4 Physical parameters of GRB970508  

From the light curve behaviour and broad-band spectrum of GRB970508, we deduced the properties of the burst required to calculate the physical parameters of the afterglow; at $t=12.1\,$d after trigger, the break frequencies are $\mbox{$\nu_{\rm a}$}=2.5\ 10^9\mbox{\rm\thinspace Hz$^{}$}$,$\mbox{$\nu_{\rm m}$}=8.6\ 10^{10}\mbox{\rm\thinspace Hz$^{}$}$, and $\mbox{$\nu_{\rm c}$}=1.6\ 10^{14}\mbox{\rm\thinspace Hz$^{}$}$(Galama et al. 1998a). The peak flux is $F_{\mbox{$\nu_{\rm m}$}}=1.7$mJy and the electron index p=2.2. After the first 500s electrons no longer cooled efficiently and the afterglow must evolve adiabatically. We use a redshift of z=0.835 for GRB970508 (Bloom et al. 1998) and $H_0=70\mbox{\rm\thinspace km$^{}$}\mbox{\rm\thinspace s$^{-1}$}\mbox{\rm\thinspace Mpc$^{-1}$}$. Finally, we adopt X=0.7 for the composition of the ambient medium. Using further that x_2.2=0.580, $\phi_{2.2}=0.611$, we find

$$\begin{eqnarray} \mbox{${\cal E}_{52}$}= 3.5 && n = 0.03 \,\, {\rm cm}^{-3}\nonu... ...\\ \mbox{$\epsilon_{\rm e}$}= 0.12 && \mbox{$\epsilon_B$}= 0.09. \end{eqnarray}$$ (9)

  

Figure:1 The X-ray to radio spectrum of GRB 970508 on May 21.0 UT (12.1 days after the event) from Galama et al. (1998a). Indicated are the inferred values of the break frequencies $\nu_{\rm a}$, $\nu_{\rm m}$ and $\nu_{\rm c}$ for May 21.0 UT