Influence of metallicity on the near-surface effect on oscillation frequencies

Context. The CoRoT and Kepler missions have provided high-quality measurements of the frequency spectra of solar-like pulsators, enabling us to probe stellar interiors with a very high degree of accuracy by comparing the observed and modelled frequencies. However, the frequencies computed with 1D models suffer from systematic errors related to the poor modelling of the uppermost layers of stars. These biases are what is commonly named the near-surface effect. The dominant effect is thought to be related to the turbulent pressure that modifies the hydrostatic equilibrium and thus the frequencies. This has already been investigated using grids of 3D hydrodynamical simulations, which also were used to constrain the parameters of the empirical correction models. However, the effect of metallicity has not been considered so far. Aims. We aim to study the impact of metallicity on the surface effect, investigating its influence across the Hertzsprung-Russell diagram, and providing a method for accounting for it when using the empirical correction models. Methods. We computed a grid of patched 1D stellar models with the stellar evolution code CESTAM in which poorly modelled surface layers have been replaced by averaged stratification computed with the 3D hydrodynamical code CO5BOLD. It allowed us to investigate the dependence of both the surface effect and the empirical correction functions on the metallicity. Results. We found that metallicity has a strong impact on the surface effect: keeping Teff and log g constant, the frequency residuals can vary by up to a factor of two (for instance from [Fe/H] = + 0.0 to [Fe/H] = + 0.5). Therefore, the influence of metallicity cannot be neglected. We found that the correct way of accounting for it is to consider the surface Rosseland mean opacity. It allowed us to give a physically grounded justification as well as a scaling relation for the frequency differences at νmax as a function of Teff, log g and κ. Finally, we provide prescriptions for the fitting parameters of the most commonly used correction functions. Conclusions. We show that the impact of metallicity through the Rosseland mean opacity must be taken into account when studying and correcting the surface effect.