Rapid expansion of polytropes

An extremely massive unevolved star may be idealized as an n = 3 polytropic sphere supported by radiation pressure. Such a polytrope is subject to explosive, supersonic expansion, whose later stages can be described by similarity solution of the dynamical equations. This picture is confirmed by numerical hydrodynamic simulation, which shows that an n = 3 polytrope, initially at rest near equilibrium, undergoes an explosive expansion which approaches the similarity solution at large times.