Fe K{\alpha} equivalent-width mapping with 3D radiative transfer calculation: A general model and application to the RS Canum Venaticorum-type stars with XRISM/Resolve
The Fe K $\alpha$ fluorescence line at 6.4 keV has long been used to probe the relative geometry between photoionizing X-ray sources and surrounding cold material in a wide range of astrophysical systems. With the advent of the X-ray microcalorimeter XRISM/Resolve, Fe K $\alpha$ lines with equivalent widths down to $\sim 5$ eV-previously inaccessible-are now detectable, and even non-detections can place upper limits of a few eV, making non-detections themselves valuable for constraining the geometry. Considering that Fe K $\alpha$-based geometric diagnostics are entering a new stage in the microcalorimeter era, we present Fe K $\alpha$ equivalent-width maps computed with the three-dimensional Monte Carlo radiative-transfer code SKIRT for a generalized configuration consisting of a spherical reflector of radius $R_{*}$ and a point source located at a height $h$ above the surface. The equivalent-width maps exhibit two characteristic features: (1) an increase toward the center of the projected surface of the sphere; and (2) an overall decrease with increasing $h/R_{*}$. The key point is that we confirm these features for equivalent widths of $< 40$ eV, a regime that has become accessible for the first time thanks to the improved detection threshold from $\sim 50$ eV with Chandra/HETG to $\sim 5$ eV with XRISM/Resolve. As an illustrative application, we compare the maps with XRISM/Resolve spectra of three RS Canum Venaticorum-type stars (GT Muscae, $\sigma$ Geminorum, and HR 1099) and constrain the locations of the flare loop and coronal bright points in these systems. Because the maps are constructed for a highly generalized point-source--spherical-reflector geometry, they are readily applicable to many other objects, including X-ray binaries and cataclysmic variables.