Self-gravitating systems with nonlocal , long-range interactions are described by nonextensive statistics .
Recently , Leubner demonstrated that the nonextensivity parameter \kappa should be negative for self-gravitating , pressureless systems , such as dark matter halos .
The equation for the spherically symmetric nonextensive dark matter halos has also been derived .
Here we demonstrate that this equation is identical to the classical Lane-Emden equation describing the structure of self-gravitating polytropic spheres .
This establishes an intimate connection between self-gravitating polytropes and nonextensive thermostatistics .
Moreover , based on this fact and observational data , we put a stronger constraint on \kappa , namely \kappa \lesssim - 3.4 .