The X-ray spectral-timing contribution of the stellar wind in the hard state of Cyg X-1

The clumpy stellar wind from the companion star in high-mass X-ray binaries causes variable, partial absorption of the emission from the X-ray source. We studied XMM-Newton observations from a 7.22 d long monitoring campaign, in order to constrain the effects of the stellar wind on the short-time-scale X-ray spectral-timing properties of Cygnus X-1. We find these properties to change significantly in the presence of the wind. In particular, the longest sampled time-scales (corresponding to temporal frequencies of ν ~ 0.1-1 Hz) reveal an enhancement of the fractional variability power, while on the shortest sampled time-scales (ν ~ 1-10 Hz), the variability is suppressed. In addition, we observe a reduction (by up to a factor of ~ 1.8) of the otherwise high coherence between soft and hard band light curves, as well as of the amplitude of the hard X-ray lags intrinsic to the X-ray continuum. The observed increase of low-frequency variability power can be explained in terms of variations of the wind column density as a consequence of motions of the intervening clumps. In this scenario (and assuming a terminal velocity of $v_{\infty }=2400\, {\rm km\ s^{-1}}$), we obtain an estimate of l ~ 0.5-1.5 × 10^-4R_* for the average radial size of a clump. On the other hand, we suggest the behaviour at high frequencies to be due to scattering in an optically thicker medium, possibly formed by collision of the stellar wind with the edge of the disc.