As part of the Mega MUSCLES Hubble Space Telescope (HST) Treasury program, we obtained time-series ultraviolet spectroscopy of the M2.5V star, GJ~674. During the FUV monitoring observations, the target exhibited several small flares and one large flare (E_FUV = 10^{30.75} ergs) that persisted over the entirety of a HST orbit and had an equivalent duration >30,000 sec, comparable to the highest relative amplitude event previously recorded in the FUV. The flare spectrum exhibited enhanced line emission from chromospheric, transition region, and coronal transitions and a blue FUV continuum with an unprecedented color temperature of T_c ~ 40,000+/-10,000 K. In this paper, we compare the flare FUV continuum emission with parameterizations of radiative hydrodynamic model atmospheres of M star flares. We find that the observed flare continuum can be reproduced using flare models but only with the ad hoc addition of hot, dense emitting component. This observation demonstrates that flares with hot FUV continuum temperatures and significant EUV/FUV energy deposition will continue to be of importance to exoplanet atmospheric chemistry and heating even as the host M dwarfs age beyond their most active evolutionary phases.
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