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Astron. Astrophys. 340, 447-456 (1998)

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1. Introduction

The discovery of an absorption line with redshift [FORMULA] in the optical afterglow of the gamma ray burst (GRB) of 8 May, 1997 has now decisively shown that atleast some of these events lie at cosmological distances (Djorgovski et al. 1997, Metzger et al. 1997). The observed fluence of [FORMULA] ergs cm-2 in the (20 keV- 1 MeV) band (Kouveliotiou et al. 1997), suggests an energy release of [FORMULA] ergs in soft gamma rays alone, where [FORMULA] is the solid angle of the beam. Further, the discovery of a redshift as high as [FORMULA] (Kulkarni et al. 1998) for the highly luminous event [FORMULA] implies a value of [FORMULA]. Taken together, they confirm the view that most of the classical GRB sources indeed lie at cosmological distances and are accompanied by an amount of energy emission (in soft gamma rays alone) which could be as large as 2-3 orders of magnitude higher than what, so far, most of the existing models have attempted to explain, i.e., [FORMULA] erg. The objective of the present paper is to consolidate the existing view (Waxman, Kulkarni & Frail 1998, Kulkarni et al. 1998, Ramprakash et al. 1998) that the observed energy liberation in the soft gamma-band with such energy liberation is preceded by a larger energy release [FORMULA] in the form of a [FORMULA] fireball (FB). Then we would like to enhance another known point that it is extremely difficult to conceive of any central engine which can liberate the [FORMULA] fireball energy [FORMULA] by a direct electromagnetic process. Therefore, as suggested by most of the original cosmological GRB models, this FB is most likely preceded by an even much more energetic [FORMULA] burst.

We develop this paper initially around the observations of GRB970508, because though it is much less energetic than GRB971214, it is the only event for which radio afterglow studies have revealed that the associated blast wave remains relatistic several months after the main event (Frail et al. 1997, Waxman et al. 1998). This suggests that the original kinetic energy of the [FORMULA] FB could be considerably higher than [FORMULA]. If the radio observations could precisely fix the epoch when the blast wave becomes marginally relativistic with a bulk Lorentz factor (LF) [FORMULA], ([FORMULA]), it may be possible to to estimate the energy of the blast wave (at this epoch). The lab frame radius of the burst at this stage would be (Waxman 1997)

[EQUATION]

where c is the speed of the light and [FORMULA] is the lab frame transition time in months. If it is assumed that during this period the blastwave has been sweeping the interstellar medium (ISM) of the host galaxy having a number density of [FORMULA] in units of 1 proton cm-3 the terminal energy would be:

[EQUATION]

[EQUATION]

It is important here to note that the foregoing expression is actually highly sensitive to the precise value of a and [FORMULA]. And also one must add [FORMULA] and all other radiated forms of electromagnetic energy to the foregoing value of [FORMULA] in order to infer the original value of the energy of the [FORMULA] FB, [FORMULA], where [FORMULA]. Assuming that, for GRB970508, the blastwave was indeed found to have [FORMULA] at [FORMULA] (Waxman et al. 1998), we would have

[EQUATION]

showing that, it is possible that [FORMULA]. As the blastwave gets dergraded to non-relativistic regime, there may be a rather sudden change in the (absolute) value of the exponet of the synchrotron spectrum ([FORMULA]). Obervational determination of such a fiducial point alone would not be sufficient to fix the precise value of [FORMULA] and what may be required is a detailed pattern on the evolution of [FORMULA] preceding this epoch. Obviously, one needs to estimate the value of [FORMULA] too. We do not know whether radio observations have actually yielded such detailed information.

The radio observations of GRB970508, have however clearly indicated that the blastwave evolution is of adiabatic nature. Then, in principle, it is possible to fix the value of [FORMULA] in terms of a simple model which involve the magnetic field equipartition parameter, [FORMULA], and electron-proton energy equipartition parameter, [FORMULA]. Since there is no theory to independently estimate [FORMULA] and [FORMULA] (which could be slowly evolving), we feel, it is really not possible to theoretically predict the value of [FORMULA] even if such models as such are quite satisfactory. On the other hand, we feel, it would be more desirable to fix the value of [FORMULA] by means of painstaking study of the evolution of [FORMULA], and this input should, in turn be used to estimate the values of [FORMULA] and [FORMULA] subject to the uncertainty about the value of [FORMULA]. Probably, by an iterative scheme involving appropriate theoretical models one may try to obtain more reliable value for all the relevant quantities.

Further, if, as suggested by the radio observations, if [FORMULA] (Waxman et al. 1998), we would finally have have

[EQUATION]

The radio observation for GRB970508 might be consistent with a value of [FORMULA] or even higher, and therefore, even if the value of [FORMULA] turns out to be considerably smaller than unity, it is possible that [FORMULA] erg.

It could be so, because, if we assume a value of [FORMULA] for GRB971214 too, the value of [FORMULA] in this case would be [FORMULA] erg. This burst being four times longer than GRB970508, it is likely that a substantial portion of [FORMULA] is already spent in producing the main burst so that the eventual value of [FORMULA] erg. We will see below that any reasonable extension of the direct electromagnetic modes of energy extraction is unlikely to yield this huge value of [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998
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