Wide binaries from the H3 survey: the thick disk and halo have similar wide binary fractions

Due to the different environments in the Milky Way's disk and halo, comparing wide binaries in the disk and halo is key to understanding wide binary formation and evolution. By using Gaia Early Data Release 3, we search for resolved wide binary companions in the H3 survey, a spectroscopic survey that has compiled $\sim$150,000 spectra for thick-disk and halo stars to date. We identify 800 high-confidence (a contamination rate of 4%) wide binaries and two resolved triples, with binary separations mostly between $10^3$-$10^5$ AU and a lowest [Fe/H] of $-2.7$. Based on their Galactic kinematics, 33 of them are halo wide binaries, and most of those are associated with the accreted Gaia-Sausage-Enceladus galaxy. The wide binary fraction in the thick disk decreases toward the low metallicity end, consistent with the previous findings for the thin disk. Our key finding is that the halo wide binary fraction is consistent with the thick-disk stars at a fixed [Fe/H]. There is no significant dependence of the wide binary fraction on the $\alpha$-captured abundance. Therefore, the wide binary fraction is mainly determined by the iron abundance, not their disk or halo origin nor the $\alpha$-captured abundance. Our results suggest that the formation environments play a major role for the wide binary fraction, instead of other processes like radial migration that only apply to disk stars.