Abstract
ABSTRACT The relative velocity distribution of wide binary (WB) stars is sensitive to the law of gravity at the low accelerations typical of galactic outskirts. I consider the feasibility of this wide binary test using the ‘line velocity’ method. This involves considering only the velocity components along the direction within the sky plane orthogonal to the systemic proper motion of each WB. I apply this technique to the WB sample of Hernandez et al., carefully accounting for large-angle effects at one order beyond leading. Based on Monte Carlo trials, the uncertainty in the one-dimensional velocity dispersion is ≈100 m s−1 when using sky-projected relative velocities. Using line velocities reduces this to ≈30 m s−1 because these are much less affected by distance uncertainties. My analysis does not support the Hernandez et al. claim of a clear departure from Newtonian dynamics beyond a radius of ≈10 kAU, partly because I use 2σ outlier rejection to clean their sample first. None the less, the uncertainties are small enough that existing WB data are nearly sufficient to distinguish Newtonian dynamics from Modified Newtonian Dynamics. I estimate that ≈1000 WB systems will be required for this purpose if using only line velocities. In addition to a larger sample, it will also be important to control for systematics like undetected companions and moving groups. This could be done statistically. The contamination can be minimized by considering a narrow theoretically motivated range of parameters and focusing on how different theories predict different proportions of WBs in this region.
Highlights
The standard cosmological paradigm relies on the assumption that general relativity applies accurately to all astronomical systems
If the anomalous rotation curves of galaxies are caused by a lowacceleration departure from the standard laws of gravity, this will have significant effects on wide binary (WB) systems with separations 3 kAU
To conclusively perform this wide binary test (WBT) and thereby detect or rule out such effects, accurate data are required for systems with separations up to ≈20 kAU (Hernandez et al 2012; Scarpa et al 2017; Banik & Zhao 2018; Pittordis & Sutherland 2018)
Summary
The standard cosmological paradigm relies on the assumption that general relativity applies accurately to all astronomical systems. Their main result was that MOND enhances the orbital velocities of Solar neighbourhood WBs by ≈ 20 per cent above Newtonian expectations, consistent with their analytic estimate (see their Section 2.2) Using statistical methods they developed, they showed that ≈500 WB systems would be required to detect this effect if measurement errors are neglected but only the more accurately known sky-projected quantities are used. This technique has the advantage of using two components of vrel, which could significantly improve the statistical power of the WBT After explaining these methods more precisely, I apply them to the Hernandez et al (2019) data set to confirm that both significantly reduce uncertainties compared to the use of conventional sky-plane velocities (Section 3).
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