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.