The Far Ultraviolet M-dwarf Evolution Survey. I. The Rotational Evolution of High-Energy Emissions

M-dwarf stars are prime targets for exoplanet searches because of their close proximity and favorable properties for both planet detection and characterization. However, the potential habitability and atmospheric characterization of these exoplanetary systems depends critically on the history of high-energy stellar radiation from X-rays to NUV, which drive atmospheric mass loss and photochemistry in the planetary atmospheres. With the Far Ultraviolet M-dwarf Evolution Survey (FUMES) we have assessed the evolution of the FUV radiation, specifically 8 prominent emission lines, including Ly$\alpha$, of M-dwarf stars with stellar rotation period and age. We demonstrate tight power-law correlations between the spectroscopic FUV features, and measure the intrinsic scatter of the quiescent FUV emissions. The luminosity evolution with rotation of these spectroscopic features is well described by a broken power-law, saturated for fast rotators, and decaying with increasing Rossby number, with a typical power-law slope of $-2$, although likely shallower for Ly$\alpha$. Our regression fits enable FUV emission line luminosity estimates relative to bolometric from known rotation periods to within $\sim$0.3 dex, across 8 distinct UV emission lines, with possible trends in the fit parameters as a function of source layer in the stellar atmosphere. Our detailed analysis of the UV luminosity evolution with age further shows that habitable zone planets orbiting lower-mass stars experience much greater high-energy radiative exposure relative the same planets orbiting more massive hosts. Around early-to-mid M-dwarfs these exoplanets, at field ages, accumulate up to 10-20$\times$ more EUV energy relative to modern Earth. Moreover, the bulk of this UV exposure likely takes place within the first Gyr of the stellar lifetime.