Studying the surface effect in Procyon A as an F-type star

Context. Procyon A is an F-type main-sequence star in a binary system. It has been the subject of numerous ground-based and space-based observing campaigns, providing precise classical constraints, including a well-determined mass. It was also among the first stars in which individual frequencies were detected, making it a crucial benchmark for F-type stars. Aims. Our goal is to investigate the surface effect, namely the discrepancy between observed and model oscillation frequencies due to inadequate modeling of the surface stellar layers, which is especially important in F-type stars. Using Procyon A as a case study, we aim to understand how different surface correction prescriptions impact the inference of the fundamental properties of this star, and to compare the results with those obtained when the surface corrections are neglected. Methods. We inferred the fundamental stellar properties by employing a grid of models computed with Modules for Experiments in Stellar Astrophysics (MESA), including gravitational settling, radiative accelerations, and turbulent mixing. We selected the best-fit models using the Asteroseismic Inference on a Massive Scale (AIMS) code, taking into account different methods to fit the individual frequencies. Results. We find that the use of surface corrections can introduce uncertainties of up to 7% in the inferred stellar mass. We obtain the most reliable stellar mass estimates when using frequency ratios, the Sonoi surface correction, or direct fitting of the individual frequencies. Conclusions. Our results indicate that the surface effects in F-type stars differ from those found in the Sun and in solar-like stars, highlighting the need for caution when considering the surface corrections for these stars.