We present new Period-Age (PA) and Period-Age-Color (PAC) relations for fundamental and first overtone classical Cepheids. Current predictions rely on homogeneous sets of evolutionary and pulsation models covering a broad range of stellar masses and chemical compositions. We found that PA and PAC relations present a mild dependence upon metal content. Moreover, the use of different PA and PAC relation for fundamental and first overtone Cepheids improves the accuracy of age estimates in the short-period (log P < 1) range (old Cepheids), because they present smaller intrinsic dispersions. At the same time, the use of the PAC relations improves the accuracy in the long-period (log P ≥ 1) range (young Cepheids), since they account for the position of individual objects inside the instability strip.We performed a detailed comparison between evolutionary and pulsation ages for a sizable sample of LMC (15) and SMC (12) clusters which host at least two Cepheids. In order to avoid deceptive uncertainties in the photometric absolute zero-point, we adopted the homogeneous set of B,V,I data for clusters and Cepheids collected by OGLE. We also adopted the same reddening scale. The different age estimates agree at the level of 20% for LMC clusters and of 10% for SMC clusters. We also performed the same comparison for two Galactic clusters (NGC6067, NGC7790) and the difference in age is smaller than 20%.These findings support the use of PA and PAC relations to supply accurate estimates of individual stellar ages in the Galaxy and in external Galaxies. The main advantage of this approach is its independence from the distance.

In this paper, we present an improved theoretical scenario concerning near‐infrared and visual magnitudes of RR Lyr variables, as based on up‐to‐date pulsating models. New relations connecting V and K absolute magnitudes with periods, mass, luminosity and metal content are discussed separately for fundamental and first‐overtone pulsators. We also show that the V−K colours are predicted to supply tight constraints on the pulsator intrinsic luminosity. On this basis, we revisit the case of the prototype variable RR Lyr, showing that the parallax inferred by this new pulsational approach appears in close agreement with Hubble Space Telescope absolute parallax. Moreover, available K and V measurements for field and cluster RR Lyr variables with known reddening and metal content are used to derive a relation connecting the K absolute magnitude to period and metallicity (MK–[Fe/H]–log P) as well as a new calibration of the MV–[Fe/H] relation. The comparison between theoretical prescriptions and observations suggests that RR Lyr stars in the field and in galactic globular clusters (GGCs) should have quite similar evolutionary histories. The comparison between theory and observations also discloses a general agreement that supports the reliability of the current pulsational scenario. On the contrary, current empirical absolute magnitudes based on the Baade–Wesselink (BW) method suggest relations with a zero‐point which is fainter than is predicted by pulsation models, together with a milder metallicity dependence. However, preliminary results based on a new calibration of the BW method provided by Cacciari et al. (2000) for RR Cet and SW And appear in a much better agreement with the pulsational predictions.

