Dynamical formation of black hole low-mass X-ray binaries in the field: an alternative to the common envelope

Very wide binaries (>500 au) are subject to numerous encounters with fly-by stars in the Galactic field and can be perturbed into highly eccentric orbits (e ∼ 0.99). For such systems, the tidal interactions at close pericentre passages can lead to orbit circularization and, possibly, to mass transfer, consequently producing X-ray binaries without the need for the common envelope. We test this scenario for the case of black hole (BH) low-mass X-ray binaries (LMXBs) by performing a population synthesis with a numerical treatment of random stellar encounters. We test various models for the threshold pericentre distance under which the tidal forces cause circularization. We estimate that fly-by interactions can produce a current population of ∼60-220 BH LMXBs in the Galactic field. The results are sensitive to assumptions on the tidal circularization efficiency and the BH natal kick, because zero to very small kick velocities of several km s^-1 are required for the wide systems to survive the BH formation (∼60 per cent of the cases in our simulations). We show that the most likely donors are low-mass stars (<1 M_⊙; at the onset of mass transfer) as observed in the population of known sources (∼20). However, the low number of systems formed along this route is in contrast with the most recent observational estimate of the number of dormant BH LMXBs in the Galaxy 10⁴-10⁸. If, indeed, the numbers are so high, alternative formation channels of BHs with low-mass donors need to be identified.