We report on the results of a broad band (0.1-200 keV) spectral study of Cyg X-2 using two BeppoSAX observations taken in 1996 and 1997, respectively, for a total effective on-source time of ~ 100 ks. The color-color (CD) and hardness-intensity (HID) diagrams show that the source was in the horizontal branch (HB) and normal branch (NB) during the 1996 and 1997 observation, respectively. Five spectra were selected around different positions of the source in the CD/HID, two in the HB and three in the NB. These spectra are fit to a model consisting of a disk blackbody, a Comptonization component, and two Gaussian emission lines at ~ 1 keV and ~ 6.6 keV, respectively. The addition of a hard power-law tail with photon index ~ 2, contributing ~ 1.5% of the source luminosity, improves the fit of the spectra in the HB. We interpret the soft component as the emission from the inner accretion disk, with inner temperature, k Tin, varying between ~ 0.8 and ~ 1.7 keV and inner radius, Rin, varying between ~ 26 and ~ 11 km (assuming an inclination angle of the system of 60o). The Comptonization component is probably emitted by hot plasma (electron temperature k Te varying between ~ 3 and ~ 20 keV, optical depth tau ~ 11-0.4, seed-photon temperature kTW ~ 1-2.4 keV) surrounding the NS. The changes in the parameters of the blackbody component indicate that the inner rim of the disk approaches the NS surface when the source moves from the HB to the NB, i.e. as the (inferred) mass accretion rate increases. The parameters of the Comptonized component also change significantly when the source moves from the HB to the NB. We discuss possible scenarios which can explain these changes
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