Three-dimensional interferometric, spectrometric, and planetary views of Procyon

Context. Procyon is one of the brightest stars in the sky and one of our nearest neighbours. It is therefore an ideal benchmark object for stellar astrophysics studies using interferometric, spectroscopic, and asteroseismic techniques. Aims. We use a new realistic three-dimensional (3D) radiative-hydrodynamical (RHD) model atmosphere of Procyon generated with the STAGGER CODE and synthetic spectra computed with the radiative transfer code OPTIM3D to re-analyze interferometric and spectroscopic data from the optical to the infrared. We provide synthetic interferometric observables that can be validated using observations. Methods. We computed intensity maps from a RHD simulation in two optical filters centered on 500 and 800 nm (Mark III) and one infrared filter centered on 2.2 mu m (VINCI). We constructed stellar disk images accounting for the center-to-limb variations and used them to derive visibility amplitudes and closure phases. We also computed the spatially and temporally averaged synthetic spectrum from the ultraviolet to the infrared. We compare these observables to Procyon data. Results. We study the impact of the granulation pattern on center-to-limb intensity profiles and provide limb-darkening coefficients in the optical as well as in the infrared. We show how the convection-related surface structures affect the visibility curves and closure phases with clear deviations from circular symmetry, from the 3rd lobe on. These deviations are detectable with current interferometers using closure phases. We derive new angular diameters at different wavelengths with two independent methods based on 3D simulations. We find that theta(Vinci) = 5.390 +/- 0.03 mas, which we confirm by comparison with an independent asteroseismic estimation (theta(seismic) = 5.360 +/- 0.07 mas. The resulting T-eff is 6591 K (or 6556 K depending on the bolometric flux used), which is consistent with the value of T-eff,T-IR = 6621 K found with the infrared flux method. We measure a surface gravity log g = 4.01 +/- 0.03 [cm/s(2)] that is higher by 0.05 dex than literature values. Spectrophotometric comparisons with observations provide very good agreement with the spectral energy distribution and photometric colors, allowing us to conclude that the thermal gradient in the simulation matches Procyon fairly well. Finally, we show that the granulation pattern of a planet-hosting Procyon-like star has a non-negligible impact on the detection of hot Jupiters in the infrared using interferometry closure phases. It is then crucial to have a comprehensive knowledge of the host star to directly detect and characterize hot Jupiters. In this respect, RHD simulations are very important to achieving this aim.