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

We study models of the gamma-ray emission of Cyg X-3 observed by Fermi. We calculate the average X-ray spectrum during the gamma-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 Klein-Nishina 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 ~ 300--1000 is required by the shape of the observed X-ray/gamma-ray spectrum in order to avoid overproducing the observed X-ray flux. The electrons giving rise to the observed \g-rays are efficiently cooled by Compton scattering, and the power-law index of the acceleration process is ~ 2.5--3. 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 ~ 2.5, and the kinetic power is ~ 10^38 erg/s, 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 gamma-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 IR and gamma-ray fluxes.