and simulations. Section \[section.conclusions\_chap\_fb\] summarizes our results.

Emission Line Data {#section.data_chap_fb}
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Our data set includes (He-like triplet at $E \approx 0.56$ keV) and (Ly$\alpha$ transition at $E \approx 0.65$ keV) emission lines, which are the dominant ions for thermal plasmas with temperatures between $T \sim 10^{5.5}$ and $10^{7}$ K [@sutherland_dopita93]. For an optically thin plasma in collisional ionization equilibrium, the emission line intensity depends on the plasma density and temperature as $I\ \propto\ n^2 \epsilon(T)$, where $\epsilon(T)$ is the volumetric line emissivity. This implies that the line strength ratio is a temperature diagnostic and the individual ion line strengths can be used to estimate the plasma density. Large, all-sky samples of emission line measurements in particular have been instrumental in constraining the Milky Way’s global density distribution of $\sim 10^6$ K gas .

The full data set used in our modeling analysis is a combination of published *XMM-Newton* emission line measurements from and a complementary sample of *Suzaku* measurements compiled specifically for this project. The *XMM-Newton* sample from contains $\sim$1000 emission line measurements distributed across the sky, making it a valuable starting point for our modeling work. While *XMM-Newton* has more collecting power than *Suzaku* near the emission lines 