Normalized additional velocity distribution: Testing the radial profile of dark matter halos and MOND

We propose a complementary and fast approach to study galaxy rotation curves directly from the sample data, instead of individual fits. With this approach, some relevant tests can be done analytically. It is based on dimensionless difference between observational curve expected one baryonic matter ($\delta V^2$) as function normalized radius $r_n$ (i.e., for all galaxies, $0 < r_n 1$). Using 153 galaxies SPARC sample, we find distribution $\delta V^2$. Considering radii with $0.2 0.9$, most data are close V^2 = r_n^{0.42}$, about $95\%$ r_n^{2.2}$ 2 r_n^{0.38} - r_n^{1.9} $. consider three well known dark halo models (NFW, Burkert DC14), simple profile purpose model comparison (Arctan$_\alpha$) modified gravity without (MOND). By comparing model-inferred confirm that NFW lacks necessary diversity reproduce several observed curves, while DC14 have better concordance data. The lowest V^2$ found linear V^2_{NFW} r_n$), V^2_{Bur} r_n^2$ (this result independent density parameter, i.e., $\rho_{c}$ or $\rho_{s}$). MOND only covers very central region distribution, hence it also diversity, which in turn related larger $\chi^2$ values. In second paper, method will extended other classes models.