The origin and fate of short-period low-mass black-hole binaries

We present results of a population synthesis study for semidetached short orbital period binaries which contain low-mass (1.5 M<SUB>o</SUB>) donors and massive ( 4 M<SUB>o</SUB>) compact accretors, which in our model represent black holes. Evolution of these binaries is determined by nuclear evolution of the donors and/or orbital angular momentum loss due to magnetic braking by the stellar wind of the donors and gravitational wave radiation. According to our model the estimated total number of this type of black-hole binaries in the Galaxy is  10 000. If the magnetic braking removing angular momentum in semidetached black-hole binaries is described by the Verbunt & Zwaan formula, the model predicts that among them around 3000 systems with periods >2 h would be transient. In addition one finds several hundreds of luminous and stable systems with periods between 3 and 8 h. Several dozens of these bright systems should be observed above the RXTE ASM sensitivity limit. The absence of such systems implies that upon Roche-lobe overflow by the low-mass donor angular momentum losses are reduced by a factor more than 2 with respect to the Verbunt & Zwaan prescription. In such a case short period black-hole soft X-ray transients (SXT) may have donors that overflow the Roche lobe in the core hydrogen-burning stage. We show that it is unlikely that the transient behaviour of black-hole short-period X-ray binaries is explained by the evolved nature of the stellar companion. On the other hand a substantial fraction of black-hole binaries with periods >3 h could be faint with truncated, stable cold accretion discs as proposed by Menou et al. Most of the semidetached black-hole binaries are expected to have periods shorter than ~2 h. Properties of such, still to be observed, very small mass-ratio (q=M<SUB>2</SUB>/M<SUB>1</SUB> < 0.02) binaries are different from those of their longer period cousins