Justham , Rappaport & Podsiadlowski ( 16 ) recently suggested that black-hole low-mass X-ray binaries ( BHLMXBs ) with short orbital periods may have evolved from black-hole intermediate-mass X-ray binaries ( BHIMXBs ) .
In their model the secondaries in BHIMXBs are assumed to possess anomalously high magnetic fields , so that magnetic braking can lead to substantial loss of angular momentum .
In this paper we propose an alternative mechanism for orbital angular momentum loss in BHIMXBs .
We assume that a small fraction \delta of the transferred mass from the donor star form a circumbinary disc surrounding the binary system .
The tidal torques exerted by the disc can effectively drain orbital angular momentum from the binary .
We have numerically calculated the evolutionary sequences of BHIMXBs , to examine the influence of the circumbinary disc on the binary evolution .
Our results indicate when \delta \la 0.01 - 0.1 ( depending on the initial orbital periods ) , the circumbinary disc can cause secular orbital shrinking , leading to the formation of compact BHLMXBs , otherwise the orbits always expand during the evolution .
This scenario also suggests the possible existence of luminous , persistent BHLMXBs , but it suffers the same problem as in Justham , Rappaport & Podsiadlowski ( 16 ) that , the predicted effective temperatures of the donor stars are significantly higher than those of the observed donor stars in BHLMXBs .