Infrared Line Diagnostics Fail to Constrain Sgr A*’s UV Output

Sgr A^⋆, the 4 × 10⁶ M_⊙ supermassive black hole at the Galactic center, exhibits frequent flaring with X-ray luminosities of L_X ∼ 10³⁵–10³⁶ erg s⁻¹, while its ultraviolet (UV) emission remains unconstrained due to extreme extinction (A_V ∼ 30 mag). We use JWST/MIRI time-resolved spectroscopy of the central (Formula presented) 0.″3 region to search for mid-infrared emission line variability driven by Sgr A^⋆ flares, comparing the results to CLOUDY photoionization models spanning flare luminosities of L_UV = 10³²–10³⁹ erg s⁻¹. We detect no continuum-correlated variability in any mid-infrared line, including [Fe ii] (5.34 μm), [Ne ii] (12.813 μm), [Fe ii] (17.936 μm), and [S iii] (18.713 μm) over lags of ∼1–8 hr. Despite expectations of a flare-driven response, we show that the lack of variability is consistent with the physical conditions in the spatially extended line-emitting gas, where light-crossing timescales of ∼0.1–10 days and recombination and cooling timescales much longer than the variability timescales suppress any observable response to individual flares. We further find that the modeled infrared spectra are dominated by continuum emission rather than isolated line emission. The brightest predicted lines are intrinsically weak (lower than 10⁻⁵ mJy), and their detectability is further reduced by the large kinematic broadening expected at the CLOUDY-predicted emitting radii, reducing their contrast against the continuum. Extending the analysis to higher-ionization mid-infrared and near-infrared lines does not improve sensitivity. These results demonstrate that infrared emission lines trace a steady-state radiation field rather than individual flaring events, and therefore infrared line diagnostics cannot be used to constrain the instantaneous UV flux of Sgr A*.