4 Discussion

 

If we make the assumption that the OT emission is due to synchrotron radiation from electrons with a power law energy distribution (with index p), one expects a relation between p, the spectral slope $\beta$, and the decay constant $\alpha$ (Sari et al. 1998). One must distinguish two cases: (i) both the peak frequency $\nu_{\rm m}$ and the cooling frequency $\nu_{\rm c}$ are below the optical/IR waveband. Then $p = (-4\alpha +2)/3 = 2.81 \pm 0.16$ and $\beta = -p/2 = -1.41 \pm 0.08$, (ii) $\nu_{\rm m}$ has passed the optical/IR waveband, but $\nu_{\rm c}$ has not yet. In that case $p = (-4\alpha +3)/3 = 3.15 \pm 0.16$ and $\beta = -(p-1)/2 = -1.07 \pm 0.08$. In both cases the expected value of $\beta$ is inconsistent with the observed $\beta = -2.71 \pm 0.12$. Following Ramaprakash et al. (1998) we assume that the discrepancy is caused by host galaxy extinction. To determine the host galaxy absorption we first blueshifted the OT flux distribution to the host galaxy rest frame (using z=0.966 determined by Djorgovski et al. 1998), and then applied an extinction correction using the Galactic extinction curve of Cardelli et al. (1989), to obtain the expected spectral slope $\beta$. For epoch t₁ (July 4.4 UT), we obtain $A_V = 1.15 \pm 0.13$ and $A_V = 1.45 \pm 0.13$ for the cases (i) and (ii), respectively (see Fig. 2).

  

Figure 2: Broad-band spectrum of GRB980703 at July 4.4 UT (i.e., at t1 in Fig. 1). The open symbols are the R, I and H OT fluxes (interpolated to July 4.4, corrected for Galactic foreground absorption and the host galaxy flux) and the MECS (2-10 keV) de-absorbed flux. The filled symbols are obtained by invoking an interstellar extinction, AV, to force the slope of the data points to take on the two possible theoretical spectral slopes. The two slopes $\beta$ and their $1\sigma$ errors are indicated by the solid and dotted lines

In case (i) we find that an extrapolation of the optical flux distribution to higher frequencies predicts an X-ray flux that is significantly below the observed value, whereas in case (ii) the extrapolated and observed values are in excellent agreement. The mismatch in case (i) is into a direction that cannot be interpreted in terms of evidence for a cooling break between the optical and X-ray wavebands. When we include the X-ray data point in the fit to obtain a more accurate determination of A_V, we find $A_V=1.50 \pm 0.11$,and $\beta = -1.013 \pm 0.016$. We estimate the (2$\sigma$) lower limit to the cooling frequency to be $\nu_{\rm c}\gt 1.3\ 10^{17}$ Hz ($\nu_{\rm c}\gt.5$ keV).

We performed the same analysis for the other epoch (t₄) with X-ray data. At this epoch, the X-ray upper limit does not allow us to discriminate between the two cases. However, we can still estimate a lower limit to the cooling break from its time dependence: $\nu_{\rm c}\propto t^{-1/2}$, which would allow the break to drop to $\nu_{\rm c} \gt 6.3\ 10^{16}$ Hz only, between epoch t₁ and t₄. On the basis of our analysis we conclude that there is no strong evidence for a cooling break between the optical/IR and the 2-10 keV passband before 1998 July 8.4 UT. This conclusion is at variance with the inference of Bloom et al. (1998). For the latter epoch we obtain $A_V = 0.86 \pm 0.25$ and $\beta = -0.90 \pm 0.06$, after inclusion of the X-ray point. On the basis of this analysis we conclude that there is no evidence for a cooling break between the optical/IR and the 2-10 keV passband before 1998 July 8.8 UT. This conclusion is at variance with that of Bloom et al. (1998).

Following the analysis of Wijers & Galama (1998) we have determined the following intrinsic fireball properties: (i) the energy of the blast wave per unit solid angle: ${\cal E}\gt 5\ 10^{52}$ erg/(4$\pi$ sterad), (ii) the ambient density: n > 1.1 nucleons cm^-3, (iii) the percentage of the nucleon energy density in electrons: $\epsilon_{\rm e}\gt.13$, and (iv) in the magnetic field: $\epsilon_{B}<6 \ 10^{-5}$. The very low energy in the magnetic field, $\epsilon_B$, is a natural reflection of the high frequency of the cooling break $\nu_{\rm c}$ (see Vreeswijk et al. 1998).