A systematic description of shocks in gamma-ray bursts - I. Formulation

Abstract

Since the suggestion of relativistic shocks as the origin of gamma-ray bursts (GRBs) in the early 1990s, the mathematical formulation of this process has stayed at a phenomenological level. One of the reasons for the slow development of theoretical works has been the simple power-law behaviour of the afterglows hours or days after the prompt gamma-ray emission. It was believed that they could be explained with these formulations. Nowadays, with the launch of the Swift satellite and implementation of robotic ground follow-ups, GRBs and their afterglow can be observed at multi-wavelengths from a few tens of seconds after trigger onwards. These observations have led to the discovery of features unexplainable by the simple formulation of the shocks and emission processes used up to now. Some of these features can be inherent in the nature and activities of the GRBs' central engines which are not yet well understood. On the other hand, the devil is in the detail and others may be explained with a more detailed formulation of these phenomena and without ad hoc addition of new processes. Such a formulation is the goal of this work. We present a consistent formulation of the kinematics and dynamics of the collision between two spherical relativistic shells, their energy dissipation and their coalescence. It can be applied to both internal and external shocks. Notably, we propose two phenomenological models for the evolution of the emitting region during the collision. One of these models is more suitable for the prompt/internal shocks and late external shocks, and the other for the afterglow/external collisions as well as the onset of internal shocks. We calculate a number of observables such as flux, lag between energy bands and hardness ratios. One of our aims has been a formulation complex enough to include the essential processes, but simple enough such that the data can be directly compared with the theory to extract the value and evolution of physical quantities. To accomplish this goal, we also suggest a procedure for extracting parameters of the model from data. In a companion paper, we numerically calculate the evolution of some simulated models and compare their features with the properties of the observed GRBs.

Binary Neutron Star (BNS) Merger: What We Learned from Relativistic Ejecta of GW/GRB 170817A

“…Observations of thousands of gamma-ray bursts and their afterglows by Swift, Fermi, Konus-wind, and other high energy satellites and ground based robotic telescopes have demonstrated that the main component in the prompt gamma-rays and their afterglows in lower energies is synchrotron emission generated in relativistic or mildly relativistic shocks. In this section we first briefly review a phenomenological shock and synchrotron emission formalism developed in [126,127]. Then, we use it to analyse both prompt gamma-ray and afterglows of GW/GRB 170817A.…”

“…The phenomenological model of [126,127] assumes that GRB emissions are synchrotron/self-Compton produced by accelerated charged leptons in a dynamically active region in the head front -wake -of shocks between density shells inside a relativistic jet for prompt and with surrounding material for afterglows in lower energies. In addition to the magnetic field generated by Fermi processes in the active region, an external magnetic field precessing with respect to the jet axis may contribute in the production of synchrotron emission.…”

“…Originally, the goal of the shock formalism developed in [126,127] was modelling prompt and early afterglow emissions, which are presumably generated by a fast and compact ejecta. For this reason, the model assumes uniform properties for the matter in the colliding shells and treats their evolution self-similarly.…”

“…‹ A dash as value for a parameter presents one of the following cases: it is irrelevant for the model; it is evolved from its initial value according to an evolution equations described in [126,127]; or it is kept constant during all regimes.…”

“…Then, in Sec. 3 we use a phenomenological model of relativistic shocks and synchrotron/self-Compton emission [126,127] (reviewed in [128]) to analyze both prompt gamma-ray and afterglows of this GRB. Interpretation of models and what they teach us about ejecta from the merger and its environment are discussed in Sec.…”