Pure and loaded fireballs in SGR giant flares

On December 27, 2004, a giant flare from SGR 1806$-$20 was detected on earth. Its thermal spectrum and temperature suggest that the flare resulted from an energy release of about $10^{47}$ erg/sec close to the surface of a neutron star in the form of radiation and/or pairs. This plasma expanded under its own pressure producing a fireball and the observed gamma-rays escaped once the fireball became optically thin. The giant flare was followed by a bright radio afterglow, with an observable extended size, implying an energetic relativistic outflow. We revisit here the evolution of relativistic fireballs and we calculate the Lorentz factor and energy remaining in relativistic outflow once the radiation escapes. We show that pairs that arise naturally in a pure pairs-radiation fireball do not carry enough energy to account for the observed afterglow. We consider various alternatives and we show that if the relativistic outflow that causes the afterglow is related directly to the prompt flare, then the initial fireball must be loaded by baryons or Poynting flux. While we focus on parameters applicable to the giant flare and the radio afterglow of SGR 1806$-$20 the calculations presented here might be also applicable to GRBs

GRB990123, The Optical Flash and The Fireball Model

We compare the ongoing observations of the remarkable burst GRB990123, the mother of all bursts, with the predictions of the afterglow theory. We show that the observations agree with the recent prediction that a reverse shock propagating into the ejecta would produce a very strong prompt optical flash. This reverse shock has also produced the 8.46GHz radio signal, observed after one day. The forward shock, which propagates into the ISM is the origin of the classical afterglow. It has produced the prompt X-ray signal as well as the late optical and IR emission. It would most likely produce a radio emission within the next few weeks. The observations suggest that the initial Lorentz factor of the ejecta was $\sim 200$. Within factors of order unity, this crude model explains all current observations of GRB990123.Comment: 14 pages including 2 figure

The Expected Duration of Gamma-Ray Bursts in the Impulsive Hydrodynamic Models

Depending upon the various models and assumptions, the existing literature on Gamma Ray Bursts (GRBs) mentions that the gross theoretical value of the duration of the burst in the hydrodynamical models is tau~r^2/(eta^2 c), where r is the radius at which the blastwave associated with the fireball (FB) becomes radiative and sufficiently strong. Here eta = E/Mc^2, c is the speed of light, E is initial lab frame energy of the FB, and M is the baryonic mass of the same (Rees and Meszaros 1992). However, within the same basic framework, some authors (like Katz and Piran) have given tau ~ r^2 /(eta c). We intend to remove this confusion by considering this problem at a level deeper than what has been considered so far. Our analysis shows that none of the previously quoted expressions are exactly correct and in case the FB is produced impulsively and the radiative processes responsible for the generation of the GRB are sufficiently fast, its expected duration would be tau ~ar^2/(eta^2 c), where a~O(10^1). We further discuss the probable change, if any, of this expression, in case the FB propagates in an anisotropic fashion. We also discuss some associated points in the context of the Meszaros and Rees scenario.Comment: 21 pages, LATEX (AAMS4.STY -enclosed), 1 ps. Fig. Accepted in Astrophysical Journa

Radiative Efficiencies of Continuously Powered Blast Waves

We use general arguments to show that a continuously powered radiative blast wave can behave self similarly if the energy injection and radiation mechanisms are self similar. In that case, the power-law indices of the blast wave evolution are set by only one of the two constituent physical mechanisms. If the luminosity of the energy source drops fast enough, the radiation mechanisms set the power-law indices, otherwise, they are set by the behavior of the energy source itself. We obtain self similar solutions for the Newtonian and the ultra-relativistic limits. Both limits behave self similarly if we assume that the central source supplies energy in the form of a hot wind, and that the radiative mechanism is the semi-radiative mechanism of Cohen, Piran & Sari (1998). We calculate the instantaneous radiative efficiencies for both limits and find that a relativistic blast wave has a higher efficiency than a Newtonian one. The instantaneous radiative efficiency depends strongly on the hydrodynamics and cannot be approximated by an estimate of local microscopic radiative efficiencies, since a fraction of the injected energy is deposited in shocked matter. These solutions can be used to calculate Gamma Ray Bursts afterglows, for cases in which the energy is not supplied instantaneously.Comment: 28 LaTeX pages, including 9 figures and 3 table