The X-ray spectrum of the prominent galactic black hole candidate Cyg
X-1 has historically been modeled by thermal Comptonization or Compton
reflection models. However, data from instruments covering different
energy ranges have produced different model parameters, indicating tha
t broad band spectra should be used to constrain the models. To find a
model which can overcome this problem, we have collected broad band d
ata from 1 keV to 1 MeV. We describe this spectrum by a new self-consi
stent accretion disk corona model where the corona is situated above a
cold disk. The coronal compactness is l(C) = 0.75 and the optical dep
th of the corona is tau(e) = 0.18, resulting in an equilibrium tempera
ture of approximate to 150 keV. We also report the tentative detection
of a S K alpha- and a Si K alpha-fluorescent line, both being much we
aker than the lines expected from our models.