  Using X-ray monitoring observations with the ASM on board the RXTE and the
BAT on board the Swift, we are able to study the spectral state transitions
occurred in about 20 bright persistent and transient black hole and neutron
star binaries. We have confirmed that there is a correlation between the X-ray
luminosity corresponding to the hard-to-soft transition and the X-ray
luminosity of the following soft state. This correlation holds over a
luminosity range spanning by two orders of magnitude, with no indication of a
flux saturation or cut-off. We have also found that the transition luminosity
correlates with the rate of increase in the X-ray luminosity during the rising
phase of an outburst or flare, implying that the origin of the variation of the
transition luminosity is associated with non-stationary accretion in both
transient sources and persistent sources. The correlation between the
luminosity corresponding to the end of the soft-to-hard transition and the peak
luminosity of the preceding soft state is found insignificant. The results
suggest that the hysteresis effect of spectral state transitions is primarily
driven by non-stationary accretion when the mass accretion rate increases
rather than the mass accretion rate decreases. Our results also imply that
Galactic X-ray binaries can reach more luminous hard states during outbursts of
higher luminosities and of similar rise time scales as those observed. Based on
the correlations, we speculate that bright hard state beyond the Eddington
luminosity will be observed in Galactic binaries in the next century. We also
suggest that some ultra-luminous X-ray sources in nearby galaxies, which stay
in the hard states during bright, short flares, harbor stellar-mass compact
stars.
