On Second Helium Ionization as a Cause of Pulsational Instability in Stars.
Abstract
The purpose of this investigation was to test the hypothesis (Zhevakin 1953, 1954a, b; Cox and Whitney 1958) that He+ ionization in the envelope is the source of the instability in cepheid variables and possibly also in other types of pulsating stars. Numerical solutions of the complete set of linearized, non adiabatic pulsation equations have been obtained for a large number of simplified stellar envelope models in radiative equilibrium. The solutions have been used to compute the (negative) dissipation in the envelopes and to estimate the (positive) dissipation in the interiors. The parameter values have been chosen so that the envelopes correspond approximately to classical cepheids, RR Lyrae variables, W Virginis variables, and zeroage mainsequence stars in the middle and late A's. We find that, with the possible exception of the W Virginis variables (for which the envelope models were probably inadequate), instability in a star of given L and M due to He+ ionization cannot occur unless the equilibrium radius R is very close to a "critical" radius, R ,ft (say log R/R,st < 0.150.2 for classical cepheids and RR Lyrae variables), which depends on L and M. Models of given L and M with R = Rcrit (called "critical models") are maximally unstable with respect to R, and the stability depends sensitively on R. For models close to the critical models and having a reasonable helium/hydrogen ratio B (say >= 0.100.15, by numbers), the negative dissipation in the envelope approximately cancels the positive dissipation in the interior, so that such models could be pulsationally unstable. We accordingly regard the critical models as possible simplified models of real pulsating stars, even though we cannot conclude definitely that these models are actually unstable. When the critical models are plotted on a HertzsprungRussell diagram, the points form "loci of maximum instability" which fall close to or within regions occupied by common types of pulsating stars; the computed periods are also close to the corresponding observed periods. Stability is far less sensitive to the location of a star along a locus of maximum instability than perpendicular to it; hence the corresponding theoretical "regions of instability" are long and narrow. We conclude that He+ ionization probably accounts for the instability in classical cepheids and RR Lyrae variables and also (but less certainly) in W Virginis variables and dwarf cepheids of the a Scuti type. Our conclusion in regard to classical cepheids is corroborated by important recent calculations of Baker and Kippenhahn (1962). Pulsational instability in the critical models increases rapidly with increasing helium abundance for small values of B and slowly for larger values of B. It is also concluded that pulsations in the first overtone are probably normally damped in models near the critical models. The dependence of pulsational stability on several other factors is examined. Some general features of the solutions of the pulsation equations and some effects of nonadiabaticity on Q = 11(p / ) are discussed. A physical interpretation of the stability results is also presented.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1963
 DOI:
 10.1086/147661
 Bibcode:
 1963ApJ...138..487C