GRB Afterglow — Relativistic Jet Break

Jet Geometry

Jet half-opening angle θ_j 6.0°

Initial Lorentz factor Γ₀ 200

Electron energy index p 2.30

Observer Time

log₁₀(t / t_dec) -1.00

Live Readouts

BEFORE JET BREAK

Bulk Lorentz factor Γ

200.0

Beaming half-angle 1/Γ

0.29°

Afterglow flux F / F(t_dec)

1.00

Jet break at log₁₀(t/t_dec)

2.10

How it works

A GRB fireball launches a narrow, ultra-relativistic jet that sweeps up the surrounding medium and decelerates. As long as the jet's Doppler beaming cone (half-angle ~1/Γ) is narrower than its true physical opening angle θ_j, a distant on-axis observer cannot tell the outflow is collimated — it radiates like an equivalent spherical fireball. Once the jet slows enough that 1/Γ widens past θ_j, the observer suddenly "sees" the missing sideways emission and edge effects (lateral spreading) kick in: the light curve steepens sharply. This is the achromatic jet break — the standard method used to infer true GRB jet opening angles and beaming-corrected energies (Rhoads 1999; Sari, Piran & Halpern 1999).

Deceleration (ISM, adiabatic):  Γ(t) = Γ0            for t ≤ t_dec (coasting)
                                 Γ(t) = Γ0 (t/t_dec)^(-3/8)   for t > t_dec

Beaming angle:   θ_beam(t) = 1 / Γ(t)

Jet-break time:  θ_beam(t_break) = θ_j
                 t_break / t_dec = (Γ0 · θ_j)^(8/3)

Light curve (slow-cooling, ISM, on-axis observer):
  F(t) ∝ t^(-α1),  α1 = 3(p-1)/4        for t_dec < t < t_break
  F(t) ∝ t^(-α2),  α2 = p                for t > t_break

θ_j — the jet's true half-opening angle; narrower jets break earlier for the same Γ0.
Γ0 — Lorentz factor at the end of coasting; larger Γ0 means a narrower initial beaming cone, delaying the break.
p — power-law index of the shocked electron energy distribution; sets both the pre- and post-break decay slopes.
Time slider / Play — scrubs or animates log₁₀(t/t_dec); the 3D beaming cone widens live and the light-curve marker tracks the kink at t_break.

Jet boundary (θ_j, fixed) Beaming cone (1/Γ, live) Shocked material — beamed toward observer

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