Modeling Solitonic Cores, Stabilization of Bar, and Suppression of Bar Dissolution in DDO 168 via GPP Formalism: A Detailed Analysis of Bose--Einstein Condensate/Fuzzy Dark Matter Halo Structure and Bar Dynamics in the Dwarf Galaxy DDO 168

Abstract

The cusp-core problem remains a challenge to the $Λ$CDM model, since dwarf galaxies often exhibit flat central density cores rather than the steep cusps ($ρ\propto r^{-1}$) predicted by collisionless $N$-body simulations. We model the dark-matter-dominated dwarf irregular galaxy DDO 168 within the Bose--Einstein condensate (BEC) or fuzzy dark matter (FDM) framework, in which ultralight bosons form a solitonic core governed by the Gross--Pitaevskii--Poisson (GPP) equations, with the soliton mass--radius relation enforced. We numerically validate the ground-state solution of the GPP system as a consistency check and fit the inner rotation curve of DDO 168 using SPARC data. Within this framework, the data are consistent with an axion mass \[ m = (1.3^{+0.3}_{-0.2}) \times 10^{-23}\,\mathrm{eV}, \] and yield a solitonic core with characteristic radius \[ R_c = 2.40^{+0.24}_{-0.22}\,\mathrm{kpc}, \] enclosing a mass \[ M(<2.47\,\mathrm{kpc}) \simeq (1.5 \pm 0.2)\times10^{9}\,M_\odot. \] The observed flat inner rotation curve is reproduced and the presence of a weak H\,I bar is compatible with multigigayear survival timescales, consistent with reduced Chandrasekhar dynamical friction in a shallow central potential. These results demonstrate that the BEC/FDM framework provides an internally consistent description of DDO 168, simultaneously reproducing the observed rotation curve, alleviating the cusp-core tension, and allowing long-lived weak bars under conservative dynamical assumptions.