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 v ˜ ≡ v p / v c of wide binary stars as a function of the normalized sky-projected radius s / r M , where v p is the sky-projected relative velocity between the pair, v c is the Newtonian circular velocity at the sky-projected separation s , and r M is the MOND radius. With a Monte Carlo method, Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the s / r M versus v ˜ plane, and a logarithmic velocity ratio parameter Γ is measured in the bins of s / r M . 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 / r M ≲ 0.15 or s ≲ 1 kau, I get Γ = 0.068 ± 0.015 (stat) − 0.015 + 0.024 (syst) for s / r M ≳ 0.7 or s ≳ 5 kau. The gravitational anomaly (i.e., acceleration boost) factor given by γ g = 10 2Γ is measured to be γ g = 1.37 − 0.09 + 0.10 (stat) − 0.09 + 0.16 (syst). With a reduced χ 2 test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at 5.8 σ ( χ ν 2 = 9.4 ) by the new sample (and 9.2 σ by the largest sample used). The Milgromian AQUAL theory is acceptable with 0.7 ≲ χ ν 2 ≲ 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.