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.
