Soft X-ray transients in the Hertzsprung gap

We apply the disc instability model for soft X-ray transients to identify system parameters along evolutionary sequences of black hole X-ray binaries (BHXBs) that are consistent with transient behaviour. In particular, we focus on the hitherto neglected group of BHXBs with intermediate-mass giant donor stars. These spend a significant fraction of their X-ray active phase crossing the Hertzsprung gap. Three case B binary sequences with a black hole accretor and 2.5-M. initial donor mass are presented in detail. We formulate rules which summarize the behaviour of these sequences and provide an approximate description for case B mass-transfer in intermediate-mass BHXBs. Chiefly, the time-scale of the overall radius expansion is given by the initial donor mass, while the surface appearance is determined by the current donor mass. With these rules we obtain a general overview of transient and persistent behaviour of all intermediate-mass BHXBs by just considering single star sequences of different mass. We find that although systems in the process of crossing the Hertzsprung gap are in general persistently bright, with Eddington or super-Eddington transfer rates, there is a narrow instability strip where transient behaviour is possible. This strip extends over a secondary mass range 2.0 less than or equal to M-2 less than or equal to 3.5 M.. GRO J1655-40 might be such a system. We predict that there are no BHXB transients with (sub)giant donors more massive than 3.5 M., and no neutron star transients in the Hertzsprung gap.