[Paper Review] Modelling of Long-Term Afterglow Counterparts to Gravitational Wave Events: The Full View of GRB 170817A

Geoffrey Ryan, Hendrik van Eerten+4 more|arXiv (Cornell University)|Oct 3, 2023

Gamma-ray bursts and supernovae6 citations

TL;DR

This paper enhances the afterglowpy modeling framework to accurately simulate long-term afterglow emission from off-axis short gamma-ray bursts, incorporating trans-relativistic electron populations, Poissonian statistics for faint X-ray sources, and astrometric centroid motion from VLBI. Applied to GRB 170817A, the model finds only weak evidence (≲2σ) for a late-time X-ray component, favoring a narrow jet viewed at ∼20° with kinetic energy ∼10⁵² erg and width 2°–3°.

ABSTRACT

The arrival of gravitational wave astronomy and a growing number of time-domain focused observatories are set to lead to a increasing number of detections of short gamma-ray bursts (GRBs) launched with a moderate inclination to Earth. Being nearby events, these are also prime candidates for very long-term follow-up campaigns and very-long-baseline interferometry (VLBI), which has implications for multi-messenger modelling, data analysis, and statistical inference methods applied to these sources. Here we present a comprehensive modelling update that directly incorporates into afterglowpy astrometric observations of the GRB position, Poissonian statistics for faint sources, and modelling of a trans-relativistic population of electrons. We use the revolutionary event GW170817 to demonstrate the impact of these extensions both for the best-fit physics parameters and model selection methods that assess the statistical significance of additional late-time emission components. By including in our analysis the latest Chandra X-ray observations of GRB 170817A, we find only weak evidence (less than two sigma) for a new emission component at late times, which makes for a slightly more natural fit to the centroid evolution and prediction for the external medium density.

Motivation & Objective

• To improve long-term afterglow modeling for off-axis short GRBs detected via gravitational wave-EM counterparts.
• To incorporate trans-relativistic electron dynamics in synchrotron emission calculations beyond the ultra-relativistic regime.
• To enhance statistical inference by applying Poissonian likelihoods to faint X-ray observations.
• To integrate astrometric centroid proper motion from VLBI as a key geometric constraint on viewing angle.
• To assess the statistical significance of potential late-time emission components in multi-wavelength data.

Proposed method

• Incorporates the Sironi & Giannios (2013) deep Newtonian regime for synchrotron emission from trans-relativistic electrons.
• Adapts the afterglowpy code to include Poissonian likelihoods for low-count X-ray observations.
• Integrates VLBI-measured afterglow centroid positions and proper motion to constrain viewing angle and jet structure.
• Uses Gaussian jet profiles with energy and Lorentz factor decreasing with off-axis angle.
• Applies Bayesian inference with emcee to fit multi-wavelength light curves and centroid motion simultaneously.
• Performs model selection using Bayesian information criteria to test for additional late-time emission components.

Experimental results

Research questions

• RQ1 Does the inclusion of trans-relativistic electron dynamics significantly alter afterglow flux and spectral evolution predictions for off-axis GRBs?
• RQ2 Can Poissonian statistics improve flux estimation and model confidence intervals for faint late-time X-ray observations?
• RQ3 To what extent does afterglow centroid proper motion constrain the viewing angle and jet structure in off-axis GRBs?
• RQ4 Is there statistically significant evidence for a new emission component in the late-time X-ray light curve of GRB 170817A?
• RQ5 How do joint constraints from GWs, EM light curves, and astrometry improve the accuracy of jet geometry and energy estimates?

Key findings

• The model with a Gaussian jet and no additional component fits the full dataset (including latest Chandra X-ray data) best, with a viewing angle of ∼20° and jet width of 2°–3°.
• The total kinetic energy of the jet is constrained to ∼10⁵² erg, consistent with typical short GRBs.
• Only weak evidence (≲2σ) supports an additional X-ray component at late times, indicating no strong statistical preference for a new emission mechanism.
• Proper motion measurements from VLBI are highly sensitive to viewing angle, especially when θobs ≳20°, making them critical for geometric inference.
• The deep Newtonian regime significantly alters flux evolution and peak frequency at late times, improving accuracy in the non-relativistic phase.
• The updated modeling framework, including centroid motion and Poisson statistics, will be released in afterglowpy v0.8.0.