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The Central 300 pc of the Galaxy Probed by Infrared Spectra of H$_3^+$ and CO: III. Locations of Sgr B2 and Star $ι$

Using a simple relation between the radial expansion velocity of diffuse gas in the Central Molecular Zone (CMZ) of the Galaxy and its distance from Sgr A$^\ast$ we estimate the physical depths within the CMZ of Star $ι$ (2MASS $J$17470898-2829561) and two Sgr B2 far-infrared continuum sources with respect to the location of Sgr A$^\ast$. To do this we use velocity profiles of mid-infrared absorption lines of H$_3^+$ and of far-infrared absorption lines of H$_2$O$^+$, OH$^+$, and $^{13}$CH$^+$. The distances to Star $ι$ and to the Sgr B2 sources are found to be $\sim$90 pc greater than the distance to Sgr A$^\ast$. Our conclusion that Sgr B2 lies toward the rear of the CMZ is contrary to many previous models in which it has been placed shallower than Sgr A$^\ast$.