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.
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
edge for various assumptions on the CBM density and extent is plotted.
The figure demonstrates that bright bursts (
)
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
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,
, inconsistent
with observations.
The iron K 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
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
line
luminosities and corresponding fluxes for a burst located
at z = 1 for a variety of CBM parameters with constant
cm-2 are plotted. We find that
the fluorescence line luminosities are generally low,
,
corresponding to
for standard
solar-system metal abundances and a quasi-isotropic CBM.
increases with increasing
. However,
there is a limit of
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
if
, in
contrast to the observed
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
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.
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.
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