Mid-infrared extinction toward the Galactic center

We determine the mid-infrared (MIR, $\sim$5~\mu m--22~\mu m) extinction towards the Galactic center using MIRI/MRS integral field unit (IFU) observations of the central $3''\times3''$ region (near 5~\mu m) to $7''\times7''$ region (near 22~\mu m). To measure the MIR extinction, we employ two approaches: modeling the intrinsic-to-observed dust thermal spectrum and assessing the differential extinction between hydrogen recombination lines. Expanding on prior work, we directly model the dust-opacity distribution along the line of sight, and we make available a Python code that provides a flexible tool for deriving intrinsic dust emission spectra. We confirm the spatial variability of extinction across the field, demonstrating that dusty sources--such as IRS~29N--exhibit higher local extinction. Furthermore, we verify the absence of PAH emission features in the Galactic center MIR spectra. Using the two complementary methods, we derive a refined ``best guess'' MIR extinction law for Sgr A* and the surrounding Galactic-center region. By applying the extinction law to a MIR flare measurement discussed in a companion paper Michail et al. 2025, we estimate a residual relative extinction uncertainty for the short MIRI/MRS grating on the order of $0.2~\mathrm{mag}$ {from $\sim$5 to $\sim$18~\mu m\ and $\sim$0.3~mag from $\sim$18 to $\sim$22~\mu m}, consistent with our uncertainty estimate.