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HAZMAT VI: The Evolution of Extreme Ultraviolet Radiation Emitted from Early M Star

Quantifying the evolution of stellar extreme ultraviolet (EUV, 100 -- 1000 $\overset{\circ}{A}$) emission is critical for assessing the evolution of planetary atmospheres and the habitability of M dwarf systems. Previous studies from the HAbitable Zones and M dwarf Activity across Time (HAZMAT) program showed the far- and near-UV (FUV, NUV) emission from M stars at various stages of a stellar lifetime through photometric measurements from the Galaxy Evolution Explorer (GALEX). The results revealed increased levels of short-wavelength emission that remain elevated for hundreds of millions of years. The trend for EUV flux as a function of age could not be determined empirically because absorption by the interstellar medium prevents access to the EUV wavelengths for the vast majority of stars. In this paper, we model the evolution of EUV flux from early M stars to address this observational gap. We present synthetic spectra spanning EUV to infrared wavelengths of 0.4 $\pm$ 0.05 M$_{\odot}$ stars at five distinct ages between 10 and 5000 Myr, computed with the PHOENIX atmosphere code and guided by the GALEX photometry. We model a range of EUV fluxes spanning two orders of magnitude, consistent with the observed spread in X-ray, FUV, and NUV flux at each epoch. Our results show that the stellar EUV emission from young M stars is 100 times stronger than field age M stars, and decreases as t$^{-1}$ after remaining constant for a few hundred million years. This decline stems from changes in the chromospheric temperature structure, which steadily shifts outward with time. Our models reconstruct the full spectrally and temporally resolved history of an M star's UV radiation, including the unobservable EUV radiation, which drives planetary atmospheric escape, directly impacting a planet's potential for habitability.