Grb Physics For Competitions Vol 2 Pdf Upd Better

A classic competition trick: A GRB prompt phase ends, but hours later the radio afterglow peaks. Why? The reverse shock crossing time. Volume 2 gives the formula:

[ t_\textpeak, RS \approx 0.1 , \textday \left( \fracE_52n_0 \right)^1/3 \left( \frac\Gamma300 \right)^-8/3 ]

Where (E_52) is the isotropic energy in (10^52) ergs, (n_0) is the density in cm(^-3), and (\Gamma) is the bulk Lorentz factor. The "upd better" version adds a derivation of this in three lines – a miracle for timed exams. grb physics for competitions vol 2 pdf upd better

Given: Two GRB pulses, same (\Gamma), but magnetic field (B) differs by factor 10.
Find ratio of peak energies (E_p,1/E_p,2).

Solution:
(E_p \propto \Gamma^2 \gamma_m^2 B). But (\gamma_m \propto \varepsilon_e \times) shock jump → independent of (B) for fixed electrons.
So (E_p,1/E_p,2 = B_1/B_2 = 10). A classic competition trick: A GRB prompt phase

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