Galaxy rotation curves in the $\mu$-deformation based approach to dark matter

We elaborate further the $\mu$-deformation-based approach to modeling dark matter, in addition to the earlier proposed use of $\mu$-deformed thermodynamics. Herein, we construct $\mu$-deformed analogs of the Lane-Emden equation (for density profiles), and find their solutions. Using these, we plot the rotation curves for a number of galaxies. Different curves describing chosen galaxies are labeled by respective (differing) values of the deformation parameter $\mu$. As result, the use of $\mu$-deformation leads to improved agreement with observational data. For all the considered galaxies, the obtained rotation curves (labeled by $\mu$) agree better with data as compared to the well known Bose-Einstein condensate model results of T.Harko. Besides, for five of the eight cases of galaxies we find better picture for rotation curves than the corresponding Navarro-Frenk-White (NFW) curves. Possible physical meaning of the parameter $\mu$, basic for this version of $\mu$-deformation, is briefly discussed.