Resolving the Core-Cusp and Diversity Problems with a Baryon-Correlated Dark Matter Profile

Abstract

The rotation velocity profiles of galaxies (rotation curves) remain unexpectedly flat at large distances, where visible matter alone should make the rotation velocity decrease with radius. To explain this missing gravity, conventional frameworks assume unseen mass or alternative gravitational effects. While the dark matter hypothesis has become the standard paradigm, this framework faces persistent small-scale challenges, such as the core-cusp and diversity problems, and struggles to explain the observed correlation between dark matter and baryons, as evidenced by the Radial Acceleration Relation and the Tully-Fisher relation. Here, we introduce a simple empirical law for the dark matter in a single galaxy, stating that the dark matter energy density $ρ_{\mathrm{DM}}$ is determined by the baryonic gravitational potential $U_b$ and the total baryonic mass of the galaxy $M_b$ as $ρ_{\mathrm{DM}} = K M_b^{-3/2} (U_b/c^2)^2$. When applied to 91 galaxies from the SPARC database with a single fitting parameter $K$, this baryon-correlated dark matter profile reproduces both the diverse inner structures and outer flat regions of the observed rotation curves, resolving the core-cusp and diversity problems. The fitted $K$ values for the 91 galaxies were concentrated within a narrow range, and our detailed analysis using specific stellar mass-to-light ratios from the THINGS survey reduced this scatter. Moreover, the alignment of all individual data points along the derived linear relation further demonstrates the validity of the empirical law at each radius for all the 91 galaxies. These results suggest the existence of new fields interacting with baryons.