The frequency difference between a model used only two-point interpolation of opacity and a model used piecewise linear interpolation of opacity is of the order of several microHertz at a certain stage, which is almost 10 times worse than the observa
tional precision of p-modes of solar-like stars. Therefore, the two-point interpolation of opacity is unsuitable in modelling of solar-like stars with element diffusion.
The purpose of this work was to obtain diffusion coefficient for the magnetic angular momentum transport and material transport in a rotating solar model. We assumed that the transport of both angular momentum and chemical elements caused by magnetic
fields could be treated as a diffusion process. The diffusion coefficient depends on the stellar radius, angular velocity, and the configuration of magnetic fields. By using of this coefficient, it is found that our model becomes more consistent with the helioseismic results of total angular momentum, angular momentum density, and the rotation rate in a radiative region than the one without magnetic fields. Not only can the magnetic fields redistribute angular momentum efficiently, but they can also strengthen the coupling between the radiative and convective zones. As a result, the sharp gradient of the rotation rate is reduced at the bottom of the convective zone. The thickness of the layer of sharp radial change in the rotation rate is about 0.036 $R_{odot}$ in our model. Furthermore, the difference of the sound-speed square between the seismic Sun and the model is improved by mixing the material that is associated with angular momentum transport.
Using reconstructed opacities, we construct solar models with low heavy-element abundance. Rotational mixing and enhanced diffusion of helium and heavy elements are used to reconcile the recently observed abundances with helioseismology. The sound sp
eed and density of models where the relative and absolute diffusion coefficients for helium and heavy elements have been increased agree with seismically inferred values at better than the 0.005 and 0.02 fractional level respectively. However, the surface helium abundance of the enhanced diffusion model is too low. The low helium problem in the enhanced diffusion model can be solved to a great extent by rotational mixing. The surface helium and the convection zone depth of rotating model M04R3, which has a surface Z of 0.0154, agree with the seismic results at the levels of 1 $sigma$ and 3 $sigma$ respectively. M04R3 is almost as good as the standard model M98. Some discrepancies between the models constructed in accord with the new element abundances and seismic constraints can be solved individually, but it seems difficult to resolve them as a whole scenario.
Aims. The purpose of this work is to investigate a new frequency separation of stellar p-modes and its characteristics. Methods. Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical adiabatic f
requencies of stellar model, we compute the frequency separations. Results. A new separation $sigma_{l-1 l+1}(n)$, which is similar to the scaled small separation $d_{l l+2}(n)/(2l+3)$, is obtained from the asymptotic formula of stellar p-modes. The separations $sigma_{l-1 l+1}(n)$ and $d_{l l+2}(n)/(2l+3)$ have the same order. And like the small separation, $sigma_{l-1 l+1}(n)$ is mainly sensitive to the conditions in the stellar core. However, with the decrease of the central hydrogen abundance of stars, the $sigma_{02}$ and $sigma_{13}$ more and more deviate from the scaled small separation. This characteristic could be used to extract the information on the central hydrogen abundance of stars.
