When ( 1/\Gamma \approx \theta_j ) (jet half-opening angle), light curve steepens: [ t_j \approx 1.2 , \textdays \left( \fracE_\gamma,\textiso10^53\text erg \right)^1/3 \left( \fracn_01 \text cm^-3 \right)^-1/3 \left( \frac\theta_j0.1 \right)^8/3 ] After jet break: [ F_\nu \propto t^-p \quad \text(ISM, \nu > \nu_c\text) ]
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Advanced Topics in Relativistic Outflows, Afterglow Modeling, and Observables