Prospects for studying million-degree gas in the Milky Way halo using the forbidden optical x and xiv intersystem lines

The Milky Way is surrounded by large amounts of hot gas at temperatures of T>10^6 K, which represents a major baryon reservoir. We explore the prospects of studying the hot coronal gas in Milky Way halo by analyzing the highly forbidden optical coronal lines of x and xiv in absorption against bright (unrelated) extragalactic background sources. We used a semi-analytic model of the Milky Way's coronal gas distribution together wih HESTIA simulations of the Local Group and observational constraints to predict the expected Fe x and Fe xiv column densities, as well as the line shapes and strengths for the x łambda 6374.5 and xiv łambda 5302.9 transitions. We provide predictions for the signal-to-noise ratio (S/N) required to detect these lines. Using archival optical data from an original sample of 739 high-resolution AGN spectra from VLT/UVES and KECK/HIRES, we generated a stacked composite spectrum to measure an upper limit for the column densities of Fe x and Fe xiv in the Milky Way's coronal gas. We predicted column densities of log N(Fe x)= 15.40 and log N(Fe xiv)=15.23 in the Milky Way's hot halo, corresponding to equivalent widths of W_ ̊m FeX,6347 =190,μÅ,and W_ ̊m FeXIV,5302 =220,μÅ. We estimated that a minimum S/N of ∼ 50,000 (∼ 25,000) is required to detect x łambda 6374.5 ( xiv łambda 5302.9) absorption at a $3σ$ level. There was no x and xiv detected in our composite spectrum, which achieves a maximum S/N$=1,240$ near 5300 Å. We derived $3σ$ upper column-density limits of log N(Fe x)łeq 16.27 and log N(Fe xiv)łeq 15.85, in line with the above-mentioned predictions. While x and xiv absorption is too weak to be detected with current optical data, we outline how upcoming extragalactic spectral surveys with millions of medium- to high-resolution optical spectra will provide the necessary sensitivity and spectral resolution to measure velocity-resolved x and xiv absorption in the Milky Way's coronal gas (and beyond). This opens up a new prospective window on studies of the dominant baryonic mass component of the Milky Way taking the form of hot coronal gas via optical spectroscopy.