A Baryonic Predictor of the Isothermal Dark Matter Profile Exponent in SPARC Galaxies: From Morphology to Concentration

We propose an extension of a cored isothermal dark matter density profile in which the exponent of the logistic equation governing the velocity profile, n, is allowed to depend on an observable galaxy property. Two versions are explored: (1) MDIP (Morphology-Dependent Isothermal Profile), with n depending on Hubble morphological type T; and (2) n_conc, with n depending on the concentration of the radial baryonic distribution, C. Fitted on the 175 galaxies of the SPARC sample, both versions statistically significantly outperform, at equal footing of two free parameters per galaxy, the Burkert, DC14, and original isothermal profiles. Compared directly against each other, MDIP and n_conc are statistically tied, and a joint fit prefers to discard T when C is available. The final conclusion is that morphological type carries no independent physical information: it is an indirect, partial proxy for the real baryonic concentration, which is the genuine predictor. We also rule out that the effect is explained by total baryonic mass, flat rotation velocity, or MOND predictions without a halo. A gas-fraction check for evolutionary history history effects was null, closing the descriptive line. A further step explored the candidate physical mechanism, comparing self-interacting dark matter (SIDM) and fuzzy/wave dark matter (FDM); FDM is found to be moderately more consistent with the pattern, though with important methodological caveats. This is an independent-research working note, not peer-reviewed. A Spanish-language version with a more detailed, pedagogical account of the full research process (including dead ends and corrections) is included alongside this English version.