Wide Binaries as a Modified Gravity test: prospects for detecting triple-system contamination

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt emulate dark matter; in essence, MOND-like (with external field effect included) predict binaries (wider than $\sim 7$ kAU) should orbit 15\%$ faster Newtonian similar parameters; such a shift is readily detectable principle the sample 9,000 candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022; PS22). However, main obstacle at present observed "fat tail" wide-binary 1.5 - 6 \times$ circular velocity; this tail population cannot be bound pure systems, but possible explanation triple or quadruple unresolved undetected additional star(s). While modelled subtracted, obtaining accurate model crucial obtain robust modified gravity. Here we explore prospects observationally constraining population: simulate hierarchical triples "observed" as PS22 random epochs viewing angles; then evaluate various methods detecting third star, including astrometry, RV drift, several imaging direct Rubin images, speckle coronagraphic imaging. Results are encouraging, typically 90 percent key regions parameter space detectable; there moderate "dead zone" cool brown-dwarf companions 25-100$ AU separation not any our baseline methods. A large feasible observing campaign clarify triple/quadruple make gravity decisive.