1 The $N_{\rm H}$-redshift plane

If $\gamma$-ray bursts (GRBs) originate in a dense environment their X-ray afterglow spectra are modified by absorption features and the imprinted edges can be used to determine their redshifts. Given the time decay law observed in the GRB X-ray afterglows, the necessary S/N ratio to reveal an absorption feature can be achieved only if the X-ray observation starts immediately after the burst itself, or if the collecting effective area of the detector is much larger than 100 cm².

We have simulated the observed spectrum by using the response matrices of some future planned missions, such as JET-X ($A\sim 200$ cm² at 1.5 keV and $A\sim 40$ cm² at 8.1 keV for the two telescopes; Citterio et al. 1996), AXAF with Back Illuminated (BI) CCDs ($A\sim 700$ cm² at 1.5 keV and $A\sim 40$ cm² at 8.1 keV; Kellogg et al. 1997) and XMM with the EPIC detectors ($A\sim 3600$cm² at 1.5 keV and $A\sim 1500$ cm² at 8.1 keV for three telescopes; Gondoin et al. 1996) and assuming: i) $F(100\,{\rm s})=10^{-8}$ erg cm^-2 s^-1 between 2 and 10 keV at the beginning of the observation; ii) a power law time decay of the flux $\propto t^{-1}$; iii) an intrinsic (unabsorbed) power law spectrum of photon index $\Gamma=1$ constant in time. All the simulations reported here refer to observations of 10 ks.

We simulated two different cases: a GRB afterglow at z=0.25 and intrinsic $N_{\rm H}=3\ 10^{21}$ cm^-2 and z=4 and $N_{\rm H}=10^{24}$cm^-2, which are relevant for the oxygen and iron edge, respectively. A galactic column density of $3\ 10^{20}$ cm^-2 has also been included (for an overview of the $N\rm _H$ values with BeppoSAX see Owens et al. 1998). In the case of the oxygen edge (at 0.52 keV) the satellite energy band is extremely important in order to recover the correct GRB redshift. We keep fixed the edge energies, even if in the case of a warm absorber fit should be worse.

In the case of JET-X, the minimum energy of 0.3 keV limits the maximum detectable redshift to $\sim 0.7$. The influence of the galactic absorption plays also a crucial role, such that only for low values ($\lsim\, 5\ 10^{20}$ cm^-2) we are able to disentangle the intrinsic and the galactic absorption.

In Fig. 1 (left side) we report the contour plots in the $N_{\rm H}-z$ plane of the simulated models as observed with different X-ray satellites. The three contours refer to 1, 2 and $3\,\sigma$ confidence levels. In Fig. 1a is shown the case of the JET-X telescope. It can be noted that the input redshift and column density are not recovered satisfactorily. In particular, the presence of different absorption features (O, Ne, Mg, Si) results in the elongated contour in the $N_{\rm H}-z$ plane. In the case of AXAF (Fig. 1b), the recovery of the GRB redshift is eased by the higher throughput at low energies guaranteed by the BI CCDs. The large effective area of XMM poses no problem for the identification of the redshift (Fig. 1c).

In the case of the Fe edge there are less problems due to the fact that beyond iron there are not prominent K edges. This is testified by Fig. 1 (right side), in which for all the considered instrument the redshift and the column density are recovered with a high degree of confidence. Note however that at these large redshift, the iron abundance may be lower than the solar value.

  

Figure 1: Column density - redshift contour plots for different X-ray instruments. LEFT SIDE: The input model has z=0.25 and $N_{\rm H}=3\ 10^{21}$ cm-2. The upper panel a) shows the case of JET-X. The middle panel b) presents the case of AXAF with BI CCDs and the lower panel c) the case of XMM. RIGHT SIDE: The input model has z=4 and $N_{\rm H}=10^{24}$cm-2