  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.
