Stellar granulation as seen in disk-integrated intensity

II. Theoretical scaling relations compared with observations^⋆

¹ LESIA, Observatoire de Paris, CNRS UMR 8109, UPMC, Université Denis Diderot, 5 place Jules Janssen, 92195 Meudon Cedex, France
e-mail: reza.samadi@obspm.fr
² Zentrum für Astronomie der Universität Heidelberg, Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany
³ GEPI, Observatoire de Paris, CNRS UMR 8111, Université Denis Diderot, 5 place Jules Janssen, 92195 Meudon Cedex, France
⁴ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
⁵ Institute for Astronomy (IfA), University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
⁶ Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁷ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁸ High Altitude Observatory, NCAR, PO Box 3000, Boulder, CO 80307, USA
⁹ Space Science Institute, 4750 Walnut street Suite 205, Boulder, CO 80301, USA
¹⁰ Laboratoire AIM, CEA/DSM CNRS Université Paris Diderot IRFU/SAp, 91191 Gif-sur-Yvette Cedex, France

Received: 29 November 2012
Accepted: 26 July 2013

Abstract

Context. 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 (τ_eff) and the root-mean-square (rms) brightness fluctuations (σ) associated with the granulation scale as a function of the peak frequency (ν_max) of the solar-like oscillations.

Aims. We aim at providing a theoretical background to the observed scaling relations based on a model developed in Paper I.

Methods. 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 published in Paper I. For each PDS we derived the associated characteristic time (τ_eff) and the rms brightness fluctuations (σ) and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the measurements made on a large set of Kepler targets.

Results. We derive theoretical scaling relations for τ_eff and σ, which show the same dependence on ν_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (ℳ_a) estimated at the photosphere. The theoretical scaling relations for τ_eff and σ match the observations well on a global scale. Quantitatively, the remaining discrepancies with the observations are found to be much smaller than previous theoretical calculations made for red giants.

Conclusions. Our modelling provides additional theoretical support for the observed variations of σ and τ_eff with ν_max. It also highlights the important role of ℳ_a 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 ℳ_a. 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 ℳ_a.