Surface-effect corrections for solar-like oscillations using 3D hydrodynamical simulations

I. Adiabatic oscillations

¹ LESIA, Observatoire de Paris, PSL Research University, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, 92195 Meudon, France
e-mail: takafumi.sonoi@obspm.fr
² Zentrum für Astronomie der Universität Heidelberg, Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany
³ GEPI, Observatoire de Paris, PSL Research University, CNRS, Université Denis Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France

Received: 26 June 2015
Accepted: 14 September 2015

Abstract

Context. The CoRoT and Kepler space-borne missions have provided us with a wealth of high-quality observational data that allows for seismic inferences of stellar interiors. This requires the computation of precise and accurate theoretical frequencies, but imperfect modeling of the uppermost stellar layers introduces systematic errors. To overcome this problem, an empirical correction has been introduced by Kjeldsen et al. (2008, ApJ, 683, L175) and is now commonly used for seismic inferences. Nevertheless, we still lack a physical justification allowing for the quantification of the surface-effect corrections.

Aims. Our aim is to constrain the surface-effect corrections across the Hertzsprung-Russell (HR) diagram using a set of 3D hydrodynamical simulations.

Methods. We used a grid of these simulations computed with the CO⁵BOLD code to model the outer layers of solar-like stars. Upper layers of the corresponding 1D standard models were then replaced by the layers obtained from the horizontally averaged 3D models. The frequency differences between these patched models and the 1D standard models were then calculated using the adiabatic approximation and allowed us to constrain the Kjeldsen et al. power law, as well as a Lorentzian formulation.

Results. We find that the surface effects on modal frequencies depend significantly on both the effective temperature and the surface gravity. We further provide the variation in the parameters related to the surface-effect corrections using their power law as well as a Lorentzian formulation. Scaling relations between these parameters and the elevation (related to the Mach number) is also provided. The Lorentzian formulation is shown to be more robust for the whole frequency spectrum, while the power law is not suitable for the frequency shifts in the frequency range above ν_max. Finally, we show that, owing to turbulent pressure, the elevation of the uppermost layers modifies the location of the hydrogen ionization zone and consequently introduces glitches in the surface effects for models with high (low) effective temperature (surface gravity).

Conclusions. Surface-effect corrections vary significantly across the HR diagram. Therefore, empirical relations like those by Kjeldsen et al. must not be calibrated on the Sun but should instead be constrained using realistic physical modeling as provided by 3D hydrodynamical simulations.