Stellar granulation as seen in disk-integrated intensity. II. Theoretical scaling relations compared with observations

TL;DR

This paper develops and tests theoretical scaling relations for stellar granulation properties, such as timescale and brightness fluctuations, based on 3D models and compares them with Kepler and CoRoT observations, highlighting the role of turbulent Mach number.

Contribution

It provides a theoretical framework for understanding the observed scaling relations of stellar granulation and introduces the influence of turbulent Mach number on these properties.

Findings

Theoretical scaling relations match observations on a global scale.

Tau_eff and sigma scale with nu_max similarly in models and observations.

Turbulent Mach number significantly influences granulation properties.

Abstract

A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale (tau_eff) and the root-mean-square (rms) brightness fluctuations (sigma) associated with the granulation scale as a function of the peak frequency (nu_max) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper. We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model. For each PDS we derived tau_eff and sigma and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the Kepler measurements. We derive theoretical scaling relations for tau_eff and sigma, which show the same dependence on nu_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (Ma) estimated at the photosphere. The theoretical scaling relations for tau_eff and sigma match the observations well on a global scale. Our modelling provides additional theoretical support for the observed variations of sigma and tau_eff with nu_m max. It also highlights the important role of Ma in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on Ma. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with Ma.