Scaling Laws in High-Energy Inverse Compton Scattering. II. Effect of
  Bulk Motions
  We study the inverse Compton scattering of the CMB photons off high-energy
nonthermal electrons. We extend the formalism obtained by the previous paper to
the case where the electrons have non-zero bulk motions with respect to the CMB
frame. Assuming the power-law electron distribution, we find the same scaling
law for the probability distribution function P_{1,K}(s) as P_{1}(s) which
corresponds to the zero bulk motions, where the peak height and peak position
depend only on the power-index parameter. We solved the rate equation
analytically. It is found that the spectral intensity function also has the
same scaling law. The effect of the bulk motions to the spectral intensity
function is found to be small. The present study will be applicable to the
analysis of the X-ray and gamma-ray emission models from various astrophysical
objects with non-zero bulk motions such as radio galaxies and astrophysical
jets.
