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The MeV spectral tail in Cyg X-1 and optically-thin emission of jets

We study the average X-ray and soft gamma-ray spectrum of Cyg X-1 in the hard spectral state, using data from INTEGRAL. We compare these results with those from CGRO, and find a good agreement. Confirming previous studies, we find the presence of a high-energy MeV tail beyond a thermal-Comptonization spectrum; however, the tail is much softer and weaker than that recently published by Laurent et al. In spite of this difference, the observed high-energy tail could still be due to the synchrotron emission of the jet of Cyg X-1, as claimed by Laurent et al. To test this possibility, we study optically-thin synchrotron and self-Compton emission from partially self-absorbed jets. We develop formalisms for calculating both emission of the jet base (which we define here as the region where the jet starts its emission) and emission of the entire jet. We require the emission to match that observed at the turnover energy. The optically thin emission is dominated by that from the jet base, and it has to become self-absorbed within it at the turnover frequency. We find this implies the magnetic field strength at the jet base of B_0 prop. to z_0^4, where z_0 is the distance of the base from the black-hole centre. The value of B_0 is then constrained from below by the condition that the self-Compton emission is below an upper limit in the GeV range, and from above by the condition that the Poynting flux does not exceed the jet kinetic power. This yields B_0 of the order of ~10^4 G and the location of the jet base at ~10^3 gravitational radii. Using our formalism, we find the MeV tail can be due to jet synchrotron emission, but this requires the electron acceleration at a rather hard power-law index, p~1.3-1.6. For acceleration indices of p> 2, the amplitude of the synchrotron component is much below that of MeV tail, and its origin is likely to be due to hybrid Comptonization in the accretion flow.