Turbulent eddy-time-correlation in the solar convective zone

TL;DR

This paper proposes a new model for the eddy-time correlation in the solar convective zone, reconciling Gaussian and Lorentzian descriptions by applying the sweeping approximation, which better matches solar oscillation observations.

Contribution

The study introduces a combined Lorentzian and cut-off frequency model based on the sweeping approximation to improve the theoretical description of eddy-time correlations.

Findings

Reproduces the low-frequency shape of solar oscillation observations.

Validates the sweeping approximation for turbulent flows in the solar context.

Bridges the gap between Gaussian and Lorentzian models of eddy correlation.

Abstract

Theoretical modeling of the driving processes of solar-like oscillations is a powerful way of understanding the properties of the convective zones of solar-type stars. In this framework, the description of the temporal correlation between turbulent eddies is an essential ingredient to model mode amplitudes. However, there is a debate between a Gaussian or Lorentzian description of the eddy-time correlation function (Samadi et al. 2003, Chaplin et al. 2005). Indeed, a Gaussian description reproduces the low-frequency shape of the mode amplitude for the Sun, but is unsatisfactory from a theoretical point of view (Houdek, 2009) and leads to other disagreements with observations (Samadi et al., 2007). These are solved by using a Lorentzian description, but there the low-frequency shape of the solar observations is not correctly reproduced. We reconcile the two descriptions by adopting the sweeping approximation, which consists in assuming that the eddy-time-correlation function is dominated by the advection of eddies, in the inertial range, by energy-bearing eddies. Using a Lorentzian function together with a cut-off frequency derived from the sweeping assumption allows us to reproduce the low-frequency shape of the observations. This result also constitutes a validation of the sweeping assumption for highly turbulent flows as in the solar case.