medium ($\gtrsim 2 \times 10^6$ K), implying that the bubbles’ thermal gas should have signatures at soft X-ray energies. Indeed, the bubbles appear to be bounded by X-ray emission seen in the *ROSAT* 1.5 keV band [@bh_cohen03; @su_etal10]; however, these observations do not constrain the bubbles’ intrinsic thermal gas structure since the broad-band images are a weak temperature diagnostic. Spectral observations with current X-ray telescopes are a much better temperature diagnostic for this type of environment.

Initial efforts to observe the bubbles in soft X-rays with *Suzaku* and *Swift* and constrain their temperature and shock strength were carried out by several groups [@kataoka_etal13; @kataoka_etal15; @tahara_etal15]. @kataoka_etal15 extracted soft X-ray background (SXRB) spectra in the 0.5–2.0 keV band for 97 sight lines that pass through the Fermi bubbles, and fit the spectra with thermal plasma models. They consistently measured plasma temperatures of $kT$ = 0.3 keV for these sight lines, which is systematically higher than the characteristic temperature measured in sight lines away from the Galactic center [$kT \approx$0.2 keV; @hs13]. From this temperature ratio, they inferred a shock Mach number of $\mathcal{M} \approx $0.3 keV / 0.2 keV = 1.5, and corresponding expansion rate of $\approx$300 km s$^{-1}$. This is 