Testing turbulent convection theory in solar models - II. Solar p-mode oscillations

The free parameters involved in the turbulent convection models are determined in the solar interior with the aid of helioseismology. We calculated solar p-mode oscillation l = 150 for a series of solar models described by Li & Yang, and compared the calculated frequencies with the helioseismic observations. It is found that, with appropriate choices of the turbulent parameters, solar model with both local and non-local turbulent convection models can give the calculated p-mode frequencies that are better consistent with the observations than the standard solar model does. The turbulent dissipation plays a major role in the frequency corrections, while the turbulent diffusion makes further improvements in the frequencies. Decreasing the values of parameters C-t and C-e or increasing the values of C-t1 and C-e1 helps reduce the calculated frequencies, indicating that the turbulent dissipation is weak and the turbulent diffusion is strong in the convection zone of the Sun. The parameters C-k and C-s have no obvious effect on the p-mode frequencies. The temperature is found to have a bump near the surface of the convection zone and a mild depression over the inner convection zone. It is just this temperature depression that makes the sound speed a little less, and the p modes spending a little longer time to travel in the convection zone. Combined with better values of the free parameters, our solar models with the TCMs can reduce the frequency differences between the model calculations and observation as much as 30 per cent for the modes of middle and high l. This result can give a clue to solar modelling, i.e., including turbulence in solar models is helpful to reproduce the observed solar p-mode frequencies.