We present a comprehensive theoretical investigation of the evolutionary properties of intermediate-mass stars. The evolutionary sequences were computed from the Zero Age Main Sequence up to the central He exhaustion and often up to the phases which precede the carbon ignition or to the reignition of the H-shell which marks the beginning of the thermal pulse phase. The evolutionary tracks were constructed by adopting a wide range of stellar masses (3 ≤M/M ⊙ ≤ 15) and chemical compositions. In order to account for current uncertainties on the He to heavy elements enrichment ratio (∆Y /∆Z ), the stellar models were computed by adopting at Z=0.02 two different He contents (Y=0.27, 0.289) and at Z=0.04 three different He contents (Y=0.29, 0.34, and 0.37). Moreover, to supply a homogeneous evolutionary scenario which accounts for young Magellanic stellar systems the calculations were also extended toward lower metallicities (Z=0.004, Z=0.01), by adopting different initial He abundances.We evaluated for both solar (Z=0.02) and super-metal-rich (SMR, Z=0.04) models the transition mass M up between the stellar structures igniting carbon and those which develop a full electron degeneracy inside the carbon-oxygen core. We found that M up is of the order of 7.7 ± 0.5M ⊙ for solar composition, while for SMR structures an increase in the He content causes a decrease in M up , and indeed it changes from 9.5 ± 0.5M ⊙ at Y=0.29, to 8.7 ± 0.2M ⊙ at Y=0.34, and to 7.7 ± 0.2M ⊙ at Y=0.37. We also show that M up presents a nonlinear behavior with metallicity, and indeed it decreases when moving from Z=0.04 to Z ≈ 0.001 and increases at lower metal contents. This finding confirms the predictions by Cassisi & Castellani (1993) and more recently by Umeda et al. (1999) and suggests that the rate of SNe type Ia depends on the 3 chemical composition of the parent stellar population.This approach allows us to investigate in detail the evolutionary properties of classical Cepheids. In particular, we find that the range of stellar masses which perform the blue loop during the central He-burning phase narrows when moving toward metal-rich and SMR structures. This evidence and the substantial decrease in the evolutionary time spent by these structures inside the instability strip bring out that the probability to detect long-period Cepheids in SMR stellar systems is substantially smaller than in more metal-poor systems.Moreover and even more importantly, we find that the time spent by Cepheids along the subsequent crossings of the instability strip also depends on the stellar mass. In fact, our models suggest that low-mass, metal-poor Cepheids spend a substantial portion of their lifetime along the blueward excursion of the blue loop, while at higher masses (M/M ⊙ ≥ 8) the time spent along the redward excursion becomes longer. Models at solar chemical composition present an opposite behavior i.e. the time spent along the redward excursion is longer than the blueward excursion among low-mass Cepheids and vice versa for high-massCepheids. Oddly ...

We present a detailed investigation of the Cepheid distance scale by using both theory and observations. Through the use of pulsation models for fundamental mode Cepheids, we found that the slope of the period-luminosity (P-L) relation covering the entire period range (0.40 log P 2.0) becomes steeper when moving from optical to near-infrared (NIR) bands, and that the metallicity dependence of the slope decreases from the B-to the K band. The sign of the metallicity dependence for the slopes of the P-L V and P-L I relation is at odds with some recent empirical estimates. We determined new homogeneous estimates of V-and I-band slopes for 87 independent Cepheid data sets belonging to 48 external galaxies with nebular oxygen abundance 7.5 12 + log(O/H) 8.9. By using Cepheid samples including more than 20 Cepheids, the χ 2 test indicates that the hypothesis of a steepening of the P-L V ,I relations with increased metal content can be discarded at the 99% level. On the contrary, the observed slopes agree with the metallicity trend predicted by pulsation models, i.e., the slope is roughly constant for galaxies with 12+log(O/H) < 8.17 and becomes shallower in the metal-rich regime, with confidence levels of 62% and 92%, respectively. The χ 2 test concerning the hypothesis that the slope does not depend on metallicity gives confidence levels either similar (PL V , 62%) or smaller (PL I , 67%). We investigated the dependence of the period-Wesenheit (P-W) relations on the metal content and we found that the slopes of optical and NIR P-W relations in external galaxies are similar to the slopes of Large Magellanic Cloud (LMC) Cepheids. They also agree with the theoretical predictions suggesting that the slopes of the P-W relations are independent of the metal content. On this ground, the P-W relations provide a robust method to determine distance moduli relative to the LMC, but theory and observations indicate that the metallicity dependence of the zero point in the different passbands has to be taken into account. To constrain this effect, we compared the independent set of galaxy distances provided by Rizzi et al. using the tip of the red giant branch with our homogeneous set of extragalactic Cepheid distances based on the P-W relations. We found that the metallicity correction on distances based on the P-WBV relation is γ B,V = −0.52 mag dex −1 , whereas it is vanishing for the distances based on the P-WVI and on the P-WJK relations. These findings fully support Cepheid theoretical predictions.