A prescription for the asteroseismic surface correction

In asteroseismology, the surface effect refers to a disparity between observed and modelled frequencies in stars with solar-like oscillations. It originates from improper modelling of layers. Correcting usually requires using functions free parameters, which are conventionally fitted frequencies. On basis that correction should vary smoothly across H--R diagram, we parameterize it as simple function gravity, effective temperature, metallicity. We determine this by fitting wide range stars. The absolute amount decreases luminosity, but ratio $\nu_{\rm max}$ increases, suggesting is more important for red giants than dwarfs. Applying prescription can eliminate unrealistic correction, improves parameter estimations stellar modelling. Using two open clusters, found reduction scatter model-derived ages each star same cluster. As an application, provide new revision $\Delta\nu$ scaling relation that, first time, accounts correction. values factor, $f_{\Delta\nu}$, up 2\% smaller those determined without considered, 4\% radii 8\% masses when asteroseismic relations. This brings properties into agreement eclipsing binaries. factor models corrected available at {https://www.github.com/parallelpro/surface}.