Low-acceleration Gravitational Anomaly from Bayesian 3D Modeling of Wide Binary Orbits: Methodology and Results with Gaia Data Release 3

Abstract Isolated wide binary stars provide natural laboratories to directly probe gravity for Newtonian acceleration of g N ≲ 10 −9 m s −2 . Recent statistical analyses of wide binaries have been performed only with sky-projected relative velocities v p in the pairs. A new method of Bayesian orbit modeling exploiting three relative velocity components including the radial (line-of-sight) component v r is developed to measure the gravitational anomaly parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo mathvariant="normal">Γ</mml:mo> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:msqrt> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msqrt> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:msqrt> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">eff</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msqrt> </mml:math> where G eff is the effective gravitational constant for pseudo-Newtonian elliptical orbits, while G N is Newton’s constant. The method infers individual probability distributions of Γ and then combines the independent distributions to obtain a consolidated distribution in a specific range of g N . Here the method is described and applied to a sample of 312 wide binaries in a broad dynamic range of 10 −11.0 ≲ g N ≲ 10 −6.7 m s −2 with v r uncertainties in the range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>168</mml:mn> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>380</mml:mn> </mml:math> m s −1 selected from the Gaia Data Release 3 database. The following results are obtained: Γ = 0.000 ± 0.011 or γ g = 1.00 ± 0.05 ( N binary = 125) for the high-acceleration regime (10 −7.9 ≲ g N ≲ 10 −6.7 m s −2 ) agreeing well with Newton, but Γ = 0.085 ± 0.040 or <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:mn>1.4</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.33</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (35) for the modified Newtonian dynamics (MOND) regime (10 −11.0 ≲ g N ≲ 10 −9.5 m s −2 ) and Γ = 0.063 ± 0.015 or <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:mn>1.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.08</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (111) for the MOND + transition regime (10 −11.0 ≲ g N ≲ 10 −8.5 m s −2 ). These results show that a gravitational anomaly is evident for g N ≲ 10 −9 m s −2 and Γ in the MOND regime (≲10 −9.5 m s −2 ) agrees with the first-tier prediction (Γ ≈ 0.07 or γ g ≈ 1.4) of MOND gravity theories.