Fluid dynamics of relativistic blast waves
TL;DR: In this paper, a fluid dynamical treatment of an ultra-relativistic spherical blast wave enclosed by a strong shock is presented, and a simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius.
Abstract: A fluid dynamical treatment of an ultra‐relativistic spherical blast wave enclosed by a strong shock is presented. A simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and this is generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius. Radiative shocks, in which the escaping photons carry away momentum as well as energy, are also discussed. Formulas that interpolate between the non‐ and ultra‐relativistic limits are proposed.
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TL;DR: In this paper, the broadband spectrum and corresponding light curve of synchrotron radiation from a power-law distribution of electrons in an expanding relativistic shock were calculated for the gamma-ray burst afterglow.
Abstract: The recently discovered gamma-ray burst afterglow is believed to be described reasonably well by synchrotron emission from a decelerating relativistic shell that collides with an external medium. To compare theoretical models with afterglow observations, we calculate here the broadband spectrum and corresponding light curve of synchrotron radiation from a power-law distribution of electrons in an expanding relativistic shock. Both the spectrum and the light curve consist of several power-law segments with related indices. The light curve is constructed under two limiting models for the hydrodynamic evolution of the shock: fully adiabatic and fully radiative. We give explicit relations between the spectral index and the temporal power-law index. Future observations should be able to distinguish between the possible behaviors and determine the type of solution.
2,295 citations
Cites background or methods from "Fluid dynamics of relativistic blas..."
...Behind the shock, the particle density and the energy density are given by 4γn and 4γ2nmpc 2, respectively, where γ is the Lorentz factor of the shocked fluid (Blandford & McKee 1976)....
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...In the adiabatic case, the energy E of the spherical shock is constant and is given by E = 16πγ2R3nmpc 2/17 (Blandford & McKee 1976, Sari 1997)....
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...Here L = [17M/(16πmpn)]1/3 (Blandford & McKee 1976, Vietri 1996, Katz & Piran 1997) is the radius at which the mass swept up from the external medium equals the initial mass M of the ejecta (We used 17/16 instead of 3/4 in order to be compatible with the adiabatic expression and to enable a smooth…...
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TL;DR: A review of the current theoretical understanding of the physical processes believed to take place in GRB's can be found in this article, where the authors focus on the afterglow itself, the jet break in the light curve, and the optical flash that accompanies the GRB.
Abstract: Gamma-ray bursts (GRB's), short and intense pulses of low-energy $\ensuremath{\gamma}$ rays, have fascinated astronomers and astrophysicists since their unexpected discovery in the late sixties. During the last decade, several space missions---BATSE (Burst and Transient Source Experiment) on the Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer)---together with ground-based optical, infrared, and radio observatories have revolutionized our understanding of GRB's, showing that they are cosmological, that they are accompanied by long-lasting afterglows, and that they are associated with core-collapse supernovae. At the same time a theoretical understanding has emerged in the form of the fireball internal-external shocks model. According to this model GRB's are produced when the kinetic energy of an ultrarelativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circumburst matter. This model has had numerous successful predictions, like the predictions of the afterglow itself, of jet breaks in the afterglow light curve, and of the optical flash that accompanies the GRB's. This review focuses on the current theoretical understanding of the physical processes believed to take place in GRB's.
1,800 citations
TL;DR: In this article, it was shown that the inner engine that accelerates the relativistic flow is hidden from direct observations and therefore it is difficult to infer its structure directly from current observations.
1,405 citations
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TL;DR: In this article, the interplay between these observations and theoretical models of the prompt gamma-ray burst and its afterglow is reviewed, and a model of the burst's origin and mechanism is proposed.
Abstract: Gamma-ray bursts are the most luminous explosions in the Universe, and their origin and mechanism are the focus of intense research and debate. More than three decades after their discovery, and after pioneering breakthroughs from space and ground experiments, their study is entering a new phase with the recently launched Swift satellite. The interplay between these observations and theoretical models of the prompt gamma-ray burst and its afterglow is reviewed.
1,294 citations
TL;DR: The formation of the first stars and quasars marks the transformation of the universe from its smooth initial state to its clumpy current state as discussed by the authors, and the study of high-redshift sources is likely to attract major attention in observational and theoretical cosmology over the next decade.
1,214 citations
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TL;DR: This paper has now been declassified, and though it has been superseded by more complete calculations, it seems appropriate to publish it as it was first written, without alteration, except for the omission of a few lines, the addition of this summary, and a comparison with some more recent experimental work as discussed by the authors.
Abstract: This paper was written early in 1941 and circulated to the Civil Defence Research Committee of the Ministry of Home Security in June of that year The present writer had been told that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission—the name atomic bomb had not then been used—and the work here described represents his first attempt to form an idea of what mechanical effects might be expected if such an explosion could occur In the then common explosive bomb mechanical effects were produced by the sudden generation of a large amount of gas at a high temperature in a confined space The practical question which required an answer was: Would similar effects be produced if energy could be released in a highly concentrated form unaccompanied by the generation of gas? This paper has now been declassified, and though it has been superseded by more complete calculations, it seems appropriate to publish it as it was first written, without alteration, except for the omission of a few lines, the addition of this summary, and a comparison with some more recent experimental work, so that the writings of later workers in this field may be appreciated An ideal problem is here discussed A finite amount of energy is suddenly released in an infinitely concentrated form The motion and pressure of the surrounding air is calculated It is found that a spherical shock wave is propagated outwards whose radius R is related to the time t since the explosion started by the equation R = S (γ)tt E tρ-t, where ρo is the atmospheric density, E is the energy released and S (γ) a calculated function of of γ, the ratio of the specific heats of air
1,281 citations
585 citations
TL;DR: In this paper, the relativistic form of the Rankine-Hugoniot equations are derived and it is shown that as a consequence of the inequality mentioned earlier that the shock wave velocity is always less than that of light in vacuum for sufficiently strong shocks.
Abstract: In Part I of this paper the stress energy tensor and the mean velocity vector of a simple gas are expressed in terms of the Maxwell-Boltzman distribution function. The rest density ${\ensuremath{\rho}}^{0}$, pressure, $p$, and internal energy per unit rest mass $\ensuremath{\epsilon}$ are defined in terms of invariants formed from these tensor quantities. It is shown that $\ensuremath{\epsilon}$ cannot be an arbitrary function of $p$ and ${\ensuremath{\rho}}^{0}$ but must satisfy a certain inequality. Thus $\ensuremath{\epsilon}=\frac{(\frac{1}{\ensuremath{\gamma}\ensuremath{-}1})p}{{\ensuremath{\rho}}^{0}}$ for $\ensuremath{\gamma}g\frac{5}{3}$ is impossible. It is known that if $\ensuremath{\epsilon}$ is given by this relation and $\ensuremath{\gamma}g2$, then sound velocity in the medium may be greater than that of light in vacuum. This difficulty is now removed by the inequality mentioned above. In Part II of this paper the relativistic form of the Rankine-Hugoniot equations are derived and it is shown that as a consequence of the inequality mentioned earlier that the shock wave velocity is always less than that of light in vacuum for sufficiently strong shocks.
416 citations