2 Procedures

We began our analysis of this burst by examining HER/HERB data from BATSE (Fishman et al. 1989) LAD 0, which is publically available from the Compton Observatory Science Support Center. This detector is the most normal to the burst ($\theta = 11.576^{\circ}$). The burst is also $132^{\circ}$ away from the geocenter, which helps reduce complications from Earth scatter. Our HER/HERB data is available spanning an energy range of 24 keV to 1996 keV and time interval of 0.03 to 21.8 s. The burst lasted for just over 40 s in this energy range, so that the two last pulses are excluded from our analysis.

At its finest resolution, with bins approximately covering 0.3 s, the signal-to-noise ratio is sufficiently high (S/N > 55) that it was possible to fit time-resolved spectra. We did this using the WINGSPAN analysis software. Examining the time-evolving spectra of GRB 970111 (see Fig. 1 of Crider et al. 1998), we have found that during the first $\sim10$ s, the asymptotic slope below the spectral break $\alpha$ is positive and inconsistent with the predictions of the unabsorbed synchrotron shock model, namely $-\frac{3}{2} \leq \alpha \leq -\frac{2}{3}$ (Katz 1994). To overcome this inconsistency, we previously included a photoelectric absorption term to account for the steep low-energy spectra (Böttcher et al. 1999). While this produced marginally acceptable fits to the BATSE data, the required ISM H column density is (assuming solar abundances) approximately $10^{26}~\rm{cm^{-2}}$ and no photons would have been detected by the BeppoSAX WFC.

  

Figure 1: A simple synchrotron self-absorption model fit to the first 5 s of GRB 970111 ($\chi_{\nu}^{2} = 1.09, \nu = 115$)

Synchrotron self-absorption (SSA) is another possible mechanism which may explain the paucity of photons just below the spectral break. We approximated SSA using a broken power law with two breaks. We fixed the photon slope below the first break to +1 (Katz 1994) and the slope between the two breaks to $-\frac{2}{3}$(for the slope expected for single electron emission synchrotron shocks; Katz 1994). This leaves 4 free parameters. The resulting $\chi^{2}$ values are similar to those found when using the Band GRB function. In Fig. 1, we show the integrated spectra during the first 5 s for this burst fit with our simple SSA function. The reduced $\chi^{2}$ ($\nu = 115$)of this fit is 1.09. Fitting this function to the time-resolved spectra reveals that the lower break energy ${E_{\rm abs}}$ decreases monotonically while it is within the range of the detector (see Fig. 2).

For fully radiative shock evolution, ${E_{\rm abs}}\propto \rm{t}^{-\frac{4}{5}}$, while for fully adiabatic shock evolution, ${E_{\rm abs}}\propto \rm{t}^{-\frac{1}{2}}$ (Sari et al. 1998). To compare the observed decay to these predictions, we fit our data with the function

$${E_{\rm abs}}= E_{\rm abs}(0) \left[ 1 + \left( \frac{t}{t_{\rm decay}} \right)^{n} \right]^{-1}$$ (1)

which becomes ${E_{\rm abs}}\propto t^{-n}$ when $(t/t_{\rm decay})^n \gg 1$. We found that this function fits our values of ${E_{\rm abs}}$ very well and find that $t_{\rm decay}=9.3 \pm 0.5$ and $n= 2.2 \pm 0.3$.

  

Figure 2: The decay of ${E_{\rm abs}}$ with respect to time fit with Eq. (1). Arrows represent time bins where ${E_{\rm abs}}$ was undetermined and presumed to be below the low energy detector cutoff