  We investigated the reported distances of Galactic black hole (BH) and
neutron star low-mass X-ray binaries (LMXBs). Comparing the distances derived
for the neutron stars CygX-2 and XTE J2123-058 using the observed Eddington
limited photospheric radius expansion bursts with the distances derived using
the observed radius and effective temperature of the companion star we find
that the latter are smaller by approximately a factor of 1.5-2. The latter
method is often employed to determine the distance to BH LMXBs. A possible
explanation for this discrepancy is that the stellar absorption lines in fast
rotating companion stars are different from those in the slowly rotating
template stars as was found before for early type stars. This could lead to a
systematic mis-classification of the spectral type of the companion star, which
in turn would yield a systematic error in the distance. We find that, using new
distances for XTE J1550-564 and V404 Cyg, the maximum outburst luminosity for
at least 5 but perhaps even 7 of the 15 BH soft X-ray transients exceeds the
Eddington luminosity for a 10 M_sun BH showing that these systems would be
classified as ultra-luminous X-ray sources had we observed them in other
Galaxies. This renders support for the idea that many ultra-luminous X-ray
sources are stellar-mass rather than intermediate-mass BHs. We find that the
rms value of the distance to the Galactic plane for BHs is consistent with that
of neutron star LMXBs. This suggests that BHs could also receive a
kick-velocity during their formation although this has to be investigated in
more detail. (Abridged).
