next previous
Up: Time-dependent photoionization and fluorescence


Subsections

3 Results

We have carried out a large number of simulations using different assumptions on the burst spectral properties and on the density and radial extent of the CBM. The two effects that are potentially relevant to observations are discussed in the following two subsections.

3.1 The Iron K absorption edge

Our simulations indicate that an iron absorption edge could be observable. However, in order to attribute the absorption unambiguously to the CBM -- rather than to foreground absorption -- a decrease of the K-edge opacity, caused by photoionization, must be observed. In Fig. 1, the time dependence of the Fe K$\alpha$ edge for various assumptions on the CBM density and extent is plotted. The figure demonstrates that bright bursts ($E_{54} \sim 1$) can ionize star-forming regions completely, leading to the required significant decrease of the Fe K edge opacity. However, if absorption features vary with time due to photoelectric absorption, this can only occur on $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ...  minute time scales. This implies that prompt GRB observations with moderate energy resolution at a few keV are required in order to detect these varying absorption features. The absorption features vary on the timescale of the burst duration because most of the fluence of the burst is emitted during the prompt burst phase. This is in contradiction to the assumption of Perna & Loeb (1998) who used a slower decay of the X-ray afterglow, $F_{\nu} (t) \propto t^{-3/4}$, inconsistent with observations.

  
\begin{figure}

\includegraphics [angle=-90,width=6cm,clip]{r61_fig1.ps}

\vspace*{-1mm}\vspace*{-2mm}\end{figure} Figure 1: Time dependence of the equivalent width of the Fe K absorption edge for a variety of CBM parameters. For the thin curves, the hydrogen column density is held constant at $N_{\rm H} = 3 \ 10^{22}$ cm-2. For heavy curves, different values of $N_{\rm H}$ are used

3.2 Fluorescence Iron K$\alpha$ lines

The iron K$\alpha$ fluorescence line flux increases on the burst duration time scale and remains at a roughly constant level over the light-travel time through the CBM. This implies that the Fe K$\alpha$ line emission dominates the flux at 6.4-6.7 keV (in the GRB's rest frame) after the continuum flux in this energy range has decayed below the line flux level. In Fig. 2 the maximum Fe K$\alpha$ line luminosities and corresponding fluxes for a burst located at z = 1 for a variety of CBM parameters with constant $N_{\rm H} = 3 \ 10^{22}$ cm-2 are plotted. We find that the fluorescence line luminosities are generally low, $L_{\rm Fe K\alpha} \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfi...
 ...fil$\scriptscriptstyle ... , corresponding to $F_{\rm Fe K\alpha} (z = 1) \mathrel{\mathchoice {\vcenter{\offinterlineskip\hal...
 ...yle ... for standard solar-system metal abundances and a quasi-isotropic CBM. $L_{\rm Fe K\alpha}$ increases with increasing $N_{\rm H}$. However, there is a limit of $N_{\rm H} \ll 10^{24}$ cm-2 since for higher values Thomson scattering effects on the hard X-ray radiation would become observable. In particular, short-timescale variability would be smeared out over the typical photon escape timescale $t_{\rm esc} \sim r_{\rm max} \, \tau_{\rm T} / c$ if $\tau_{\rm T} \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\di...
 ...\offinterlineskip\halign{\hfil$\scriptscriptstyle ... , in contrast to the observed $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ...  1 ms variability in some GRB pulses. In Fig. 2, the line luminosities increase with density for small densities since in this limit the entire CBM is ionized, and an incrasing density leads to an increasing amount of material contributing to the fluorescence line emission. In the high-density limit, an increasing density leads to a decrease of the ionization radius and thus to a decrease of the fluorescence-line emitting volume. Our results indicate that if the CBM is quasi-isotropic and metals have abundances close to the solar-system values, fluorescence lines will hardly be detectable even with future X-ray telescopes (AXAF, XMM, Astro-E). The recent marginal detections of the Fe K$\alpha$ fluorescence line in the X-ray afterglows of GRB 970508 (Piro et al. 1998) and GRB 980828 (Yoshida et al. 1998) can not have originated in an isotropic medium as investigated in this paper.

  
\begin{figure}

\includegraphics [angle=-90,width=6cm]{r61_fig2.eps}

\vspace*{-1mm}\vspace*{-2mm}\end{figure} Figure 2: The maximum line luminosities in the Fe K$\alpha$lines for different CBM parameters. The hydrogen column is held constant at $N_{\rm H} = 3 \ 10^{22}$ cm-2. The right scale indicates the corresponding line fluxes if the burst is located at z = 1

Acknowledgements

We wish to thank Jon C. Weisheit and Tim Kallman for helpful discussions. This work was partially supported by NASA grant NAG 5-4055.


next previous
Up: Time-dependent photoionization and fluorescence

Copyright The European Southern Observatory (ESO)