Competition among the different timescales. Left panels: case of β_exp = 0.1. Right panels: case of β_exp = 0.001. The top row refers to the case of R₀ = 1 × 10¹⁵ cm, the middle row to the case of R₀ = 1 × 10¹⁵, and the bottom row to the case of R₀ = 1 × 10¹⁶ cm. The times are in the blob frame, and the total duration is such that R(t_stop) = 1000 R₀. The x axis reports on the bottom side the value of R(t)/R₀, whilst on the opposite side the corresponding value of ν_SSA(t)/ν_SSA(0) is reported, for the case of no particle escape. The orange shaded area represents the synchrotron cooling timescales, with the lower bound corresponding to the case of γ = 10 and B₀ = 1.0 G, and the upper bound corresponding to the case of γ = 10 and B₀ = 0.01 G. The red shaded area, represents the same trend for the case of γ = 1000. The blue line represents the adiabatic cooling time (Eq. (4)), the black red line represents the geometrical decay time (Eq. (12)), and the green line the light crossing time (R(t)/c).