tokens: photons via the inverse Compton process makes it necessary to simultaneously compute the photon distribution . It becomes time dependent and is integrated according toSince all radiation processes are calculated in the isotropic approximation, i.e., from , and no external photon fields are considered, the gradient of the photon distribution is very small. Hence, in this case photon propagation can be neglected. The synchrotron power spectrumis computed in the Melrose approximation (Brown et al. 1983 ): Employing the same approximation, the synchrotron self-absorption coefficientis calculated (Ginzburg Syrovatskii 1965 ). As pointed out earlier, the inverse Compton process takes place in the Klein–Nishina regime. The resulting losses and gains are obtained fromThe catastrophic loss is parameterized by the escape timescale and depends on the radius of the cell. The total flux emerging from all spatial cells is calculated similar to the model of Blandford Konigl ( 1979 ). The integrated flux per cell can be calculated viaThe observed frequency depends on the Doppler factor and the redshift . The flux from one cell is proportional to the photon density and the surface of the cylindrical cell , where is the cell size along z . The speed of light c reflects the escape timescale given above. In the time domain, light-travel times have to be accounted for. The total flux from the source is then the sum over the fluxes F i from all zn cells at the time when they were causally connected to the reference point. This point is chosen to be the end point at , i.e., closest to the observer:The time delay t i can be calculated from the additional distance along the line of sight:where is the angle between the z -axis and the line of sight. For time-dependent simulations any time interval in the observer’s frame is boosted from the shock frame according to . 3. RESULTS In this section we will first present a classical SSC fit to the high-energy data of the observational campaign by Abdo et al. ( 2011a ). Based on the resulting fit, we argue that the artificial spatial boundary condition should and can be replaced by a specific morphology of the radial confinement behind the shock. 3.1. High-energy SSC Fit Similar to our previous work RS13 , the starting point is a classical SSC fit, meaning that the size of the emission region is a free parameter, shown as sim1 in Figure 2 . In addition to the parameters in Table 2 , the parameters r = 2.5, , an injection energy , and an isotropization timescale were used. These values were used for all simulations, except log2c. The fit was done “by eye,” as is common for complex radiation codes. Figure 2. Overall SEDs for various simulations and a detailed view of the radio band. sim1 was obtained with a variable box size z max , altering the resulting SED. Simulations log[1–3] were obtained with a fixed but large z max and show the effect of an increase in expansion speed. The peak in the optical is due to the host
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