3.6.2. Comptonized Thermal Radiation

Photospheric (thermal) emission is inherent to the "fireball" model as, following the initial explosion, the plasma is optically thick, and photons cannot escape. Rather, they are coupled to the expanding gas, converting their internal energy to kinetic energy of the expanding gas. Only when the gas sufficiently expands does the optical depth decrease such that the photons escape. It is therefore of no surprise that the very first cosmological GRB models considered photospheric emission as a leading radiative process [81,86,87,189]. However, the fact that the prompt spectra appears non-thermal has led to focus on other broad-band models, in particular synchrotron.

Renewed interest in this model resumed in the early 2000s, with the realization that the synchrotron model appears too broad to explain the steep low energy spectral slope (the 'synchrotron line of death') [190]. Several authors considered a possible contribution from photospheric photons to the observed spectra [27,82,90,91,191,192]. It was realized that the observed spectrum of photons originating from the photosphere did not necessarily resemble a "Planck" function, due to two complementary effects. The first is possibly sub-photospheric energy dissipation, e.g., by lateral shock waves at the boundary between the relativistic jet and collapsing star, or reconnection of magnetic field lines, which heats the electrons in the plasma [158,161,193,194]. The dissipation heats the electrons, which then serve as seeds for inverse-Compton scattering. When such events occur below the photosphere, the original 'Planck' spectrum can be heavily modified, and the result depends on the details of the energy exchange between the particles and photon fields; this is demonstrated in Figure 4.

A second, independent effect is the aberration of light, which is essentially the relativistic version of the well-known limb darkening effect from solar observations. Due to the probabilistic nature of the scattering process, the photosphere is in fact 'vague', namely

the last scattering location of photons can occur in various spatial locations (as opposed to a single surface) [83,92,93,95,195,196]. This location is angle-dependent: at high angles, it occurs, on the average, at larger radii than at angles < 1/Γ (the jet Lorentz factor). In a spherical explosion, this aberration leads to a modification (mainly) of the Rayleigh–Jeans part of the spectrum. However, the jets are not spherical, but have some lateral shape (angle-dependent Lorentz factor). In this case this effect becomes very pronounced and affects both the low as well as the high energy spectral slopes making both of them shallower than the naively expected Rayleigh–Jeans shape [95,197,198], although steeper than the expected from synchrotron radiation, making the spectral slopes consistent with the data [36,164,199,200].

An interesting version of the photospheric model is the 'back scattering' dominated model [201,202]. In this model, the jet drills a funnel through the stellar envelope, and accelerates a 'cork' made of stellar material ahead of it. The photons originate from *e* ± pair annihilation close to the central engine, across the virtually empty jet before being back-scattered from the cork material ahead of them (if the cork does not disintegrate too rapidly). Although in the cork frame they are scattered backward, they will be detected by an observed located off axis, due to the relativistic angle change between the cork and observer's frame. It was recently demonstrated [203,204] that the resulting spectra in this setup is in excellent agreement with the observed, both at low and high energy. Furthermore, this model naturally explained the observed peak energy—total energy relation (known as "Amati" correlation; [205]) without the need to invoke any additional assumption.

**Figure 4.** Left: time averaged broadband spectra expected following kinetic energy dissipation at various optical depths. For low optical depth, the two low energy bumps are due to synchrotron emission and the original thermal component, and the high energy bumps are due to inverse Compton. At high optical depth, *τ* ≥ 100, a Wien peak is formed at 10 keV and is blue-shifted to the MeV range by the bulk Lorentz factor of ∼100 expected in GRBs. In the intermediate regime, 0.1 . *τ* . 100, a flat energy spectrum above the thermal peak is obtained by multiple Compton scatterings. Figure taken from [194]. ©AAS. Reproduced with permission. Right: spectral decomposition of GRB 090902B (taken 9.6–13.0 s after the GBM trigger) enables clear identification of the physical origin of the emission. The dash-dotted (red) curve shows the spectrum that would have been obtained if synchrotron radiation was the only source of emission. The dashed (green) curve shows the resulting spectrum from synchrotron and synchrotron self-Compton SSC, and the solid (blue) curve shows the spectrum with the full radiative ingredients (synchrotron, SSC, the MeV thermal peak, and Comptonization of the thermal photons). From [206]. Reprinted (and modified) permission of Oxford University Press on behalf of the Royal Astronomical Society.
