Effective absorbing column density in the gamma-ray burst afterglow X-ray spectra

We investigate the scaling relation between the observed amount of absorption in the X-ray spectra of Gamma Ray Burst (GRB) afterglows and the absorber redshift. Through dedicated numerical simulations of an ideal instrument, we establish that this dependence has a power law shape with index 2.4. However, for real instruments, this value depends on their low energy cut-off, spectral resolution and on the detector spectral response in general. We thus provide appropriate scaling laws for specific instruments. Finally, we discuss the possibility to measure the absorber redshift from X-ray data alone. We find that 10^5-10^6 counts in the 0.3-10 keV band are needed to constrain the redshift with 10% accuracy. As a test case we discuss the XMM-Newton observation of GRB 090618 at z=0.54. We are able to recover the correct redshift of this burst with the expected accuracy.