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abstract: 'The Fermi bubbles are two lobes filled with non-thermal particles that emit gamma rays, extend $\approx$10 kpc vertically from the Galactic center, and formed from either nuclear star formation or accretion activity on Sgr A\*. Simulations predict a range of shock strengths as the bubbles expand into the surrounding hot gas halo distribution ($T_{halo} \approx 2 \times 10^6$ K), but with significant uncertainties in the energetics, age, and thermal gas structure. The bubbles should contain thermal gas with temperatures between $10^6$ and $10^8$ K, with potential X-ray signatures. In this work, we constrain the bubbles’ thermal gas structure by modeling the and emission line strengths from archival *XMM-Newton* and *Suzaku* data. Our emission model includes a hot thermal volume-filled bubble component cospatial with the gamma-ray region, and a shell of compressed material. We find that a bubble/shell model with $n \approx 1 \times 10^{-3}$ cm$^{-3}$ and with log($T$) $\approx$ 6.60-6.70 is consistent with the observed line intensities. In the framework of a continuous Galactic outflow, we infer a bubble expansion rate, age, and energy injection rate of $490_{-77}^{+230}$ km s$^{-1}$, $4.3_{-1.4}^{+0.8}$ Myr, and $2.3_{-0.9}^{+5.1} \times 10^{42}$ erg s$^{-1}$. These estimates are consistent with the bubbles forming from a 