A hierarchical Bayesian pipeline for soliton-plus-NFW inference on SPARC rotation curves: diagnostics and prior-boundary behaviour

Galaxy rotation curves provide a direct test of how baryonic matter and dark matter combine to determine the mass profiles of disk galaxies. In ultralight or fuzzy dark matter models, numerical simulations predict a central solitonic core surrounded by an outer halo, but the population-level relation between the core and the host halo remains an important modelling choice. We present a hierarchical Bayesian pipeline for fitting soliton-plus-NFW rotation-curve models to the SPARC database while treating the core-halo scaling exponent as a global free parameter. The model uses a Schive-normalized soliton, a regularized NFW envelope with a smooth transition, halo-mass priors tied to $V_{\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}}$, and stellar-to-halo-mass information. We apply the pipeline to 106 SPARC galaxies, including 26 systems with bulges, and sample the resulting 346-dimensional posterior with JAX/NumPyro NUTS. The free-scaling run has zero divergences and $\widehat{r}\simeq 1.000$ for the global parameters. The posterior reaches the upper edge of the standard mass prior and the lower edge of the scaling prior, with ${\log }_{10}(m_{\phi }\mathrm{/}\mathrm{e}\mathrm{V})=-19.20_{-0.11}^{+0.12}$ and $\alpha =0.014_{-0.011}^{+0.023}$. This boundary behaviour persists after removing UGC06787 and after widening the high-mass stellar-to-halo-mass prior. Within the adopted Schive-normalized model and standard SPARC fuzzy-dark-matter prior range, the selected SPARC sample does not identify an interior population-level soliton component. The main contribution is the hierarchical inference framework and the diagnostic workflow for recognizing boundary solutions in full-sample rotation-curve analyses.