Abstract
The application of the full potential of stellar seismology is made difficult by the improper modelling of the upper-most layers of solar-like stars and their influence on the modelled frequencies. Our knowledge of these so-called ‘surface effects’ has improved thanks to the use of 3D hydrodynamical simulations, however, the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure, namely: the reduced-Γ1 model (RGM) and the gas-Γ1 model (GGM). Starting from the fully compressible turbulence equations, we derived both the GGM and RGM models by using a closure to model the flux of turbulent kinetic energy. We find that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. We also demonstrate that they are both compatible with the adiabatic approximation and, additionally, that they imply a number of questionable assumptions, mainly with respect to mode physics. Among other hypotheses, it is necessary to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.
Highlights
Systematic differences between observed and modelled eigenfrequencies is a long-standing problem in stellar seismology
Our knowledge of these so-called ‘surface effects’ has improved thanks to the use of 3D hydrodynamical simulations, the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure, namely: the reduced-Γ1 model (RGM) and the gas-Γ1 model (GGM)
We find that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure
Summary
Systematic differences between observed and modelled eigenfrequencies is a long-standing problem in stellar seismology. To be able to exploit all the information contained in the observed frequencies, the physics underlying the surface effects must be understood To this end, Rosenthal et al (1999) used 3D hydrodynamical simulations, which allowed them to account for the mean turbulent pressure (as well as convective backwarming; see Trampedach et al 2017) in the equilibrium structure. Most of the above-mentioned works applied the GGM, except in a few cases (e.g. Jørgensen & Weiss 2019), where the RGM was guided by the non-adiabatic calculation from Houdek et al (2017) The latter was recently challenged by Schou & Birch (2020), using the eigenfunctions as inferred directly from 3D numerical simulations. We aim at deriving and assessing the theoretical validity of the GGM and RGM empirical models
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