Breakdown of the Newton–Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars
Kyu‐Hyun Chae
Abstract
Abstract A gravitational anomaly is found at weak gravitational acceleration g N ≲ 10 −9 m s −2 from analyses of the dynamics of wide binary stars selected from the Gaia DR3 database that have accurate distances, proper motions, and reliably inferred stellar masses. Implicit high-order multiplicities are required and the multiplicity fraction is calibrated so that binary internal motions agree statistically with Newtonian dynamics at a high enough acceleration of ≈10 −8 m s −2 . The observed sky-projected motions and separation are deprojected to the 3D relative velocity v and separation r through a Monte Carlo method, and a statistical relation between the Newtonian acceleration g N ≡ GM / r 2 (where M is the total mass of the binary system) and a kinematic acceleration g ≡ v 2 / r is compared with the corresponding relation predicted by Newtonian dynamics. The empirical acceleration relation at ≲10 −9 m s −2 systematically deviates from the Newtonian expectation. A gravitational anomaly parameter δ obs−newt between the observed acceleration at g N and the Newtonian prediction is measured to be: δ obs−newt = 0.034 ± 0.007 and 0.109 ± 0.013 at g N ≈ 10 −8.91 and 10 −10.15 m s −2 , from the main sample of 26,615 wide binaries within 200 pc. These two deviations in the same direction represent a 10 σ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At g N = 10 −10.15 m s −2 , the observed to Newton-predicted acceleration ratio is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>obs</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>pred</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msqrt> <mml:msub> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>obs</mml:mi> <mml:mo>−</mml:mo> <mml:mi>newt</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>1.43</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.06</mml:mn> </mml:math> . This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.