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We elaborate further the $\mu$-deformation-based approach to modeling darkmatter, in addition to the earlier proposed use of $\mu$-deformedthermodynamics. Herein, we construct $\mu$-deformed analogs of the Lane-Emdenequation (for density profiles), and find their solutions. Using these, we plotthe rotation curves for a number of galaxies. Different curves describingchosen galaxies are labeled by respective (differing) values of the deformationparameter $\mu$. As result, the use of $\mu$-deformation leads to improvedagreement with observational data. For all the considered galaxies, theobtained rotation curves (labeled by $\mu$) agree better with data as comparedto 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 rotationcurves than the corresponding Navarro-Frenk-White (NFW) curves. Possiblephysical meaning of the parameter $\mu$, basic for this version of$\mu$-deformation, is briefly discussed.

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