Chapter 34: Rotation Curves Without Dark Matter

The flat rotation curves of spiral galaxies are the single most cited piece of evidence for the existence of dark matter. The observation is simple: stellar and gas velocities at the periphery of spiral galaxies do not decline as v ∝ r^{-1/2} (the Keplerian falloff predicted for the visible mass distribution) but remain approximately constant out to the last measured point. In the dark matter paradigm, this flatness is explained by embedding the visible galaxy in an extended halo of non-baryonic dark matter whose density profile is tuned to produce the observed curve.

This chapter provides the τ-native explanation. The D-sector coupling κ(D;1) = 1 - ι_τ produces a capacity gradient ∇ C_D at galactic scales (the relevant chapter, Proposition [prop:ch34-capacity-gradient-dark-matter]) that enhances the gravitational acceleration beyond the Newtonian prediction (§). The enhancement is sufficient to flatten the rotation curve without introducing any new matter (§).

The chapter proceeds to galaxy-by-galaxy predictions (§), a comparison with MOND (§), the structural impossibility of dark matter halos (§), and a catalogue of falsifiable signatures (§).