Searching for FUV line emission from $10^7$ K gas in massive elliptical galaxies and galaxy clusters as a tracer of turbulent velocities

Non-thermal pressure from turbulence and bulk flows is a fundamental ingredient in hot gaseous halos, and in the intracluster medium it will be measured through emission line kinematics with calorimeters on future X-ray spacecraft. In this paper we present a complementary method for measuring these effects, using forbidden FUV emission lines of highly ionized Iron which trace $10^7$ K gas. The brightest of these is [Fe XXI] $\lambda$1354.1. We search for these lines in archival HST-COS spectra from the well-known elliptical galaxies M87 and NGC4696, which harbor large reservoirs of $10^7$ K gas. We report a 2.2$\sigma$ feature which we attribute to [Fe XXI] from a filament in M87, and positive residuals in the nuclei of M87 and NGC4696, for which the 90\% upper limits on the line flux are close to the predicted fluxes based on X-ray observations. In a newer reduction of the data from the Hubble Spectroscopic Legacy Archive, these limits become tighter and the [Fe XXI] feature reaches a formal significance of 5.3$\sigma$, neglecting uncertainty in fitting the continuum. Using our constraints, we perform emission measure analysis, constraining the characteristic path length and column density of the $\sim10^7$ K gas. We also examine several sightlines towards filaments or cooling flows in other galaxy clusters, for which the fraction of gas at $10^7$ K is unknown, and place upper limits on its emission measure in each case. A medium-resolution HST-COS observation of the M87 filament for $\sim$10 orbits would confirm our detection of [Fe XXI] and measure its width.