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Astron. Astrophys. 344, L37-L40 (1999)

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3. Discussion and conclusion

We now check our model against the observed data. Here we assume a fixed opening jet angle and a minimum electron Lorentz factor, and the equipartition parameters [FORMULA] and [FORMULA] are referenced to unity.

For GRB970208, using the equation (9), at a time of [FORMULA], we obtain a frequency [FORMULA] Hz.

Substituting the same numbers into the equations for the flux (13), we have [FORMULA] [FORMULA] [FORMULA] [FORMULA] [FORMULA] [FORMULA] [FORMULA] [FORMULA], where [FORMULA].

Again using GRB970208 as reference, we obtain for the flux in the X-band at a frequency of [FORMULA] Hz and a time [FORMULA] s: [FORMULA] [FORMULA] [FORMULA] [FORMULA].

For the optical depth in the optical band we obtain [FORMULA] [FORMULA] [FORMULA] [FORMULA], hence, within our model the optical emission region is optically thin, except very early.

In our model, the condition [FORMULA] corresponds to the early phase, when [FORMULA] is actually in the gamma-ray regime. In this phase, the corresponding maximum flux in the observer frame is [FORMULA] [FORMULA]. This is derived from using all available energy in energetic electrons, and redistributing it into emission; photons are generated by various emission processes, including pion decay, upscattered by inverse Compton emission, and redistributed in photon energy by pair opacity (Rachen & Mészáros 1998). The integration of this flux in time from [FORMULA] s to 10 s gives a value of about [FORMULA] [FORMULA]. This we identify with the initial gamma-ray emission.

Concerning the variability at times when [FORMULA], we note that in observed jets, one often finds inhomogeneities on the scale of a few jet-diameters parallel to the axis, and down to some fraction of the diameter perpendicular to the axis. However, any variability derived from such inhomogeneities is smeared out by arrival time differences for the observer. Therefore, using the jet diameter as a reference scale, this smearing limits any temporal variability


Inhomogeneities on transverse scales smaller than the jet diameter can shorten this. This variability may explain the complex features of the optical rise in GRB970508 (Galama et al. 1998).

The way in which our model can reproduce the observed properties of GRBs depends strictly on two sets of parameters, one set which is verifiable, because it derives from known active binary stars, and a second set which characterizes the explosion. The explosion depends on the initial shock energy [FORMULA], and the equipartition parameter [FORMULA]. On the other hand, the binary set is composed of the mass loss rate [FORMULA] of the jet, the jet opening angle [FORMULA], the bulk velocity in the jet [FORMULA] and the equipartition parameter [FORMULA]. To produce shock waves and the observed emission in the jet, it is necessary that the initial amount of matter in the shock is comparable with the mass in the jet. This implies that the binary system necessary in our model has to have a super Eddington accretion rate to get the required mass loss rate. In our Galaxy, one such binary system is known, SS433 (Murata and Shibazaki, 1996), for which [FORMULA]. In our model, we have used the parameters characteristic of this system, implying that there are system like SS433 where the central object indeed is a neutron star.

In the context of the Falcke & Biermann jet-disk model, SS433 is a radio-weak jet-disk system, while here we have used their radio-loud model; but it has been noted that systems such as GRS1915+105 and perhaps also SS433 can switch from radio-weak to radio-loud in the terminology of Falcke & Biermann (1995, 1999). Considering that the jet ejection rate is bound to the disk accretion rate by the relation [FORMULA], we find that for an initial bulk Lorentz factor [FORMULA], the mass in the shock [FORMULA] is equal to the mass present in the jet. Therefore, SS433 might be a good candidate to explode as the next violent GRB in our Galaxy.

To summarize, our model can explain the initial gamma ray burst, the spectrum and temporal behaviour of the afterglows, the low baryon load, an optical rise, and do all this with a modest energy budget. Moreover, this GRB model is developed within an existing framework for galactic jet sources, using a set of well determined parameters.

Obviously, we have simplified in many places, using a naive version of shock acceleration, only strong shocks, a conical jet geometry, etc., but the good agreement with the data we obtain within our framework shows that more detailed calculations may be worthwhile.

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© European Southern Observatory (ESO) 1999

Online publication: March 18, 1999