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 ΛCDM model, since dwarf galaxies often exhibit flat central density cores rather than the steep cusps ( ρ ∝ 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>23</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">eV</mml:mi> </mml:math> , and yield a solitonic core with characteristic radius <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.4</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.24</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.22</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">kpc</mml:mi> </mml:math> , enclosing a mass M (&lt;2.47 kpc) ≃ (1.5 ± 0.2) × 10 9 M ⊙ . 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.