2.3.2. Inverse-Compton Emission

If the energy density of the (isotropic) radiation field (*U*0 *<sup>γ</sup>* = 3*Lγ*/16*πR* 2Γ 2 *c*, where *L<sup>γ</sup>* is the isotropic-equivalent luminosity) advected with the flow is much larger than that of the magnetic field (*U*0 *<sup>B</sup>* = *B* <sup>0</sup>2/8*π*), relativistic particles with LF *γ<sup>e</sup>* cool predominantly by inverse-Compton upscattering softer seed photons, with energy *E* 0 *s* , to higher energies with a mean value (for an isotropic seed photon field in the comoving frame), *E* 0 = (4/3)*γ* 2 *e E* 0 *s* . When the Thomson optical depth of the flow is *τ<sup>T</sup>* > 1, these seed photons undergo multiple Compton scatterings, where the process is usually referred to as *Comptonization*, until they are able to stream freely when *τ<sup>T</sup>* < 1. Comptonization has been argued as a promising alternative to optically thin synchrotron emission where it is able to explain a broader range of low-energy spectral slopes, provide a characteristic energy scale for the peak of the emission, and yield narrower spectral peaks [99,113] It is the main radiation mechanism in a general class of models known as *photospheric emission* models in which the outflow is heated across the photosphere due to some internal dissipation.

At the base of the flow, where *τ<sup>T</sup>* 1, the radiation field is thermalized and assumes a Planck spectrum. If the outflow remains non-dissipative the Planck spectrum is simply advected with the flow, cooled due to adiabatic expansion, and then released at the photosphere [33,34]. However, only a few GRBs show a clearly thermally dominated narrow spectral peak [114], whereas most have a broadened non-thermal spectrum with a low-energy photon index (*α*ph < 1) softer than that obtained for the Planck spectrum (*α*ph = 1). In many cases, a sub-dominant thermal component in addition to the usual Band function has been identified [115,116]. These observations imply that photospheric emission plays an important role [117], but the pure thermal spectrum must be modified by dissipation across the photosphere [54,95,118–120]. Several theoretical works tried to understand the thermalization efficiency of different radiative process, e.g., Bremmstrahlung, cyclo-synchrotron, and double Compton, below the photosphere to explain the location of the spectral peak and the origin of the low-energy spectral slope e.g., [121–123].

While sub-photospheric dissipation and Comptonization is able to yield the typical low-energy slope, further dissipation near and above the photosphere is needed to generate the high-energy spectrum above the thermal spectral peak. This can be achieved by inverse-Compton scattering of the thermal peak photons by mildly relativistic electrons [24,100,124–127]. If the flow is uniform, the net polarization of the Comptonized spectrum is negligible due to random orientations of the polarization vector at each point of the flow, which, upon averaging over the visible part, adds up to zero polarization. Alternatively, if the flow has an angular structure, particularly in the bulk-Γ profile, then net polarization as large as Π . 20% can be obtained [24,57].
