A Polytropic Model of the Solar Interior

In this work we considered different processes in the solar interior that can be described using polytropes. This assumption implies a radially variable continuous polytropic exponent, that is, our model is a multi-polytropic model of the Sun. We derived the equations for this type of multi-polytropic structure and solved them using numerical integration methods. Both, the exponent and proportionality factor in the polytropic model equation of state were taken as input functions, for each spherical layer in the solar interior. Using the spatial distribution of the density and pressure terms from a solar standard model (SSM) we obtained the variable with depth polytropic exponents. We found that the radial distribution of these exponents show four different zones. These can be interpreted as a first region where the energy transport is controlled by radiation. The second region is defined by a sudden change in the polytropic index, which can be associated to the tachocline, followed by a region with a nearly constant polytropic index which suits well a convective zone. Finally, the exponent decreases radially at the photosphere.