The connection between stellar granulation and oscillation as seen by the Kepler mission

We then aim to define empirical scaling relations between the granulation properties and νmax and various other stellar parameters. Methods. We use a probabilistic method to compare different approaches to extracting the granulation signal.

We fit the power density spectra of a large set of Kepler targets, determine the granulation and global oscillation parameter, and quantify scaling relations between them. Results. We establish that a depression in power at about νmax/2, known from the Sun and a few other main-sequence stars, is also statistically significant in red giants and that a super-Lorentzian function with two components is best suited to reproducing the granulation signal in the broader vicinity of the pulsation power excess.

We also establish that the specific choice of the background model can affect the determination of νmax, introducing systematic uncertainties that can significantly exceed the random uncertainties. We find the characteristic frequency (i.e., inverse timescale) and amplitude of both background components to tightly scale with νmax for a wide variety of stars (about 2–2000 μHz in νmax), and quantify a mass dependency of the latter.

To enable comparison with theoretical predictions (which do not include the observed power depression), we computed effective timescales and bolometric intensity fluctuations and found them to approximately scale as τeff ∝ g-0.85T-0.4 and Agran ∝ (g2M)− 1/4 (or more conveniently R/M3/4), respectively. Similarly, the bolometric pulsation amplitude scales approximately as Apuls ∝ (g2M)− 1/3 (or R4/3/M), which implicitly verifies a separate mass and luminosity dependence of Apuls.

We have also checked our scaling relations with solar reference values and find them in good agreement. Conclusions. We provide a thorough analysis of the granulation background signal in a large sample of stars, from which we establish a unified model that allows us to accurately extract the granulation and global oscillation parameter.

The resulting scaling relations allow a simple estimate of the overall spectral shape of any solar-type oscillator and might serve as a starting point for future large-sample studies or as a reference for theoretical modelling of granulation.