Galactic rotation curves from boundary-stabilized pressure geometry: a cored alternative to cuspy dark matter halos

The dark matter problem in galaxies is usually framed as a choice between collisionless halos and modified dynamics. We investigate a third possibility: a galaxy-scale effective model in which halo support is represented by a boundary-stabilized exterior pressure configuration in an effectively incompressible gravitational medium. In this framework, Laplace-type equilibrium in the outer halo yields an asymptotic pressure gradient dP/dr ∝ 1/r, producing approximately flat rotation curves at large radius. A finite-radius completion gives a regular cored profile with asymptotically constant outer speed. We test this profile on the full SPARC sample of 175 nearby disk galaxies. The model yields successful fits for 171 galaxies and, with a Gaussian prior on the stellar mass-to-light ratio, achieves a median χ²/dof = 0. 64. In a matched three-parameter comparison against the canonical cuspy Navarro–Frenk–White halo, the pressure model is preferred in 132 galaxies, while NFW is preferred in only 16, with 23 ties; the median Δχ² = 8. 5 favors the pressure model. The fitted characteristic acceleration scale aPᶜhar = V_∞²/ (2rc) also clusters near MOND's a₀ without that value being imposed. The same pressure profile, with V_∞ and rc fixed by the rotation-curve fits, also yields a closed-form prediction for the galaxy-scale weak-lensing excess surface density ΔΣ (R) at radii beyond the kinematic calibration regime.