Interferometric Survey of Stellar Parameters: Towards homogeneous FGK stars parameters and surface-brightness color relation in the context of PLATO space mission
The estimation of stellar angular diameters can be performed from the surface brightness - color relation (SBCR) and photometry. The SBCR have been considered by the PLATO space mission as an independent empirical alternative for estimating stellar radii of FGK stars. In this context, we have implemented an homogeneous approach not only for calibrating the SBCR for FGK-IV/V stars but, also for determining their fundamental parameters in order to place the stars reliably on the HR diagram and to study their impact on the SBCR. We have performed interferometric observations of 18 quiescent FGK-IV/V stars in the Gaia color range of $3.088 \leq G \leq 5.498$. For the first time, we used 3 different interferometers operating in the $R$, $H$ , and $K$ bands to measure polychromatic limb-darkened angular diameters (LDAD). In parallel, by using public domain spectra we have estimated the stellar parameters ($T_{eff}$, $log g$ and Z) by using the open python tool iSpec. We achieved an average accuracy of 2.3% for the LDAD based on polychromatic observations. However, we have observed that our SBCR does not follow the calibration of the relation between surface brightness and color in Gaia found in the literature. Furthermore, we found that $log g$ and $Z$ have no impact on the SBC relation; given the characteristics of our sample of quiescent stars, it constitutes an ideal set of targets for conducting a new SBCR calibration within the framework of the PLATO space mission. In this context, we reported a SBCR calibration with $\sigma_{RMS} = $ 0.012, 0.009, 0.009 in the $G, G_{BP}$ and $G_{RP}$ Gaia bands, respectively. This article is part of a series of papers reporting the first results obtained using a polychromatic approach to measure LDAD, employing a fully homogeneous methodology for both determining the fundamental parameters of stars and measuring the LDAD, $\theta_{LD}$.