Probing the star-forming environment of GRB across cosmic ages with high-resolution X-ray spectroscopy: From \textit{XMM-Newton}/RGS and \textit{XRISM}/Resolve to \textit{NewAthena}/X-IFU

Abstract

Optical and infrared GRB absorption spectroscopy provides valuable insight into host-galaxy properties across cosmic time. However, the star-forming region embedding the progenitor, on scales $\lesssim 100~\mathrm{pc}$ is heavily ionized by the GRB emission, making X-ray spectroscopy the sole probe of its physical and chemical conditions. We characterize the GRB-embedding medium as a function of progenitor type and cosmic epoch via high-resolution X-ray spectroscopy. We extend our study to high-redshift GRBs to evaluate how effectively X-ray absorption signatures can distinguish between pristine, Pop~III-, and Pop~II-enriched environments. Using the time-dependent photoionization code \texttt{TEPID}, we self-consistently calculate the ionization structure of the absorber, the energies and the strengths of the resulting absorption lines. We analyze a flux-selected sample of GRBs showing strong evidence for time-dependent photoionization, and search for predicted narrow features in the RGS spectra. We also assess the performance of \textit{XRISM}/Resolve and \textit{NewAthena}/X-IFU in detecting these features. In the single archival case with sufficient RGS signal-to-noise ratio (GRB~090618 at $z=0.54$), we find $\approx 3σ$ combined evidence for narrow, highly ionized Fe~L absorption lines. For bright nearby GRBs, \textit{XRISM}/Resolve can detect Fe~K absorption lines even in its current gate-valve-closed configuration ($\sim 3$ expected events/yr). \textit{NewAthena}/X-IFU will enable systematic population studies of GRB environments, delivering redshifts with precision comparable to optical/IR spectroscopy, unaffected by dust obscuration and Ly-$α$ forest absorption. Crucially, it will precisely diagnose the density, size, metallicity, and abundance patterns, ultimately revealing whether high-$z$ GRBs originate in pristine, Pop~III-, or Pop~II-enriched media.