A Semi-analytic Formulation for Relativistic Blast Waves with a Long-lived Reverse Shock

• Published in: The Astrophysical journal Vol. 733; no. 2; pp. 86 - jQuery1323907967364='48'
• Main Author: Uhm, Z. Lucas
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2011; IOP
• Subjects: AFTERGLOW; Astronomy; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMIC GAMMA BURSTS; COSMIC RADIATION; Earth, ocean, space; EQUATIONS; EQUATIONS OF STATE; Exact sciences and technology; FLUID MECHANICS; HYDRODYNAMICS; IONIZING RADIATIONS; MECHANICS; PRIMARY COSMIC RADIATION; RADIATIONS; SHOCK WAVES; SIMULATION; gamma-ray burst: general; Relativistic shock wave; Cosmic gamma sources; Mechanical model; Digital simulation; Light curves; Relativistic hydrodynamics; Gamma ray burst; hydrodynamics; Shock waves; Afterglow; Equations of state; Dynamical evolution; Energy conservation; Dynamics; Modelling; Stratification
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1088/0004-637X/733/2/86

This paper performs a semi-analytic study of relativistic blast waves in the context of gamma-ray bursts. Although commonly used in a wide range of analytical and numerical studies, the equation of state (EOS) with a constant adiabatic index is a poor approximation for relativistic hydrodynamics. Adopting a more realistic EOS with a variable adiabatic index, we present a simple form of jump conditions for relativistic hydrodynamical shocks. Then we describe in detail our technique of modeling a very general class of GRB blast waves with a long-lived reverse shock. Our technique admits an arbitrary radial stratification of the ejecta and ambient medium. We use two different methods to find dynamics of the blast wave: (1) customary pressure balance across the blast wave and (2) the 'mechanical model.' Using a simple example model, we demonstrate that the two methods yield significantly different dynamical evolutions of the blast wave. We show that the pressure balance does not satisfy the energy conservation for an adiabatic blast wave while the mechanical model does. We also compare two sets of afterglow light curves obtained with the two different methods.