Probing the Nature of Gravity in the Low-acceleration Limit: Wide Binaries of Extreme Separations with Perspective Effects

Abstract Recent statistical analyses of wide binaries have revealed a boost in gravitational acceleration with respect to the prediction by Newtonian gravity at low internal accelerations ≲10 −9 m s −2 . This phenomenon is important because it does not permit the dark matter interpretation, unlike galaxy rotation curves. We extend previous analyses by increasing the maximum sky-projected separation from 30 to 50 kilo astronomical units (kau). We show that the so-called “perspective effects” are not negligible at this extended separation and, thus, incorporate it in our analysis. With wide binaries selected with very stringent criteria, we find that the gravitational acceleration boost factor, γ g ≡ g obs / g N , is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.6</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.29</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.37</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">obs</mml:mi> <mml:mo>−</mml:mo> <mml:mi mathvariant="normal">newt</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≡</mml:mo> <mml:mo stretchy="false">(</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:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>0.147</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.062</mml:mn> </mml:math> ) at Newtonian accelerations g N = 10 −11.0 m s −2 , corresponding to separations of tens of kau for solar mass binaries. At Newtonian accelerations g N = 10 −10.3 m s −2 , we find <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>1.2</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ( δ obs−newt = 0.072 ± 0.027). For all binaries with g N ≲ 10 −10 m s −2 from our sample, we find <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>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.11</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ( δ obs−newt = 0.085 ± 0.027). These results are consistent with the generic prediction of modified Newtonian dynamics-type modified gravity, although the current data are not sufficient to pin down the low-acceleration limiting behavior. Finally, we emphasize that the observed deviation from Newtonian gravity cannot be explained by the perspective effects or any separation-dependent eccentricity variation that we have taken into account.