Measurements of the Low-Acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories

Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile ṽ≡ vₚ/vc of wide binary stars as a function of the normalized sky-projected radius s/rM where vₚ is the sky-projected relative velocity between the pair, vc is the Newtonian circular velocity at the sky-projected separation s, and rM is the MOND radius. With a Monte Carlo method Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the s/rM versus ṽ plane and a logarithmic velocity ratio parameter Γ is measured in the bins of s/rM. With three samples of binaries covering a broad range in size, data quality, and implied fraction of hierarchical systems including a new sample of 6389 binaries selected with accurate distances and radial velocities, I find a unanimous systematic variation from the Newtonian flat line. With Γ=0 at s/rM 0.15 or s 1~kilo astronomical units (kau), I get Γ=0.068± 0.015 (stat) -0.015+0.024 (syst) for s/rM 0.7 or s 5~kau. The gravitational anomaly (i.e.\ acceleration boost) factor given by γg = 102Γ is measured to be γg = 1.37-0.09+0.10 (stat) -0.09+0.16 (syst). With a reduced χ² test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at 5.8σ (χ²_ν=9.4) by the new sample (and 9.2σ by the largest sample used). The Milgromian AQUAL theory is acceptable with 0.5 χ²_ν 3.1. These results agree well with earlier results with the ``acceleration-plane analysis'' for a variety of samples and the ``stacked velocity profile analysis'' for a pure binary sample.