3 Results and discussion

As the instantaneous observed spectrum results from sampling of the contributions from different parts of the flow emitted at different times in the flow's evolution its shape may be different from that of the intrinsic one. For example, the expansion of the emitting region (or, alternatively, the increase of the ${\rm e}^-$number density) makes the comoving self-absorption frequency increase with time which, in turn, results in spectral slopes of the observed spectra that are flatter by 0.5 (i.e., the portion of slope 2 (2.5) in spectral flux of the co-moving spectrum is mapped to a slope 1.5 (2) part in the observed spectrum). None of the scenarios examined here can cause the low energy photon number slope to exceed the "death line'' limit.

Consider first the simplest approach where the ${\rm e}^-$s are injected instantaneously and fill up the whole volume. For the self-absorption frequency to fall in the BATSE range and the peak ${\rm e}^-$ s' radiation be self-absorbed, the physical parameters have to take values (in cgs units) in the following range: $10^2 \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}B \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}10^{3.5}$ and $10^{15} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}n_{\rm e} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}10^{18.5}$ for $\gamma_{\rm m,o} \simeq 10^3$, while $n_{\rm e}$ can be low ($10^{10} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}n_{\rm e} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}10^{15}$)provided $10^9 \lower.5ex\hbox{$\; \buildrel \gt \over \sim \;$}B \lower.5ex\hbox{$\; \buildrel \gt \over \sim \;$}10^{7}$ for $\gamma_{\rm m,o} \simeq 2$. In all cases, at least one of the parameters has to take values that are substantially higher than the equipartition ones, in the framework of dissipative flows.

In Fig. 1, I present a sequence of time resolved spectra for a flow of L₅₂=1, $t_{\rm var}= 0.1$ s, $\Theta_{\rm o}=0^\circ$, $n_{\rm e}$ and B equal to the equipartition values, $\gamma_{\rm m,o} =3000$, and $t_{\rm inj}=t_{\rm var}/10$. This set of parameters will favor high values of the self-absorption frequency for a relativistic flow that develops internal shocks. The lower panel shows the instantaneous spectra in the fluid frame in $F_{\nu}$ vs. $\nu$.During injection, there is brightening and progression of the optically thick part to harder frequencies while, after that, rapid softening takes place. The upper panel shows the observed BATSE spectrum. The pulse is detectable for 60 ms during which time it is dimming always retaining the typical sy slopes.

One way to circumvent the problem of the high values of the slopes is to increase the ${\rm e}^-$ content of the flow. This might happen if the flow has a high compactness and produces a large density of pairs that live long enough to contribute to the sy emission and turn it optically thick in the BATSE range. [] have stressed the importance of the pairs in internal shocks, although they do not calculate any effect these might have on the optical depth. To assess the importance of pairs in the flow, I include, in the lower panel of Fig. 1, the spectrum of the first snapshot as this is modified by the pairs that result from the absorption of the IC photons. At this time, all the hard photons above 1 MeV are absorbed (which is consistent with the limits on the hard GRB counterparts) and some $10^{13}~{\rm cm}^{-3}$ pairs with $\gamma \lower.5ex\hbox{$\; \buildrel \gt \over \sim \;$}1$ and a power law distribution fill up the region resulting into brightening and steepening of the soft part of the sy component. Their annihilation timescale is of the order of s and they will cool mainly through IC. I stress that this is preliminary only, and one has to include the pairs in the emitting population in a self consistent way. Therefore, while sy is responsible for the BATSE component, in flows with high $n_{\rm e}$ and thus bright IC component, pairs might be able to provide the required opacity for the sy component to become self-absorbed in a transient fashion. For high pair production rates, the self-absorption peak can fall in the BATSE window.

  

Figure 1: Spectral evolution series. a) Broad band comoving spectra. b) Time resolved (sampled over $\Delta T_{\rm det}=10$ ms every 10 ms) spectra in the BATSE window

Acknowledgements

I thank Ph. Papadopoulos, A. Celotti and P. Mészáros for useful comments. This work was supported by the Italian MURST .