2007MNRAS.375..793S

We present results of our detailed theoretical study of the observed orbital modulation of the radio emission in Cygnus X-1 (Cyg X-1). The modulation occurs due to free-free absorption in the wind from the companion star varying with the orbital phase, and our results put strong constraints on the spatial distribution of the jet radio emission at the frequencies of 2-15 GHz. A crucial role in enhancing the asymmetry of the wind absorption suffered by the jet emission is played by the irradiation by X-rays emitted in the vicinity of the black hole. This increases the wind temperature by more than an order of magnitude with respect to that of the wind of an isolated supergiant. The observed phase lags of the minima of the radio emission with respect to the spectroscopic zero phase strongly imply that the bulk of the mass of the jet is non-relativistic (∼ 5x10⁸ cm/s) within the jet core. The jet can, however, become relativistic outside the core. Also, the jet can have a two-component structure, being slow on the outside and fast inside, in which case its synchrotron-emitting part may be relativistic already in the core. We also consider the observed superorbital modulation of the radio emission (with the period of ∼150 d) and find that it can be explained by a jet precession both causing variable wind absorption and changing the jet Doppler factor. Finally, we consider the case of Cyg X-3, and show that its lack of observable orbital radio modulation (in spite of strong modulation of X-rays) is explained by that system being both much more compact and much more luminous than Cyg X-1.