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

Abstract

Sgr A*, the 4 x 10^6 solar-mass supermassive black hole at the Galactic Center, exhibits frequent flaring with X-ray luminosities of L_X ~ 10^35--10^36 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 Galactic Center's 0.3 arcsec 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 = 10^32--10^39 erg s^-1 in a dense medium. We detect no statistically significant variability in any mid-infrared line, including [Fe II] 5.34 micron, [Ne II] 12.813 micron, [Fe II] 17.936 micron, and [S III] 18.713 micron. 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 flare timescale suppress any observable response to individual flares. We further find that the predicted emission is continuum dominated and that even the brightest lines are intrinsically weak and broadened by velocities of order 10^3 km s^-1, reducing their contrast against the continuum and limiting their detectability. 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*.