Reverse Shock: Forward vs Reverse Decomposition¶

This example demonstrates the reverse shock capability by decomposing the afterglow into forward and reverse shock contributions using the Jet class directly.

Background¶

When a GRB jet decelerates into the circumburst medium, two shocks form:

Forward shock (FS) --- propagates into the ambient medium, producing the standard long-lived afterglow
Reverse shock (RS) --- propagates back into the ejecta, producing a bright, short-lived flash

The reverse shock emission peaks early (minutes to hours) and fades rapidly, while the forward shock dominates at late times. The relative strength depends on the ejecta magnetization (\(\sigma\)): unmagnetized ejecta (\(\sigma = 0\)) produce a strong RS; highly magnetized ejecta suppress the RS.

Key references:

Sari & Piran 1999, ApJ, 520, 641 --- reverse shock theory
Kobayashi 2000, ApJ, 545, 807 --- reverse shock emission model
Zhang, Kobayashi & Meszaros 2003, ApJ, 595, 950 --- magnetized reverse shocks

Using the Jet class directly¶

To access the individual forward and reverse shock components, we use the Jet class rather than the shortcut functions:

import numpy as np
from blastwave import Jet, TopHat, ForwardJetRes

DAY = 86400.0
theta_c = 0.1

jet = Jet(
    TopHat(theta_c, 1e53, lf0=300.0),
    0.0,                    # nwind (no wind)
    1.0,                    # nism
    tmin=1.0,
    tmax=500 * DAY,
    grid=ForwardJetRes(theta_c, 129),
    tail=True,
    spread=True,
    cal_level=1,
    include_reverse_shock=True,
    sigma=0.0,              # unmagnetized ejecta → strong RS
    eps_e_rs=0.1,
    eps_b_rs=0.01,
    p_rs=2.2,
)

Key parameters:

include_reverse_shock=True --- enables RS dynamics and emission
sigma=0.0 --- unmagnetized ejecta, producing the strongest possible reverse shock
eps_e_rs, eps_b_rs, p_rs --- microphysical parameters for the RS (can differ from the FS)

Computing forward and reverse components¶

The Jet class provides three flux methods:

P = {
    "Eiso":    1e53,
    "lf":      300.0,
    "theta_c": theta_c,
    "A":       0.0,
    "n0":      1.0,
    "eps_e":   0.1,
    "eps_b":   0.01,
    "p":       2.3,
    "theta_v": 0.0,
    "d":       1000.0,
    "z":       0.2,
}

t = np.geomspace(10.0, 300.0 * DAY, 200)
nu_radio = 3e9 * np.ones_like(t)

# Total (FS + RS)
F_total   = jet.FluxDensity(t, nu_radio, P)

# Forward shock only
F_forward = jet.FluxDensity_forward(t, nu_radio, P)

# Reverse shock only
F_reverse = jet.FluxDensity_reverse(t, nu_radio, P)

Plotting¶

import matplotlib.pyplot as plt

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5.5))
t_days = t / DAY

# Radio 3 GHz
ax1.plot(t_days, F_total, '-', color='black', lw=2.5, label='Total')
ax1.plot(t_days, F_forward, '--', color='C0', lw=2, label='Forward shock')
ax1.plot(t_days, F_reverse, '--', color='C3', lw=2, label='Reverse shock')
ax1.set_xscale('log'); ax1.set_yscale('log')
ax1.set_xlabel('Time (days)'); ax1.set_ylabel('Flux density (mJy)')
ax1.set_title('Radio 3 GHz'); ax1.legend()

# Optical R-band
nu_opt = 4.56e14 * np.ones_like(t)
F_opt_total   = jet.FluxDensity(t, nu_opt, P)
F_opt_forward = jet.FluxDensity_forward(t, nu_opt, P)
F_opt_reverse = jet.FluxDensity_reverse(t, nu_opt, P)

ax2.plot(t_days, F_opt_total, '-', color='black', lw=2.5, label='Total')
ax2.plot(t_days, F_opt_forward, '--', color='C0', lw=2, label='Forward shock')
ax2.plot(t_days, F_opt_reverse, '--', color='C3', lw=2, label='Reverse shock')
ax2.set_xscale('log'); ax2.set_yscale('log')
ax2.set_xlabel('Time (days)'); ax2.set_ylabel('Flux density (mJy)')
ax2.set_title('Optical R-band'); ax2.legend()

fig.suptitle('Forward vs Reverse Shock Decomposition', fontweight='bold')
plt.tight_layout()
plt.savefig('reverse_shock.png', dpi=150)

Reverse shock decomposition

Discussion¶

Radio (3 GHz): The reverse shock produces a bright early flash that peaks within the first day, then fades as the RS-heated electrons cool. The forward shock rises more gradually and dominates after \(\sim 1\) day. At late times (\(\gtrsim 10\) days) the light curve is entirely FS-dominated.

Optical (R-band): The RS optical flash is even more pronounced relative to the FS at early times, since the RS electrons are initially very energetic. The optical RS fades faster than the radio RS due to stronger synchrotron cooling at higher frequencies.

Magnetization effects

Setting sigma > 0 introduces ejecta magnetization, which suppresses the reverse shock. For \(\sigma \gtrsim 1\), the RS becomes negligible and the afterglow is entirely FS-dominated. Try varying sigma from 0 to 10 to see this transition.

RS microphysical parameters

The RS microphysical parameters (eps_e_rs, eps_b_rs, p_rs) are independent of the FS values. In practice, the RS magnetic field may be stronger than the FS field (higher eps_b_rs) if the ejecta carry ordered magnetic fields, while eps_e_rs is often assumed similar to eps_e.

Full script¶

The complete analysis script is at examples/reverse_shock.py. To regenerate the plot:

python examples/reverse_shock.py