The Density and Ionization Profiles of Optically Dark and High-Redshift GRBs Probed by X-ray Absorption

The X-ray column density ($N_{\mathrm{HX}}$) of gamma-ray bursts (GRBs) can probe the local environment of their progenitors over a wide redshift range. Previous work has suggested an increasing trend as a function of redshift. The relevance of this current analysis relies on investigating the selection bias method, such as the effect of the X-ray spectrum in high-redshift GRBs, which complicates the measurement of small $N_{\mathrm{HX}}$; this has yet to be fully evaluated or discussed elsewhere. In this work, we evaluated these effects through simulations to define appropriate observational limits in the $N_{\mathrm{HX}}$ versus redshift plane. We then applied a one-sided nonparametric method developed by Efron and Petrosian. Within the framework of this method, we investigated the redshift dependence of $N_{\mathrm{HX}}$ and the local distribution function. Our results show that the evolution of $N_{\mathrm{HX}}$ with redshift firmly exists with a significance of more than four sigma and follows a power law of ${(1+z)}^{1.39(+0.22,-0.27)}$. Based on these analyses and previous studies, the GRB progenitor mass varies but is more massive in the high-redshift environment and has a higher gas column density. This suggests that part of the luminosity evolution of GRBs, which has been widely reported, may be due to the evolution of the progenitor’s mass. Using the same method, we demonstrate that optically dark GRBs show a consistent evolution: ${(1+z)}^{1.15(+0.67,-0.83)}$. By applying the Kolmogorov–Smirnov (KS) test, it is shown that optically dark GRBs have statistically identical flux and photon index distributions compared to normal GRBs, but the $N_{\mathrm{HX}}$ is systematically larger. This result suggests that the darkness of some GRB populations is not due to an intrinsic mechanism, but rather because a higher density surrounds them.