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GRB 200826A: The Shortest Collapsar GRB

This example demonstrates FluxDensity_tophat for modeling a real GRB afterglow with an ISM density profile, using multi-wavelength data from the shortest-duration gamma-ray burst associated with a collapsar.

Background

GRB 200826A was a short-duration (\(T_{90} \sim 1\) s) gamma-ray burst at redshift \(z = 0.748\), discovered by Fermi-GBM on 2020 August 26. Despite its short duration, it was conclusively identified as a collapsar (massive star core collapse) through the detection of an associated supernova, making it the shortest collapsar GRB known.

Key references:

  • Ahumada et al. 2021, Nature Astronomy, 5, 917 (arXiv:2105.05067) --- Discovery and multi-wavelength modeling
  • Zhang et al. 2021, Nature Astronomy, 5, 911 --- Prompt emission analysis

Data

Multi-wavelength afterglow data from Ahumada+2021:

Band Instrument Frequency Detections
X-ray Swift XRT 1 keV 7 epochs (0.7--17 days)
g-band ZTF \(6.3 \times 10^{14}\) Hz 3 detections
r-band ZTF/LDT \(4.8 \times 10^{14}\) Hz 2 detections
i-band Gemini/GMOS \(3.9 \times 10^{14}\) Hz 1 detection (SN component)
Radio VLA 6 GHz \(6 \times 10^9\) Hz 1 detection at 2.3 days
Radio GMRT 1.3 GHz \(1.3 \times 10^9\) Hz 2 upper limits

Physical parameters

Best-fit afterglow parameters from Ahumada+2021 (tophat jet, ISM density):

Parameter Value Notes
\(E_\mathrm{K,iso}\) \(6.0 \times 10^{52}\) erg Isotropic kinetic energy
\(\Gamma_0\) 300 Initial Lorentz factor
\(\theta_c\) 0.24 rad (14 deg) Jet half-opening angle
\(n_0\) 0.055 cm⁻³ ISM number density
\(\varepsilon_e\) 0.42 Electron energy fraction
\(\varepsilon_B\) \(6.4 \times 10^{-5}\) Magnetic energy fraction
\(p\) 2.4 Electron spectral index
\(\theta_v\) 0.0 Viewing angle (on-axis)
\(z\) 0.748 Redshift

Note

The very low \(\varepsilon_B\) and high \(\varepsilon_e\) reflect the highly degenerate nature of afterglow fitting with sparse data. The electron spectral index \(p = 2.4\) is the best-constrained parameter.

Computing the model

import numpy as np
from blastwave import FluxDensity_tophat
from scipy.integrate import quad

DAY = 86400.0

# Cosmology
z = 0.748
def luminosity_distance(z, H0=70.0, Om=0.3):
    OL = 1.0 - Om
    c_km_s = 299792.458
    result, _ = quad(lambda zp: 1.0 / np.sqrt(Om * (1 + zp)**3 + OL), 0, z)
    return (c_km_s / H0) * (1 + z) * result

d_L = luminosity_distance(z)

P = dict(
    Eiso=6e52, lf=300, theta_c=0.24,
    n0=0.055, A=0.0,
    eps_e=0.42, eps_b=6.4e-5, p=2.4,
    theta_v=0.0, d=d_L, z=z,
)

t = np.geomspace(100, 200 * DAY, 300)

# Multi-band model
flux_xray = FluxDensity_tophat(t, 2.4e17, P, spread=True)   # 1 keV
flux_opt   = FluxDensity_tophat(t, 6.29e14, P, spread=True)  # g-band
flux_radio = FluxDensity_tophat(t, 6e9, P, spread=True)      # 6 GHz

Key choices:

  • TopHat jet --- standard GRB jet structure with sharp edges
  • ISM density (\(k = 0\)) --- constant-density circumburst medium
  • model="sync" (default) --- standard synchrotron radiation
  • spread=True --- lateral spreading enabled for jet break

Plotting

GRB 200826A multi-band afterglow

The model reproduces the multi-band afterglow evolution:

  • X-ray (1 keV): Power-law decay \(\propto t^{-0.9}\), consistent with slow cooling (\(\nu_m < \nu_X < \nu_c\)) in an ISM
  • Optical (g, r bands): Tracks the X-ray decay at early times (\(< 3\) days), with a similar temporal slope \(\alpha \approx -1.05\)
  • Radio (6 GHz): Single VLA detection at 2.3 days matches the model prediction
  • Late-time i-band excess: The Gemini i-band point at 28 days is significantly brighter than the afterglow model --- this is the associated supernova (SN), confirming the collapsar origin

Discussion

The shortest collapsar

GRB 200826A challenges the traditional duration-based classification of GRBs: its \(T_{90} \sim 1\) s places it firmly in the "short GRB" regime, yet the supernova association proves it originated from a massive star. This suggests that the central engine can produce arbitrarily short-duration jets even in collapsar events.

Microphysics

The best-fit parameters feature a very low magnetic energy fraction (\(\varepsilon_B \sim 10^{-5}\)) and high electron fraction (\(\varepsilon_e \sim 0.4\)). While these values are individually unusual, they are broadly consistent with the wide range observed in GRB afterglows and reflect the inherent degeneracies in afterglow fitting with limited multi-band coverage.

Full script

The complete analysis script is at examples/grb200826a.py. To regenerate the plot:

python examples/grb200826a.py