polytrope

thumb|350x350px|The normalized density as a function of scale length for a wide range of polytropic indices

In astrophysics, a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form P = K \rho^{(n+1)/n} = K \rho^{1 + 1/n}, where is pressure, is density and is a constant of proportionality. The constant is known as the polytropic index; note however that the polytropic index has an alternative definition as with n as the exponent.