Distinct Stellar Parameter Dependencies of Granulation and Mesogranulation in Red Giants

Granulation and mesogranulation represent different spatial and temporal scales of convection, but are commonly assumed to follow the same stellar atmospheric scaling relations in red giants. We test this assumption using the largest sample assembled for this purpose to date—9328 Kepler red giants spanning the red giant branch and red clump phase, crossmatched with APOGEE stellar parameters. We model each star's power spectrum background to obtain the radius-corrected amplitude and characteristic frequency of both components, and derive empirical scaling relations with effective temperature, surface gravity, and metallicity through Bayesian model comparison. Gaussian Process and symbolic regression provide independent validation. We find that granulation and mesogranulation are not self-similar: their surface-gravity dependencies are statistically indistinguishable, consistent with a shared envelope geometry, but their temperature dependencies diverge: mesogranulation’s amplitude rises steeply with T eff , whereas granulation’s shows no statistically justified dependence, and both frequencies respond weakly and similarly. We propose that this pattern is consistent with granulation forming in a thin near-surface layer, where radiation takes over from convection and the Mach number depends only weakly on T eff . Mesogranulation originates deeper, where convection carries the full flux and its Mach number and cell size increase with T eff . Metallicity raises both amplitudes but has little effect on the frequencies. Our results indicate that the self-similarity assumption underlying two-component background models does not hold, with direct implications for background modeling and its downstream application in Galactic archaeology.