SHOT MODEL PARAMETERS FOR CYGNUS-X-1 THROUGH PHASE PORTRAIT FITTING

We have developed shot models for systems having a approximately 1/f power density spectrum by utilizing a distribution of shot durations. Parameters of the distribution are determined by fitting the power spectrum either with analytic forms for the spectrum of a shot model with a given shot profile, or with the spectrum derived from numerical realizations of trial shot models. The shot fraction is specified by fitting the phase portrait, which is a plot of intensity at a given time versus intensity at a delayed time and in principle is sensitive to different shot profiles. We have applied these techniques extensively to the X-ray variability of Cygnus X-1, using a HEAO 1 A-2 and an EXOSAT ME observation. We have found that the power spectra suggest models having characteristic shot durations lasting from milliseconds to a few seconds, while the phase portrait fits give shot fractions of approximately 50%. Best fits to the portraits are obtained if we let the amplitude of the shot be a power-law function of the duration of the shot. These fits prefer shots having a symmetric exponential rise and decay. We interpret our result in terms of a distribution of magnetic flares in the accretion disk.