The wide binary fraction of solar-type stars: emergence of metallicity dependence at a < 200 au

We combine a catalogue of wide binaries constructed from Gaia DR2 with [Fe/H] abundances from wide-field spectroscopic surveys to quantify how the binary fraction varies with metallicity over separations 50 less than or similar to s/au <= 50 000. At a given distance, the completeness of the catalogue is independent of metallicity, making it straightforward to constrain intrinsic variation with [Fe/H]. The wide binary fraction is basically constant with [Fe/H] at large separations (s greater than or similar to 250 au) but becomes quite rapidly anticorrelated with [Fe/H] at smaller separations: for 50 < s/au < 100, the binary fraction at [Fe/H] = -1 exceeds that at [Fe/H] = 0.5 by a factor of 3, an anticorrelation almost as strong as that found for close binaries with a < 10 au. Interpreted in terms of models where disc fragmentation is more efficient at low [Fe/H], our results suggest that 100 < a/au < 200 is the separation below which a significant fraction of binaries formed via fragmentation of individual gravitationally unstable discs rather than through turbulent core fragmentation. We provide a public catalogue of 8407 binaries within 200 pc with spectroscopically determined [Fe/H] for at least one component.