Bayesian Comparison of BEC, NFW, and gNFW Halo Models Using Galaxy Rotation Curves

We present a Bayesian comparison of three dark-matter halo models—Navarro–Frenk–White (NFW),generalized NFW (gNFW, with free inner slope α), and Bose–Einstein condensate (BEC) halosincluding a rotating variant—fitted to galaxy rotation curves from the SPARC database to addressthe core–cusp problem. Unlike earlier studies that relied on heuristic or genetic-algorithm searchesof parameter space, we sample the full posterior distributions with Markov Chain Monte Carlo,marginalizing over baryonic nuisance parameters and using both the Bayesian Information Criterion(BIC) and a posterior-based harmonic-mean evidence estimator to assess model support. Across thesample most galaxies are statistically indistinguishable between models, but allowing a free innerslope yields a modest, systematic evidence gain for gNFW relative to fixed-slope NFW. BEC modelsshow a much broader spread in performance: a subset of galaxies strongly favour BEC, but manyexhibit substantial evidence loss compared to gNFW, with the rotating BEC giving the best meanperformance yet large galaxy-to-galaxy variability. These results highlight that flexibility in theinner slope is crucial for rotation-curve fits, and demonstrate that full Bayesian evidence estimationprovides a more robust, population-level assessment of halo models than previous genetic-algorithmor point-estimate approaches.