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High-precision photometric data from space missions have improved ourunderstanding of stellar granulation. These observations have shown withprecision the stochastic brightness fluctuations of stars across the HRdiagram, allowing us to better understand how stellar surface convection reactsto a change in stellar parameters. These fluctuations need to be understood andquantified in order to improve the detection and characterization ofexoplanets. In this work, we provide new scaling relations of twocharacteristic properties of the brightness fluctuations time series, thestandard deviation ($\sigma$) and the auto-correlation time ($\tau\rm_{eff}$).This was done by using long time series of 3D stellar atmosphere models atdifferent metallicities and across the HR diagram, generated with a 3Dradiative hydrodynamical code: the STAGGER code. We compared our syntheticgranulation properties with the values of a large sample of Kepler stars, andanalyzed selected stars with accurate stellar parameters from the Kepler LEGACYsample. 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 solarmetallicity. We showed that both $\sigma$ and $\tau\rm_{eff}$ decrease withmetallicity, 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 goodcorrelation between the stars and models with $\log{g}\geq3.5$. For$\tau\rm_{eff}$, we found that the 3D models reproduced well the Kepler LEGACYstar values. Overall, this study shows that 3D stellar atmosphere modelsreproduce the granulation properties of stars across the HR diagram.

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