External field effect in the substrate framework The parent galaxy's ebbing current imposes a DC phase bias on counter-rotating boundaries within its gravitational influence. TDGs closer to the parent experience stronger bias, partially breaking parity symmetry and reducing the MOND enhancement. DC phase bias field Ebbing current → parent Ebbing current → parent Parent galaxy NGC 5291 M ~ 10¹¹ M☉ TDG A (near) TDG B (mid) TDG C (far) Strong g_ext Parity broken Moderate g_ext Weak g_ext Parity intact D_p (kpc) ~30 ~60 ~100 MOND enhancement g_ext ≈ √(a₀ G M_parent) / D_p — calculable, zero free parameters Testable: compare rotation curves of TDGs at different projected distances Inner TDG → weaker MOND enhancement than outer TDG from same parent
The external field effect in the substrate framework. The parent galaxy's ebbing current imposes a DC phase bias on counter-rotating boundaries within its gravitational influence (purple gradient). At each TDG, two arced arrows represent the counter-rotating substrate flows whose parity symmetry produces the MOND gravitational response (GD2–GD4). Near the parent (TDG A): the external field is strong, the bias breaks the parity — one flow dominates (thick arrow), suppressing the MOND enhancement. Far from the parent (TDG C): the external field is weak, the two flows remain symmetric, and the full MOND response is recovered. The teal bars below show the resulting MOND enhancement gradient. This effect is calculable from the parent's baryonic mass and the TDG's orbital distance ($g_\text{ext} \approx \sqrt{a_0 G M_\text{parent}}/D_p$), with zero free parameters — and directly testable by comparing rotation curves of TDGs at different projected distances from the same parent system. CDM predicts no such distance-dependent effect.