Numerical simulations of downward convective overshooting in giants

TL;DR

This study uses 3D simulations to explore downward convective overshooting in giant stars, examining how flux, velocity, and turbulence influence penetration depth and non-local transport models.

Contribution

It provides new insights into the scaling relations and turbulence anisotropy in convective overshooting through detailed 3D simulations of giant stars.

Findings

Penetration depth is about one pressure scale height.

Scaling relations between flux, velocity, and penetration are confirmed.

Turbulence anisotropy significantly affects non-local transport models.

Abstract

An attempt at understanding downward overshooting in the convective envelopes of post-main-sequence stars has been made on the basis of three-dimensional large-eddy simulations, using artificially modified OPAL opacity and taking into account radiation and ionization in the equation of state. Two types of star, an intermediate-mass star and a massive star, were considered. To avoid a long thermal relaxation time of the intermediate-mass star, we increased the stellar energy flux artificially while trying to maintain a structure close to the one given by a 1D stellar model. A parametric study of the flux factor was performed. For the massive star, no such process was necessary. Numerical results were analysed when the system reached the statistical steady state. It was shown that the penetration distance in pressure scaleheights is of the order of unity. The scaling relations between penetration distance, input flux and vertical velocity fluctuations studied by Singh et al. were checked. The anisotropy of the turbulent convection and the diffusion models of the third-order moments representing the non-local transport were also investigated. These models are dramatically affected by the velocity fields and no universal constant parameters seem to exist. The limitations of the numerical results were also discussed.