The gamma-ray emitting region of the jet in Cyg X-3

We study models of the ?-ray emission of Cyg X-3 observed by Fermi. We calculate the average X-ray spectrum during the ?-ray active periods. Then, we calculate spectra from Compton scattering of a photon beam into a given direction by isotropic relativistic electrons with a power-law distribution, both based on the KleinNishina cross-section and in the Thomson limit. Applying the results to scattering of stellar blackbody radiation in the inner jet of Cyg X-3, we find that a low-energy break in the electron distribution at a Lorentz factor of similar to 300103 is required by the shape of the observed X-ray/?-ray spectrum in order to avoid overproducing the observed X-ray flux. The electrons giving rise to the observed ?-rays are efficiently cooled by Compton scattering, and the power-law index of the acceleration process is ?2.53. The bulk Lorentz factor of the jet and the kinetic power before the dissipation region depend on the fraction of the dissipation power supplied to the electrons; if it is ?1/2, the Lorentz factor is similar to 2.5, and the kinetic power is similar to 1038 erg s-1, which represents a firm lower limit on the jet power, and is comparable to the bolometric luminosity of Cyg X-3. Most of the power supplied to the electrons is radiated. The broad-band spectrum constrains the synchrotron and self-Compton emission from the ?-ray emitting electrons, which requires the magnetic field to be relatively weak, with the magnetic energy density ? a few times 10-3 of that in the electrons. The actual value of the magnetic field strength can be inferred from a future simultaneous measurement of the infrared and ?-ray fluxes.