Inclusion of Turbulence in Solar Modeling

The general consensus is that in order to reproduce the observed solar p-modeoscillation frequencies, turbulence should be included in solar models.However, until now there has not been any well-tested efficient method toincorporate turbulence into solar modeling. We present here two methods toinclude turbulence in solar modeling within the framework of the mixing lengththeory, using the turbulent velocity obtained from numerical simulations of thehighly superadiabatic layer of the sun at three stages of its evolution. Thefirst approach is to include the turbulent pressure alone, and the second is toinclude both the turbulent pressure and the turbulent kinetic energy. Thelatter is achieved by introducing two variables: the turbulent kinetic energyper unit mass, and the effective ratio of specific heats due to the turbulentperturbation. These are treated as additions to the standard thermodynamiccoordinates (e.g. pressure and temperature). We investigate the effects of bothtreatments 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 3Dsimulations, and produces a p-mode frequency correction an order of magnitudebetter than the first method.Comment: 10 pages, 12 figure