We present our analysis of the high-energy radiation from black hole (BH) t
ransients using archival data obtained primarily with RXTE and a comprehens
ive test of the bulk-motion Comptonization (BMC) model for the high-soft st
ate continuum. The emergent spectra of over 30 separate measurements of the
GRO J1655-40, GRS 1915 + 105, GRS 1739-278, 4U 1630-47 XTE J1755-32, and E
XO 1846-031 X-ray sources are successfully fitted by the BMC model, which h
as been derived from basic physical principles in previous work. This in tu
rn provides direct physical insight into the innermost observable regions,
where matter impinging on the event horizon can effectively be directly vie
wed. The BMC model is characterized by three parameters: the disk color tem
perature, a geometric factor related to the illumination of the BH site by
the disk, and a spectral index related to the efficiency of the bulk-motion
upscattering. For the case of GRO J1655-40, where there are distance and m
ass determinations, a self-consistency check of the BMC model has been made
, in particular of the assumption regarding the dominance of gravitational
forces over the pressure forces within the inner few Schwarzschild radii. W
e have also examined the time behavior of these parameters, which can provi
de information on the source structure. Using our inferred model parameters
: color temperature, spectral index, and an absolute normalization, we pres
ent new, independently derived constraints on the BH mass, mass accretion r
ate, and the distance for the aforementioned sources. Also notable is the r
elationship between the color temperature and flux, which for CRO J1655-40
is entirely distinct from a simple T-4 dependence and strikingly consistent
with the disk model we have invoked: a standard Shakura-Sunyaev disk with
the modification to the electron scattering. This provides insight into the
origin of the seed soft photons and allows us to impose an important estim
ation of the hardening parameter, T-h, which is the ratio of the color temp
erature to the effective temperature: we find T-h similar or equal to 12.6,
higher than previous estimates used in the literature.