An analytic approximation to the isothermal sphere
  We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index - the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii. 
Priyamvada Natarajan (IoA, Cambridge) and Donald Lynden-Bell (IoA,   Cambridge and University, Belfast)