Evolutionary and pulsational constraints for super-metal-rich stars with Z = 0.04

We investigate the evolutionary behavior of stellar structures with metallicity Z = 0.04 in order to disclose theoretical expectations for both evolutionary and pulsational behaviors of super-metal-rich (SMR) objects, which are found in the solar neighborhood, in the Galactic bulge, and in elliptical galaxies. A suitable set of stellar models is presented for the given metallicity value but for two alternative assumptions 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 behavior of He-burning structures is discussed for suitable assumptions about the mass of the progenitors and the amount of mass loss. For both quoted assumptions of original He abundance, we confirm that at metal contents larger than the solar value the luminosity of the horizontal branch (HE) at the RR Lyrae gap increases as the metal content increases, a direct consequence of the expected simultaneous increase of original He. We find that, at the exhaustion of central helium, SMR stars definitely undergo the gravonuclear instabilities previously found in some He-burning structures with solar metallicity. On the basis of such an evolutionary scenario, we investigate the expected pulsational behavior of He-burning SMR stars for suitable assumptions on the pulsators' evolutionary parameters. Linear blue boundaries for pulsational instability in the fundamental and in the first-overtone modes are derived, and their dependence on stellar mass and chemical composition is investigated. Nonlinear, nonlocal, and time-dependent convective models are discussed, the modal stability is investigated for the first two modes, and the theoretical predictions about the period distribution inside the instability strip and the shape of both light and velocity curves are presented. Full-amplitude, nonlinear envelope models show that the range of effective temperatures in which SMR RR Lyrae variables present a stable limit cycle is smaller than that of pulsators characterized by lower metal abundances. In fact, the width of the instability strip at the zero-age horizontal branch luminosity level decreases from 1400 to 1100 K. Also taking into account the peculiar narrow mass range characterizing SMR pulsators, we estimate that these two factors alone cause a decrease in the occurrence of RR Lyrae pulsators by a factor of 7 compared with metal-poor, globular cluster-like stellar populations. We find that canonical analytical relations connecting the nonlinear periods of metal-poor variables to their luminosity, mass, and effective temperature cannot be safely extrapolated to the range of SMR pulsators. We show that gravonuclear instabilities largely increase the lifetimes of stars crossing the instability strip at luminosity levels higher than the HE luminosity, thus increasing the expected occurrence of luminous low-mass variables. We show that both periods and light curves of different groups of type II Cepheids with periods shorter than 6 days, presented by Diethelm, can be all reproduced by suitable variations in the effective temperature or in the luminosity level of our SMR post-HE models, supporting evidence of a substantial homogeneity of these variables. On the basis of both evolutionary and pulsation findings, we finally predict the rate of period change for a typical type II, metal-rich, held Cepheid across the instability strip and discuss an observational test for validating the present theoretical scenarios. In an appendix, we discuss in detail the physics of gravonuclear instabilities, which appear as a surprisingly exact confirmation of the theoretical predictions given by Schwarzschild & Harm as early as 1965.