(a) On the same graph, plot the density structure of stars of polytropic indices n=0, n=1, and n=5. Hint: You will want to plot ρn/ρc vs. r/λn.
(b) What can you conclude about the concentration of density with radius for increasing polytropic index?
(c) From the trend that you observe for the analytic solutions to the Lane--Emden equation, what would you expect regarding the density concentration of an adiabatically convective stellar model compared to a model in radiative equilibrium?
(d) Explain your conclusion in part (c) in terms of the physical processes of convection and radiation.