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Wide hot subdwarf B (sdB) binaries with main-sequence companions are outcomesof stable mass transfer from evolved red giants. The orbits of these binariesshow a strong correlation between their orbital periods and mass ratios. Theorigins of this correlation have, so far, been lacking a conclusiveexplanation. We aim to find a binary evolution model which can explain theobserved correlation. Radii of evolved red giants, and hence the resultingorbital periods, strongly depend on their metallicity. We have performed asmall but statistically significant binary population synthesis study with thebinary stellar evolution code MESA. We have used a standard model for binarymass loss and a standard Galactic metallicity history. The resulting sdBs wereselected based on the same criteria as used in observations and then comparedwith the observed population. We have achieved an excellent match to theobserved period - mass ratio correlation without explicitly fine-tuning anyparameters. Furthermore, our models produce a good match to the observed period- metallicity correlation. We predict several new correlations which link theobserved sdB binaries to their progenitors, and a correlation between theperiod, metallicity and core mass for subdwarfs and young low-mass He whitedwarfs. We also predict that sdB binaries have distinct orbital propertiesdepending on whether they formed in the bulge, thin or thick disc, or the halo.We demonstrate, for the first time, how the metallicity history of the MilkyWay is imprinted in the properties of the observed post-mass transfer binaries.We show that Galactic chemical evolution is an important factor in binarypopulation studies of interacting systems containing at least one evolvedlow-mass (Mi < 1.6 Msol) component. Finally, we provide an observationallysupported model of mass transfer from low-mass red giants onto main-sequencestars.

Observed binary populations reflect the Galactic history. Explaining the orbital period-mass ratio relation in wide hot subdwarf binaries