Classical Cepheid Pulsation Models. I. Physical Structure

Abstract

The pulsation properties and modal stability of Cepheid models are investigated in both linear and nonlinear regimes. The linear survey is based on nonadiabatic, radiative models, whereas the nonlinear one relies on full-amplitude models that include a nonlocal and time-dependent treatment of stellar convection. To account for Cepheid pulsation characteristics over a substantial portion of the region in which they are expected to be pulsationally unstable, a wide range of stellar masses (5 ¹ M/M _ ¹ 11) and e †ective temperatures K) was adopted. The luminosity of each model was Ðxed (4000 ¹ T e ¹ 7000 according to the mass-luminosity (ML) relations predicted by evolutionary models that either neglect or take into account a mild convective core overshooting. Moreover, in order to estimate the e †ects of the helium and metal content on the limiting amplitude behavior of both Magellanic Clouds and Galactic Cepheids we adopted three di †erent chemical compositions, namely, Y \ 0.25, Z \ 0.004 ; Y \ 0.25, Z \ 0.008 ; and Y \ 0.28, Z \ 0.02. For each set of input parameters we investigated the modal stability of both fundamental and Ðrst-overtone modes.The results of recent linear investigations are conÐrmed by our Ðnding that linear observables such as periods and blue edges of the instability strip are only marginally a †ected by the chemical composition and that either an increase in metallicity or an increase in both the helium and metal content causes a mild shift of these edges toward lower e †ective temperatures.The approach to the nonlinear limit cycle stability, the physical structure, and the mechanisms that govern the pulsation instability are described in detail. The main results of this analysis are as follows :(1) At Ðxed chemical composition the width of the instability strip changes going from low-to high-mass Cepheids. (2) At Ðxed mass and luminosity an increase in metallicity shifts the instability strip toward lower e †ective temperatures. A thorough analysis of the total nonlinear work inside the instability strip points out that this e †ect is due to a decrease in the pulsation destabilization caused by the H ionization region. Therefore, the current theoretical scenario suggests that, at Ðxed period, metal-poor pulsators are brighter than metal-rich pulsators. (3) The dynamical structure of full-amplitude, Ðrst-overtone models supports the evidence that their nonlinear limit cycle behavior has been properly identiÐed.The variations over a full pulsation cycle of the convective structure of fundamental and Ðrst-overtone pulsators located close to the blue and the red edges of the instability strip are discussed by taking into account the changes of the convective quantities across the convectively unstable region. As expected, we Ðnd that the main e †ect of convection on the limit cycle behavior is either to reduce the local radiative driving of the destabilizing regions, thus reducing the Ðnal amplitudes, or to damp the oscillations toward lower e †ective temperatures. We also Ðnd that th...

On the Distance of Magellanic Clouds: First Overtone Cepheids

“…The discrepancies we found are somehow at odds with the results obtained by BA01 concerning the difference between the slopes of their W functions and the slopes predicted by Caputo, Marconi, & Musella (2000) for F pulsators. The main difference is that BA01 were forced to extrapolate the W function given by .…”

“…To assess whether the FO instability 0.28 Z p 0.02 strip presents a change in the slope when moving from long to short periods, we adopted several stellar masses. For each mass value and chemical composition, the luminosities were fixed according to the same mass-luminosity (ML) relation adopted in previous investigations (Bono, Marconi, & Stellingwerf 1999b), which is consistent, within the errors, with the ML relation derived by . To mimic the luminosities predicted by evolutionary models that account for mild convective core overshooting during H-burning phases (noncanonical), the luminosities predicted by canonical models were increased by 0.25 dex (Chiosi, Wood, & Capitanio 1993).…”

“…As for the other chemical compositions, we constructed five new FO sequences with stellar masses ranging from to 5.6 and stellar luminosities rang-M/M p 3.0 , ing from to 3.60 to constrain the instability log (L/L ) p 2.58 , strip in the short-period range. The input physics and physical assumptions adopted to construct the models are discussed in Bono et al (1999b). For each model the stability analysis was performed for only the first two modes.…”

Uncertainties on the theoretical predictions for classical Cepheid pulsational quantities

“…Our pulsational models are based on a nonlinear nonlocal time-dependent convective hydrodynamical code (Bono & Stellingwerf 1994;Bono et al 1999a, and references therein). This code has been successfully applied to several classes of pulsating stars (see e.g.…”

Pulsational constraints to the metallicity gradient in the Galactic disk

“…On the contrary, recent nonlinear, non-local and timedependent convective pulsating models computed with various chemical abundances show that an increase in the total metal content Z moves the instability strip towards cooler effective temperature, and that consequently the bolometric magnitude of metal-rich pulsators is on average fainter, for fixed period, than that of metal-poor ones (Bono et al 1999a;Bono et al 1999b). As a result, both the slope and zero-point of the predicted PL relations at the various wavelengths, as well as the predicted period-luminosity-color (PLC) and color-color (CC) relations (Caputo et al 2000), turn out to depend, to different extent, on the pulsator metallicity.…”