Temporal and spectral variations of the superposed shot as causes of powerspectral densities and hard S-ray time lags of Cygnus X-l

We examined the temporal and spectral variations of Cyg X-1 in the hard sta te by average shot properties obtained by superposing a number of large sho ts by aligning their peaks. The average shot shows an almost symmetric time profile and a softer energy spectrum than the average spectrum. The energy spectrum also exhibits rapid hardening around the peak intensity, followed by complex changes. Importantly, not only power spectral density (PSD) but also hard X-ray time lags (cross spectrum) of the average shot can give a good representation of those of the entire light curves (all the data) at f requencies below a few Hz. In other words, low-frequency parts of the PSD a nd time-lag diagrams simply reflect the temporal and spectral structures of such large shots. Higher frequency parts of the diagrams, in contrast, see m to be related to smaller time variations with shorter time constants. Our findings provide unprecedent, severe constraints on theoretical models for variability; namely, it is not enough to reproduce the observed PSDs and/o r time lags, since neither has relative phase information between different frequencies, but successful models should also account for the complex spe ctral variations during the shot as described above as well as the symmetri c shot profile. No models proposed so far can satisfy all these requirement s. The presence of at least two different timescales characterizing the sho t profile and the rapid hardening seemingly indicate two (or more) physical processes being involved, e.g., disturbance propagation and magnetic flare s.