1998A&A...338...69E

Several evolutionary sequences with low mass secondaries as donors and black holes as accretors are calculated. Adopting a simple estimate for the efficiency of magnetic braking we have determined the bifurcation period P_bif, separating converging from diverging binary systems, to be ∼1 day. It is shown that in converging binary systems, similar to neutron star binaries with low-mass secondaries, evolution proceeds towards very short orbital periods with continous accretion or it ends by formation of system with a low mass helium white dwarf and a black hole. If the final orbital period of the latter system is less than 10 hours, it is possible that the system will reappear as a persistent X-ray source with ultra-short orbital period. For systems which evolve towards very short orbital periods there always is a phase in which the mass accretion rate exceeds a certain {dot}(M)_crit^irr above which the system is a persistent X-ray source. By comparing evolutionary sequences for different black hole masses it is shown that for a more massive black hole as accretor the range in which mass transfer is unstable is larger than for a less massive black hole. It is shown that after the common envelope (CE) phase, during the extensive high-velocity wind stage (before the collapse to a black hole) only helium stars of rather low mass end up with orbital periods lower than P_bif which enables them to evolve towards the short orbital period range where the majority of the low-mass X-ray binaries ( LMXB) with black holes as accretors are observed. This implies that the pre-CE progenitors of black holes in these systems had masses ≤25M_☉.