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The Energy Density of Soft Photons at the Jet Center: the Case with Velocity Structures

On the basis of observational facts and theoretical speculation, it has been suggested that bulk velocity structures along and perpendicular to the jet axis are present in relativistic jets. There are some clues that these velocity structures influence the energy density of seed photons from synchrotron emission. In this paper, we adopt a rigorous method to investigate the energy density in the case of continuous velocity structures. As shown by numerical results, the energy densities are similar in accelerating and stationary jets. However, in a decelerating jet or a transversely structured jet the energy density is much higher, sometimes reaching ~20-200 times the value estimated for a uniform blob. The emitting region that produces most of the observed radiation flux is determined by the location of the dissipation and the area in which the peak bulk Lorentz factor Γp appears. The inverse Compton radiation in the cases Γ0 ≤ Γp and Γc ≤ Γp is studied. We think that, in the comoving frame, the inverse Compton scattering process in a structured jet has properties similar to the external Compton (EC) model; i.e., soft photons are injected just from the slower, downstream part. In this regard, the EC models in which seed photons come from outside the jet are not necessary if the velocity structures exist in regions very close to the core and the structure index is suitable. In particular, the jet model in which the two kinds of velocity structures coexist can be applied to TeV blazars, large-scale X-ray jets, and possibly γ-ray bursts.