The formation of black-holes derived from X-ray binaries

This Thesis revolves around the topic of black holes (BHs) in X-ray binaries (XRBs). The trigger of this work was to understand how stellar-mass BHs form, a question which we tackled both with theoretical as well as observational studies. The formation mechanism of BHs is an unsolved problem in high-energy astrophysics, in particular when it comes to the amount of mass ejected at formation and to how large is the velocity BHs acquire at birth (the so-called natal kick), if they acquire a velocity at all. One way of tackling these uncertainties is to perform physically-motivated simulations of the core-collapse supernova, which is computationally challenging. Another way is to study the birth and evolution of XRBs hosting a BH accreting from a stellar companion, which is the method we use in this Thesis. On the theoretical side, we combine an approach typical of binary population synthesis calculations with a more detailed approach which solves for the binary evolution of each source. When possible, we describe the different evolutionary paths of the binary via analytical calculations and timescale arguments. On the observational side, we combine the techniques of optical spectroscopy and photometry, with the goal of increasing the sample of Galactic BHs.