A Preliminary Analysis of the Effectiveness of Second Helium Ionization in Inducing Cepheid Instability in Stars.
A program of numerical calculations, carried out by the author, is described and summarized. The purpose of the program was to test the suggestion (Zhevakin 1953, 1954a, b; Cox and Whitney 1958; Cox 1959) that second helium ionization, occurring at a critical depth in a stellar envelope, is the ultimate source of cepheid instability. All calculations were performed on an IBM 704 electronic computer. Simplified, purely radiative envelope models were adopted for stars of prescribed mass, luminosity, radius, and chemical composition, and the negative dissipation in the envelopes was computed numerically as a function of these parameters. The Woltjer theory in the first approximation was used to obtain the non- adiabatic flux and temperature variations, from which the negative dissipation in the envelopes could be computed. Second helium ionization was explicitly included in the calculations, but first helium ionization and hydrogen ionization were omitted. A strong destabilizing influence, resulting from second helium ionization, was revealed in the envelope models for population I cepheids, assuming reasonable helium abundances. The magnitude of the negative dissipation in the envelopes was comparable to the estimated positive dissipation in the interiors, for reasonable radii. While no definitive conclusions could thus be drawn concerning the sign of the total dissipation for the entire star, the possibility of pulsational instability is, at any rate, not excluded by these calculations. For log L (solar units) = 3.13 and B (helium/hydrogen ratio, by numbers) = 0.15, maximxm instability for the entire star was attained for a value of the radius about 1.6 times larger than the empirical value. For these same values of log L and B and for radii near the observed values, the amplitude of the surface flux variations was about 0w7 or OWS and the phase lag (relative to minimum radius) was about 40 or 50 these values may be considered to be very roughly consistent with observations of classical cepheids. It may be inferred from the calculations that, for stars in the cepheid region, first helium ionization and hydrogen ionization are not primary causative agents in producing pulsational instability, at least for the kinds of envelopes considered here. These ionizations, however, had they been included in the calculations, would have increased the magnitude of the pulsational instability (through indirect effects) and would have brought the surface flux variations into closer agreement with observation than the present calculations show. Results for population II cepheids were inconclusive because the low surface gravities of these stars (assuming M = 1.25 Mo) invalidated some of the approximations that were used. It is concluded that the results of the calculations are generally favorable to the helium-ionization hypothesis, at least as applied to the population I cepheids. Because of various uncertainties, however, this conclusion must be regarded as tentative.