Practical flux-prescriptions for gamma-ray burst afterglows, from early to late times

TL;DR

This paper provides analytic flux prescriptions for gamma-ray burst afterglows across all dynamical phases, enabling accurate model fitting to observational data for spherical outflows in various media.

Contribution

The authors develop generalized, analytic flux formulas based on hydrodynamic simulations that apply to any observer time and dynamical phase of spherical outflows producing synchrotron radiation.

Findings

Approximate flux prescriptions achieve ~10% accuracy.

The formulas are applicable from early to late afterglow times.

A software tool for fitting observational data is provided.

Abstract

We present analytic flux prescriptions for broadband spectra of self-absorbed and optically thin synchrotron radiation from gamma-ray burst afterglows, based on one-dimensional relativistic hydrodynamic simulations. By treating the evolution of critical spectrum parameters as a power-law break between the ultrarelativistic and non-relativistic asymptotic solutions, we generalize the prescriptions to any observer time. Our aim is to provide a set of formulas that constitutes a useful tool for accurate fitting of model-parameters to observational data, regardless of the dynamical phase of the outflow. The applicability range is not confined to gamma-ray burst afterglows, but includes all spherical outflows (also jets before the jet-break) that produce synchrotron radiation as they adiabatically decelerate in a cold, power-law medium. We test the accuracy of the prescriptions and show that numerical evidence suggests that typical relative errors in the derivation of physical quantities are about 10 per cent. A software implementation of the presented flux prescriptions combined with a fitting code is freely available on request and on-line. Together they can be used in order to directly fit model parameters to data.