Polytrope

In astrophysics, a polytrope refers to a solution of the Lane-Emden equation in which the pressure depends upon the density in the form, where is pressure, is density and is a constant. The constant is known as the polytropic index. This relation need not be interpreted as an equation of state, although a gas following such an equation of state does indeed produce a polytropic solution to the Lane-Emden equation. Rather, this is simply a relation that expresses an assumption about the change of with radius in terms of the change of with radius, yielding a solution to the Lane-Emden equation.