This is a $265,915.11 grant awarded by the National Aeronautics and Space Administration (NASA) to the California Institute of Technology (Caltech) to support research on modeling the atomic processes and data required to accurately interpret observations of iron K-shell emission lines from gas orbiting black holes. The research aims to address discrepancies in current models that suggest unrealistically high iron abundances in these systems, which is likely due to a lack of modeling of key high-density atomic processes. The outputs will include updated atomic data, ionization balance calculations, and public software tools to enable more accurate modeling and interpretation of high-resolution X-ray spectra of relativistic iron lines, which will be crucial for analyzing data from the recently launched Hitomi (Astro-H) X-ray astronomy mission. This is a basic research grant without any set-aside designation.