EVOLUTIONARY AND PULSATIONAL CONSTRAINTS FOR SUPER-METAL-RICH STARS WITH Z = 0.04

We investigate the evolutionary behavior of stellar structures with me tallicity Z = 0.04 in order to disclose theoretical expectations for b oth evolutionary and pulsational behaviors of super-metal-rich (SMR) o bjects, which are found in the solar neighborhood, in the Galactic bul ge, and in elliptical galaxies. A suitable set of stellar models is pr esented for the given metallicity value but for two alternative assump tions about the amount of original He, namely, Y = 0.34 and Y = 0.37. Theoretical isochrones for H-burning evolutionary phases are presented for ages ranging from 18 to less than 1 Gyr. The evolutionary behavio r of He-burning structures is discussed for suitable assumptions about the mass of the progenitors and the amount of mass loss. For both quo ted assumptions of original He abundance, we confirm that at metal con tents larger than the solar value the luminosity of the horizontal bra nch (HE) at the RR Lyrae gap increases as the metal content increases, a direct consequence of the expected simultaneous increase of origina l He. We find that, at the exhaustion of central helium, SMR stars def initely undergo the gravonuclear instabilities previously found in som e He-burning structures with solar metallicity. On the basis of such a n evolutionary scenario, we investigate the expected pulsational behav ior of He-burning SMR stars for suitable assumptions on the pulsators' evolutionary parameters. Linear blue boundaries for pulsational insta bility in the fundamental and in the first-overtone modes are derived, and their dependence on stellar mass and chemical composition is inve stigated. Nonlinear, nonlocal, and time-dependent convective models ar e discussed, the modal stability is investigated for the first two mod es, and the theoretical predictions about the period distribution insi de the instability strip and the shape of both light and velocity curv es are presented. Full-amplitude, nonlinear envelope models show that the range of effective temperatures in which SMR RR Lyrae variables pr esent a stable limit cycle is smaller than that of pulsators character ized by lower metal abundances. In fact, the width of the instability strip at the zero-age horizontal branch luminosity level decreases fro m 1400 to 1100 K. Also taking into account the peculiar narrow mass ra nge characterizing SMR pulsators, we estimate that these two factors a lone cause a decrease in the occurrence of RR Lyrae pulsators by a fac tor of 7 compared with metal-poor, globular cluster-like stellar popul ations. We find that canonical analytical relations connecting the non linear periods of metal-poor variables to their luminosity, mass, and effective temperature cannot be safely extrapolated to the range of SM R pulsators. We show that gravonuclear instabilities largely increase the lifetimes of stars crossing the instability strip at luminosity le vels higher than the HE luminosity, thus increasing the expected occur rence of luminous low-mass variables. We show that both periods and li ght curves of different groups of type II Cepheids with periods shorte r than 6 days, presented by Diethelm, can be all reproduced by suitabl e variations in the effective temperature or in the luminosity level o f our SMR post-HE models, supporting evidence of a substantial homogen eity of these variables. On the basis of both evolutionary and pulsati on findings, we finally predict the rate of period change for a typica l type II, metal-rich, held Cepheid across the instability strip and d iscuss an observational test for validating the present theoretical sc enarios. In an appendix, we discuss in detail the physics of gravonucl ear instabilities, which appear as a surprisingly exact confirmation o f the theoretical predictions given by Schwarzschild & Harm as early a s 1965.