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

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 CO 5 BOLD 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.

MESA meets MURaM

“…We present here a preliminary exploration of how the surface effect varies with spectral type on the main sequence, based on these simulations. This is the same procedure as followed in the recent results by Sonoi et al (2015). Their models A and B have similar atmospheric parameters to our G2 and F3 simulations.…”

“…The process is similar in spirit to the study by Piau et al (2014) but we have neither incorporated information from the MURaM simulations into the stars' evolution nor considered the effects of magnetic fields. Our method is in essence identical to the method of Sonoi et al (2015) though we have used low-degree modes up to = 3, whereas they restricted themselves to radial modes.…”

“…Finally, the Brunt-Väisälä frequency was computed from the adiabatic index, pressure gradient and density gradient. Like Sonoi et al (2015), we assumed that the relative Lagrangian perturbation to the turbulent pressure is the same as that of the gas pressure, which Rosenthal et al (1999) referred to as the "gas Γ 1 approximation".…”

“…(3)), as proposed by Kjeldsen et al (2008), and s 0 and s 1 are the amplitude and index of the modified Lorentzian (Eq. (4)) suggested by Sonoi et al (2015). The last parameter c corresponds to the amplitude of a scaled solar surface term, computed as in Schmitt & Basu (2015).…”

Determining stellar parameters of asteroseismic targets: going beyond the use of scaling relations

“…see Sonoi et al 2015;Ball et al 2016), and by trying to mitigate surface effects when comparing models and observations. In this respect a way forward would be to determine the star's mean density by using the full set of observed acoustic modes, not just their average frequency spacing.…”