Predicting the Milky Way rotation curve beyond 18 kpc ahead of Gaia DR4: a two-regime radial acceleration relation

We combine 108 Gaia DR3 circular-velocity measurements of the Milky Way published by four independent groups (Jiao et al., Ou et al., Wang et al., Zhou et al., 2023) and analyse the observed radial acceleration gobs as a function of the baryonic acceleration gbar, without any assumption on dark matter. With the baryonic model of Zhou et al. (B1) and an error-weighted fit, the data are described by two straight lines: gobs=a.gbar+b.as at high gbar and gobs=d.gbar at low gbar, with a=1.201±0.019,b=0.412±0.014, d=2.380±0.020. The slope ratio d/(2a) =0.991±0.023 is consistent with unity: within the uncertainties, the break occurs at the maximum of the function β(ρ) introduced in our previous work. Imposing d=2a gives a=1.19±0.03 and b=0.42±0.02 (statistical and catalogue-to-catalogue uncertainties combined), a critical radius rc=18.3±0.7 kpc and a dynamical mass Mdyn=2aMb=(2.01±0.05)⨯1011M⊙ , in agreement with the dark-matter-based estimates of Jiao et al. and Ou et al. A second baryonic model (B2, Jiao et al.) leads to the same critical radius and dynamical mass. We introduce a new representation of the radial acceleration relation, D = gobs / gbar versus ρ²= as / gbar , in which both regimes are straight lines. The analysis is purely empirical and does not rely on any particular theory of gravity or dark matter. We freeze quantitative predictions for the rotation curve between 18 and 40 kpc, to be confronted with Gaia DR4: V(30kpc) ≈ 163–170 km s⁻¹, versus about 202 km s⁻¹ for the McGaugh (MOND-type) relation.