Scaling relations of convective granulation noise across the HR diagram from 3D stellar atmosphere models

High-precision photometric data from space missions have improved our understanding of stellar granulation. These observations have shown with precision the stochastic brightness fluctuations of stars across the HR diagram, allowing us to better understand how stellar surface convection reacts to a change in stellar parameters. These fluctuations need to be understood and quantified in order to improve the detection and characterization of exoplanets. In this work, we provide new scaling relations of two characteristic properties of the brightness fluctuations time series, the standard deviation ($\sigma$) and the auto-correlation time ($\tau\rm_{eff}$). This was done by using long time series of 3D stellar atmosphere models at different metallicities and across the HR diagram, generated with a 3D radiative hydrodynamical code: the STAGGER code. We compared our synthetic granulation properties with the values of a large sample of Kepler stars, and analyzed selected stars with accurate stellar parameters from the Kepler LEGACY sample. Our 3D models showed that $\sigma\propto\nu\rm_{max}^{-0.567\pm0.012}$ and $\tau\rm_{eff}\propto\nu\rm_{max}^{-0.997\pm0.018}$ for stars at solar metallicity. We showed that both $\sigma$ and $\tau\rm_{eff}$ decrease with metallicity, although the metallicity dependence is more significant on $\sigma$. Unlike previous studies, we found very good agreement between $\sigma$ from Kepler targets and the 3D models at $\log{g}\leq3.5$, and a good correlation between the stars and models with $\log{g}\geq3.5$. For $\tau\rm_{eff}$, we found that the 3D models reproduced well the Kepler LEGACY star values. Overall, this study shows that 3D stellar atmosphere models reproduce the granulation properties of stars across the HR diagram.