Evolution of low-mass binaries with black-hole components

We consider evolutionary models for the population of short-period (Porb ≲ 10 h) low-mass black-hole binaries (LMBHB) and compare them with observations of soft X-ray transients (SXT). Evolution of LMBHB 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. We show that the absence of observed stable luminous LMBHB implies that upon RLOF by the low-mass donor angular momentum losses are substantially reduced with respect to the Verbunt and Zwaan “standard” prescription for magnetic braking. Under this assumption masses and effective temperatures of the model secondaries of LMBHB are in a satisfactory agreement with the masses and effective temperatures (as inferred from their spectra) of the observed donors in LMBHB. Theoretical mass-transfer rates in SXTs are consistent with the observed ones if one assumes that accretion discs in these systems are truncated (“leaky”). We find that the population of short-period SXT is formed mainly by systems which had unevolved or slightly evolved (Xc ≳ 0.35) donors at the Roche-lobe overflow. Longer period (Porb ≃ (0.5–1) day) SXT might descend from systems with initial donor mass about 1 M⊙ and Xc ≲ 0.35. It is unnecessary to invoke donors with almost hydrogen-depleted cores to explain the origin of LMBHB. Our models suggest that a very high efficiency of common-envelopes ejection is necessary to form LMBHB, unless currently commonly accepted empirical estimates of mass-loss rates by winds for pre-WR and WR-stars are significantly over-evaluated.