RXTE observation of Cygnus X-1 - I. Spectral analysis

We present the results of the analysis of the broad-band spectrum of Cygnus X-1 from 3.0 to 200 keV, using data from a 10-ks observation by the Rossi X-ray Timing Explorer (RXTE). The spectrum can be well described phenomenologically by an exponentially cut-off power law with a photon index Gamma = 1.45(-0.02)(+0.01) (a value considerably harder than is typically found), e-folding energy E-f = 162(-8)(+9) keV, plus a deviation from a power law that formally can be modelled as a thermal blackbody with temperature kT(BB) = 1.2(-0.1)(+0.0) keV, Although the 3-30 keV portion of the spectrum can be fitted with a reflected power law with Gamma = 1.81 +/- 0.01 and covering fraction f = 0.35 +/- 0.02, the quality of the fit is significantly reduced when the HEXTE data in the 30-100 keV range are included, as there is no observed softening in the power law within this energy range. As a physical description of this system, we apply the accretion disc corona models of Dove, Wilms & Begelman, in which the temperature of the corona is determined self-consistently. A spherical corona with a total optical depth tau = 1.6 +/- 0.1 and an average temperature kT(C) = 87 +/- 5 keV, surrounded by an exterior cold disc, does provide a good description of the data (chi(red)(2) = 1.55). These models deviate from the data by up to 7 per cent in the 5-10 keV range, and we discuss possible reasons for these discrepancies. However, considering how successfully the spherical corona reproduces the 10-200 keV data, such 'photon-starved' coronal geometries seem very promising for explaining the accretion processes of Cygnus X-1.