Self-gravitating quantum stars with a globally relevant Bohm potential

The microphysics underlying nonbaryonic dark matter remains unknown. I derive the two-species Schrödinger-Poisson-Yukawa system for spin- 1 2 dark-sector fermion fields, ψ (mass m 1 ) and χ (mass m 2 ), coupled through a scalar mediator of mass m ϕ via a universal Yukawa coupling, within an orbital-free density-functional framework with the Kirzhnits gradient coefficient λ B = 1 / 9 . A central result is that the Bohm potential, far from being negligible in the Thomas-Fermi regime, contributes a species-dependent surface-energy correction analogous to the nuclear liquid-drop model; the heavier fermion species generates an outward quantum-pressure wall whilst the lighter species provides an inward surface tension, with degeneracy pressure furnishing the bulk confinement. In the single-species Schrödinger-Poisson limit the ground state recovers the benchmarked invariants M dim ≃ 3.883 and x T ≃ 2.562 , yielding M R T ≃ 9.95 λ B ℏ 2 / ( G m 1 2 ) . For polytropic index γ = 5 / 3 the mass-radius relation satisfies R ∝ M − 1 / 3 ; for γ = 4 / 3 a limiting mass emerges above which no stable equilibrium exists. Illustrative configurations span M = 10 − 8 – 5 M ⊙ , m 1 ∼ 10 − 14 − 10 − 6 eV , and radii from a few km to ∼ 10 3 R ⊙ , with gravitational-wave contact frequencies in the Einstein Telescope and LISA bands and microlensing signatures accessible to current surveys. The predictive rigidity of the resulting mass-radius relation, in which the single microphysical parameter m 1 determines the equilibrium radius once the total mass is specified, furnishes a reproducible, first-principles reference for constraining the dark-fermion mass in multicomponent dark sectors.