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

K. Leventis; H. J. van Eerten; Z. Meliani; R. A. M. J. Wijers

doi:10.1111/j.1365-2966.2012.21994.x

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

¹Astronomical Institute ‘Anton Pannekoek’, PO box 94248, 1090, SJ Amsterdam, the Netherlands
²Department of Physics, Center for Cosmology and Particle Physics, New York University, New York, NY, 10003, USA
³Laboratoire Univers et Théories, Observatoire de Paris, Université Paris Diderot, UMR 8102 du CNRS, 92190, Meudon, France

↵*E-mail: k.leventis{at}uva.nl

In original form 2012 April 18.
Received 2012 August 15.
Accepted 2012 August 24.
First published online January 28, 2013.

Abstract

We present analytic flux prescriptions for broad-band spectra of self-absorbed and optically thin synchrotron radiation from gamma-ray burst afterglows, based on 1D 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 online.¹ Together they can be used in order to directly fit model parameters to data.