Periodic long-term X-ray and radio variability of Cygnus X-1
  We present a comprehensive analysis of long-term periodic variability of Cyg X-1 using the method of multiharmonic analysis of variance (mhAoV) applied to available monitoring data since 1969, in X-rays from Vela 5B, Ariel 5, Ginga, CGRO and RXTE satellites and in radio from the Ryle and Green Bank telescopes. We confirm a number of previously obtained results, and, for the first time, find an orbital modulation at 15 GHz in the soft state and show the detailed non-sinusoidal shape of that modulation in the hard state of both the 15-GHz emission and the X-rays from the RXTE/ASM. We find the CGRO/BATSE data are consistent with the presence of a weak orbital modulation, in agreement with its theoretical modelling as due to Compton scattering in the companion wind. We then confirm the presence of a ~150-d superorbital period in all of the data since ~1976, finding it in particular for the first time in the Ariel 5 data. Those data sets, covering >65 superorbital cycles, show a remarkable constancy of both the period and the phase. On the other hand, we confirm the presence of a ~290-d periodicity in the 1969-1979 Vela 5B data, indicating a switch from that period to its first harmonic at some time <~1980. We find the superorbital modulation is compatible with accretion disc precession. Finally, we find a significant modulation in the RXTE/ASM data at a period of 5.82-d, which corresponds to the beat between the orbital and superorbital modulations provided the latter is prograde. 
Pawel Lachowicz, Andrzej A. Zdziarski, Alex Schwarzenberg-Czerny, Guy   G. Pooley and Shunji Kitamoto