Surface effects and turbulent pressure. Assessing the Gas-${\Gamma }_1$ and Reduced-${\Gamma }_1$ empirical models

Abstract

The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-${\Gamma }_1$ model (RGM) and the gas-${\Gamma }_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found 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. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.

7 pages, 1 figure. Accepted as a Letter in Astronomy and Astrophysic

References in corpus (11)

• Correcting stellar oscillation frequencies for near-surface effects
• A new correction of stellar oscillation frequencies for near-surface effects
• On the surface physics affecting solar oscillation frequencies
• The asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres
• Theoretical oscillation frequencies for solar-type dwarfs from stellar models with $⟨3\mathrm{D}⟩$-atmospheres
• Solar $p$-mode damping rates: insight from a 3D hydrodynamical simulation
• Mending the structural surface effect of 1D stellar structure models with non-solar metallicities based on interpolated 3D envelopes
• Damping rates and frequency corrections of Kepler LEGACY stars
• On the computation of eigenfrequencies for equilibrium models including turbulent pressure
• Bayesian inference of stellar parameters based on 1D stellar models coupled with 3D envelopes
• Estimating the nonstructural component of the helioseismic surface term using hydrodynamic simulations

Cited by in corpus (1)

• PLATO Hare-and-Hounds exercise: Asteroseismic model fitting of main-sequence solar-like pulsators