Implementation of polytropic method to study initial structures of gas giant protoplanets

In this paper we have determined the initial structures of gas giant protoplanets, formed via disk instability, having a mass range of 0.3–10 Jupiter masses by the simple polytropic method. The polytropic protoplanets or polytropes have been assumed to be spheres of solar composition, each of which is in a steady state of quasi-static equilibrium, where the only source of energy is the gravitational contraction of the gas. The results of our calculations for the polytropes with polytropic indices n = 1 and n = 1.5 are found to be closer to reality and are in good agreement with the findings obtained by other investigations with more rigorous treatment of the problem.