A comprehensive study of high-energy gamma-ray and radio emission from Cyg X-3

We study high-energy $\gamma$-rays observed from Cyg X-3 by the Fermi Large Area Telescope and the 15-GHz emission observed by the Ryle Telescope and the Arcminute Microkelvin Imager. We determine the $\gamma$-ray spectrum averaged over strong flares much more accurately than before, and find it well modelled by Compton scattering of stellar radiation by relativistic electrons with the power law index of $\simeq$3.5 and a low-energy cutoff at the Lorentz factor of $\sim\!10^3$. We find a weaker spectrum in the soft spectral state, but only upper limits in the hard and intermediate states. We measure strong orbital modulation during the flaring state, well modelled by anisotropic Compton scattering by jet relativistic electrons. We measure weaker orbital modulation of the 15 GHz radio emission, which is well modelled by free-free absorption by the stellar wind. We find the peak of the power spectrum of the radio emission is at a period shorter by 20 s than the orbital one, which can be due to a beat of the orbital modulation with a retrograde jet precession at a period of $\simeq$170 d. A definite evidence for the jet precession is provided by a strong dependence of the amplitude and phase of the orbital modulation on the precession phase. We then study cross-correlations between radio, $\gamma$-ray and X-ray emissions. We find no measurable delay of the radio emission with respect to $\gamma$-rays, but find a radio lag of $\sim$50 d with respect to the soft X-rays in the soft state.