Investigating interstellar dust along the line of sight of GX 13+1 using different dust-size distributions

High-resolution X-ray spectroscopy offers a powerful tool to investigate the physical and chemical properties of dust grains, especially through the analysis of absorption edges of elements such as oxygen, magnesium, silicon, and iron, which are the main constituents of interstellar dust. In all previous X-ray studies, these absorption edges have been modeled assuming the MRN grain-size distribution. This model successfully reproduces the average interstellar extinction curve. However, with the advent of new observations, it shows important limitations, indicating that more complex grain-size distributions are required to fully describe interstellar dust properties. We aim to constrain the composition and size distribution of interstellar dust along the line of sight to the bright low-mass X-ray binary GX 13+1. We analyzed high-resolution X-ray spectra obtained with the HETG instrument (MEG+1 and MEG-3) and simultaneously modeled the Si K and Mg K absorption edges. For the first time, we compared the classical Mathis et al. (1977, ApJ, 217, 425) grain-size distribution with other grain-size distributions, thus exploring different ISM densities. Chandra Our analysis rules out scenarios of both very diffuse and very dense ISM, favoring grain-size distributions associated with average Galactic conditions along this line of sight. The dust composition is found to be dominated by amorphous olivine and the crystallinity contribution is about 2%. The depletion patterns and elemental abundances derived are consistent with prior X-ray and infrared studies.