Photons' Scattering in Relativistic Plasma with Velocity Shear: Generation of High Energy Power-law Spectra

A high energy power law is a common feature in the spectra of many astrophysical objects. We show that the photons in an unmagnetized relativistic plasma composed of electrons and protons with a variable Lorentz factor (or a velocity shear) go through repeated scattering with electrons to gain energy. The escaped population of photons naturally produces a power-law-shaped spectrum making it a photon's analog to the conventional Fermi acceleration mechanism for charged particles. Thus, this mechanism provides a natural alternative to current explanations of high energy power-law spectra via synchrotron or thermal Comptonization. The model is applicable to any relativistic plasma beam with an arbitrary Lorentz factor profile. We implement the theory to the gamma-ray burst prompt phase and show that the obtained range of the photon indices is compatible with the observed values and the results of Monte Carlo simulations that we carry out independently. Therefore, the observed high energy spectral indices provide a unique indicator of the jet structure.