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
Kyu‐Hyun Chae
Abstract
Abstract Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:math> 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) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow/> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.015</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.024</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.37</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (stat) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow/> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.16</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>9.4</mml:mn> </mml:math> ) by the new sample (and 9.2 σ by the largest sample used). The Milgromian AQUAL theory is acceptable with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.7</mml:mn> <mml:mo>≲</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:mn>3.1</mml:mn> </mml:math> . 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.