3.1. Nova Sco 1994
Shahbaz et al., Shahbaz et al. (1999) have recently determined the present stellar masses in Nova Sco 1994 (GRO J1655-40). They find and . The mass transfer in Nova Sco 1994 may already have been going on for a long period of time. From the luminosity and effective temperature of the donor star in this system one finds, using stellar evolution tracks, that the donor can not have started out with a mass larger than at the onset of the X-ray phase van der Hooft et al. 1998. As an example of combinations of present masses we use () = (6, 2.5) and (7.75, 3.25). Assuming conservative mass transfer ( ) some possibilities for the system configuration at the onset of mass transfer are the following combinations of : (4.5, 4.0, 1.52), (7.0, 4.0, 1.91) and (7.5, 3.5, 2.31). With these values and Eq. (7) we find that the present runaway velocity of 106 km s-1 is obtained for and respectively. This is shown in the left panel of Fig. 1 (solid lines). Note that all these lines are terminated at the amount of mass ejection that would result in a pre-SN orbit in which the companion would fill its Roche lobe. The minimum amount of mass that must be lost is 4.1 in the case of a black hole of 4.5 , given km s-1.
If we relax the assumption of conservative mass transfer (as is suggested by the observation of jets from Nova Sco), and assuming the lost material drags along three times the specific angular momentum (Pols & Marinus Pols and Marinus (1994)), we calculated the orbits for the first two cases, assuming 0.5 was lost from the system. The resulting system parameters at the onset of the mass transfer then become (5, 4, 1.96) and (7.5, 4, 2.42) for the first two examples. These curves are plotted as dashed lines in Fig. 1. In this case at least 5 and 8 are lost, respectively.
3.2. Cygnus X-1
For Cygnus X-1 the presently best estimate of the masses of the stellar components is and . Extremes of the allowed masses are given by = (3.9, 11.7) and (15.2, 19.2) respectively Herrero et al. 1995. We assume no orbital evolution since the beginning of the mass transfer phase, because Roche lobe overflow can not have started long ago since the expected mass transfer rates then would be much higher. We use the values of the masses as given above and the present day orbital period of 5.6 days. We also neglect the small eccentricity that the orbit still has. The right hand panel in Fig. 1 shows the resulting allowed range of mass ejected in the formation of the black hole. For a present black hole mass of 3.9 at least 2.6 must have been ejected to produce the observed space velocity. For a black hole of 15.2 at least 6 must have been ejected.
3.3. The remaining black hole X-ray transients
Table 1 shows that all the black hole X-ray binaries with low mass donors have low velocities. As derived by White & van Paradijs White and van Paradijs (1996), the expected additional velocity component of these X-ray binaries is of the order of 20-40 km s-1. In Cyg X-1 and Nova Sco at least 28 and 48% of the mass of the progenitor must have been ejected in the SN. Therefore we computed the velocities for these systems assuming a constant fraction of 35% of the helium star mass to be ejected and show the obtained range in velocities given the range in black hole masses in Fig. 2. The last five systems are all expected to have evolved during mass transfer to smaller periods, and all seem to be compatible with an initial systems close to (m, P) = (1 , 0.74 d), cf. Ergma & Fedorova Ergma and Fedorova (1998). The systems shrink due to magnetic braking, so we assume = 1 d (see e.g. Kalogera Kalogera (1999)). For V 404 Cyg we assumed an re-circularized period of 4 days and an donor mass of 1 .
© European Southern Observatory (ESO) 1999
Online publication: December 2, 1999