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Contact. The large quantity of high-quality asteroseismic data that have been obtained from space-based photometric missions and the accuracy of the resulting frequencies motivate a careful consideration of the accuracy of computed oscillation frequencies of stellar models, when applied as diagnostics of the model properties. Aims. Based on models of red-giant stars that have been independently calculated using different stellar evolution codes, we investigate the extent to which the differences in the model calculation affect the model oscillation frequencies and other asteroseismic diagnostics. Methods. For each of the models, which cover four different masses and different evolution stages on the red-giant branch, we computed full sets of low-degree oscillation frequencies using a single pulsation code and, from these frequencies, typical asteroseismic diagnostics. In addition, we carried out preliminary analyses to relate differences in the oscillation properties to the corresponding model differences. Results. In general, the differences in asteroseismic properties between the different models greatly exceed the observational precision of these properties. This is particularly true for the nonradial modes whose mixed acoustic and gravity-wave character makes them sensitive to the structure of the deep stellar interior and, hence, to details of their evolution. In some cases, identifying these differences led to improvements in the final models presented here and in Paper I; here we illustrate particular examples of this. Conclusions. Further improvements in stellar modelling are required in order fully to utilise the observational accuracy to probe intrinsic limitations in the modelling and improve our understanding of stellar internal physics. However, our analysis of the frequency differences and their relation to stellar internal properties provides a striking illustration of the potential, in particular, of the mixed modes of red-giant stars for the diagnostics of stellar interiors. 

Context. With the advent of space-based asteroseismology, determining accurate properties of red-giant stars using their observed oscillations has become the focus of many investigations due to their implications in a variety of fields in astrophysics. Stellar models are fundamental in predicting quantities such as stellar age, and their reliability critically depends on the numerical implementation of the physics at play in this evolutionary phase. Aims. We introduce the Aarhus red giants challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes that aim to establish the minimum level of uncertainties in properties of red giants arising solely from numerical implementations. We present the first set of results focusing on stellar evolution tracks and structures in the red-giant-branch (RGB) phase. Methods. Using nine state-of-the-art stellar evolution codes, we defined a set of input physics and physical constants for our calculations and calibrated the convective efficiency to a specific point on the main sequence. We produced evolutionary tracks and stellar structure models at a fixed radius along the red-giant branch for masses of 1.0  M ⊙ , 1.5  M ⊙ , 2.0  M ⊙ , and 2.5  M ⊙ , and compared the predicted stellar properties. Results. Once models have been calibrated on the main sequence, we find a residual spread in the predicted effective temperatures across all codes of ∼20 K at solar radius and ∼30–40 K in the RGB regardless of the considered stellar mass. The predicted ages show variations of 2–5% (increasing with stellar mass), which we attribute to differences in the numerical implementation of energy generation. The luminosity of the RGB-bump shows a spread of about 10% for the considered codes, which translates into magnitude differences of ∼0.1 mag in the optical V -band. We also compare the predicted [C/N] abundance ratio and find a spread of 0.1 dex or more for all considered masses. Conclusions. Our comparisons show that differences at the level of a few percent still remain in evolutionary calculations of red giants branch stars despite the use of the same input physics. These are mostly due to differences in the energy generation routines and interpolation across opacities, and they call for further investigation on these matters in the context of using properties of red giants as benchmarks for astrophysical studies. 

We provide homogeneous optical ( U B V R I ) and near-infrared (NIR, J H K ) time series photometry for 254 cluster ( ω Cen, M 4) and field RR Lyrae (RRL) variables. We ended up with more than 551 000 measurements, of which only 9% are literature data. For 94 fundamental (RRab) and 51 first overtones (RRc) we provide a complete optical/NIR characterization (mean magnitudes, luminosity amplitudes, epoch of the anchor point). The NIR light curves of these variables were adopted to provide new light-curve templates for both RRc and RRab variables. The templates for the J and the H bands are newly introduced, together with the use of the pulsation period to discriminate among the different RRab templates. To overcome subtle uncertainties in the fit of secondary features of the light curves we provide two independent sets of analytical functions (Fourier and periodic Gaussian series). The new templates were validated by using 26 ω Cen and Bulge RRLs. We find that the difference between the measured mean magnitude along the light curve and the mean magnitude estimated by using the template on a single randomly extracted phase point is better than 0.01 mag ( σ = 0.04 mag). We also validated the template on variables for which at least three phase points were available, but without information on the phase of the anchor point. We find that the accuracy of the mean magnitudes is also ∼0.01 mag ( σ = 0.04 mag). The new templates were applied to the Large Magellanic Cloud (LMC) globular cluster Reticulum and by using literature data and predicted PLZ relations we find true distance moduli μ = 18.47 ± 0.10 (rand.) ± 0.03 (syst.) mag ( J ) and 18.49 ± 0.09 ± 0.05 mag ( K ). We also used literature optical and mid-infrared data and we found a mean μ of 18.47 ± 0.02 ± 0.06 mag, suggesting that Reticulum is ∼1 kpc closer than the LMC.