Analytic Expressions for the Surface Brightness Profile of GRB Afterglow Images

Abstract

The exact profile of a gamma-ray burst (GRB) afterglow image on the plane of the sky can provide important constraints on the underlying physics. In particular, it can test whether the magnetic field in the emitting shocked external medium decreases significantly with the distance behind the shock front, or remains roughly constant. Moreover, it enables more accurate measurements of the afterglow image size and the expected scintillation properties. In this work analytic expressions are derived for the afterglow image in power law segments (PLSs) of the afterglow synchrotron spectrum in which the emission originates from a very thin layer just behind the shock, while simple semi-analytic expressions are derived for the remaining PLSs in which the emission arises from the bulk of the shocked fluid. In all cases the expressions are for a general power law external density profile, and are convenient to use in afterglow studies.

arXiv comment5 pages, 2 figures

References in corpus (21)

• The Shape of Spectral Breaks in GRB Afterglows
• Images and Spectra From the Interior of a Relativistic Fireball
• Implications of the radio afterglow from the gamma-ray burst of May 8, 1997
• Angular size and emission time scales of relativistic fireballs
• The Angular Size and Proper Motion of the Afterglow of GRB 030329
• Synchrotron Self Absorption in GRB Afterglow
• The Observed Size and Shape of GRB Afterglow
• Opacity Build-up in Impulsive Relativistic Sources
• Smooth Light Curves from a Bumpy Ride: Relativistic Blast Wave Encounters a Density Jump
• Rings in Fireball Afterglows
• The Synchrotron Spectrum of Fast Cooling Electrons Revisited
• Resolving Gamma-Ray Burst 000301C with a Gravitational Microlens
• Afterglow Light Curves from Impulsive Relativistic Jets with an Unconventional Structure
• Stirring the Embers: High Sensitivity VLBI Observations of GRB030329
• Gamma-Ray Burst Afterglow emission with a decaying magnetic field
• Late Time Observations of the Afterglow and Environment of GRB 030329
• Implications of the Measured Image Size for the Radio Afterglow of GRB 030329
• The apparent size of GRB afterglows as a test of the Fireball model
• Chromatic Signatures in the Microlensing of GRB Afterglows
• Microlensing and the Surface Brightness Profile of the Afterglow Image of GRB 000301C
• Microlensing of collimated Gamma-Ray Burst afterglows

Cited by in corpus (8)

• Afterglow Imaging and Polarization of Misaligned Structured GRB Jets and Cocoons: Breaking the Degeneracy in GRB 170817A
• Simulations of GRB Jets in a Stratified External Medium: Dynamics, Afterglow Lightcurves, Jet Breaks and Radio Calorimetry
• Off-axis afterglow light curves and images from 2D hydrodynamic simulations of double-sided GRB jets in a stratified external medium
• GRBs from Magnetic Reconnection: Variability and Robustness of Lightcurves
• Modeling the Linear Polarization of GRB Afterglows Across the Electromagnetic Spectrum
• The expansion of the GRB 221009A afterglow
• Afterglow Linear Polarization Signatures from Steep GRB Jets: Implications for Orphan Afterglows
• The luminosity evolution over the EQuiTemporal Surfaces in the prompt emission of Gamma-Ray Bursts