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 ρ ρ ( n + 1 ) / n = K ρ ρ 1 + 1 / n , where P is pressure, ρ is density and K is a constant of proportionality. The constant n is known as the polytropic index; note however that the polytropic index has an alternative definition as with n as the exponent.