Astronomy & Astrophysics

Table 1: Overview of the shell properties (densities $\rho _1$ and $\rho _2$ , Lorentz factors $\Gamma _1$ and $\Gamma _2$ , and inertial masses ${\cal {M}}_1$ and ${\cal M}_2$ ) of the seven 1D models. The initial thickness of the shells is 10¹⁴ cm, their volume is V, and their initial separation is D₀ = 10¹⁴ cm. The density of the external medium $\rho _{\rm ext} = 10^{-23}$ g cm^-3, and its Lorentz factor $\Gamma _{\rm ext} = 2.9$ . Initially $p/\rho c^2 = 10^{-4}$ everywhere. The parameters of the type-E shock acceleration model (see MAMB04 for details) are: $\alpha _{\rm e} = 10^{-2}$ , $\gamma _{\rm min} = 30$ , $\eta = 7$ $\times$ 10³. The last two columns give the Lorentz factor of the reverse ( $\Gamma _{\rm b}^{\rm sim}$ ) and forward ( $\Gamma _{\rm f}^{\rm sim}$ ) shocks, computed from the hydrodynamic simulations.
Table 2: Maximum conversion efficiency $\epsilon _{\rm max}$ , final conversion efficiency $\epsilon _{\rm fin}$ , and theoretically predicted conversion efficiency $\epsilon _{\rm pred}$ (see Eq. (1)) for the seven simulated models.
Table 3: Results of the fit of the normalized analytic model to the soft (0.1-1 keV) light curves of all simulated models. $\gamma _{\rm b}^{\rm sim}$ is the ratio $\Gamma _{\rm b}^{\rm sim}/\Gamma _{\rm f}^{\rm sim}$ computed from the models (see Table 1). The rest of the columns provide the other parameters obtained by fitting the normalized analytic model.