et al. (1979) studied this question.