Inclusion of Turbulence in Solar Modeling

Abstract

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer of the sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass, and the effective ratio of specific heats due to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g. pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in 3D simulations, and produces a p-mode frequency correction an order of magnitude better than the first method.

Matching Stellar Models to Oscillation Data

“…The systematic growth in error at higher frequencies (higher n) is associated with the inherent uncertainties in the modeling of the superadiabatic layer of the Sun via the mixing-length theory. Li et al (2002) have shown that much of this discrepancy can be eliminated by incorporating the results of numerical stellar convection in both the model and the p-mode frequency calculation (see also Rosenthal et al 1999;Robinson et al 2003). We assume that the stellar model frequency uncertainties are similar to the discrepancies found between our solar model frequencies and the observed frequencies.…”

Presupernova structure of massive stars

“…A stronger foundation for interpreting helioseismic data (e.g. Stein & Nordlund 2001;Li et al 2002) and inferring the abundances of various elemental constituents of the sun (e.g. Asplund et al 2005;Caffau et al 2008) are benefitting tremendously from this work: these almost brute force approaches to solar surface convection are offering sufficiently precise information about interior structure to shed light on deeper astrophysical conundrums including the formation scenario of the sun (Guzik & Mussack 2010) and, in combination with solar neutrino observations, standard model physics (Serenelli et al 2009).…”

YREC: the Yale rotating stellar evolution code

“…A method to incorporate the effects of turbulence into the outer layers of one-dimensional (1D) stellar models has been implemented in YREC (Li et al 2002). The method requires a detailed three-dimensional hydrodynamical simulation (3D RHD) of the atmosphere and highly superadiabatic layer of stars (Robinson et al 2003).…”

“…1 and Fig. 2 for the case of a solar model, taken from the work of Li et al (2002). In the Li et al (2002) paper, the p-mode frequencies for two calibrated solar models that include the effects of turbulence are compared to the standard solar model (ssm) p-mode frequencies.…”

“…2 for the case of a solar model, taken from the work of Li et al (2002). In the Li et al (2002) paper, the p-mode frequencies for two calibrated solar models that include the effects of turbulence are compared to the standard solar model (ssm) p-mode frequencies. The psm model is obtained by including turbulent pressure alone in the solar modeling, while the esm models are obtained by introducing the turbulent variables χ and γ which include both turbulent pressure and kinetic energy.…”