Constraining the formation of black-holes in short-period Black-Hole Low-Mass X-ray Binaries

The formation of stellar mass black holes is still very uncertain. Two main uncertainties are the amount of mass ejected in the supernova event (if any) and the magnitude of the natal kick the black hole receives at birth (if any). Repetto et al. (2012), studying the position of Galactic X-ray binaries containing black holes, found evidence for black holes receiving high natal kicks at birth. In this Paper we extend that study, taking into account the previous binary evolution of the sources as well. The seven short-period black-hole X-ray binaries that we use, are compact binaries consisting of a low-mass star orbiting a black hole in a period less than $1$ day. We trace their binary evolution backwards in time, from the current observed state of mass-transfer, to the moment the black hole was formed, and we add the extra information on the kinematics of the binaries. We find that several systems could be explained by no natal kick, just mass ejection, while for two systems (and possibly more) a high kick is required. So unless the latter have an alternative formation, such as within a globular cluster, we conclude that at least some black holes get high kicks. This challenges the standard picture that black hole kicks would be scaled down from neutron star kicks. Furthermore, we find that five systems could have formed with a non-zero natal kick but zero mass ejected (i.e. no supernova) at formation, as predicted by neutrino-driven natal kicks.