2025AJ....170..159F

The extreme-ultraviolet (EUV; 100-911 Å) spectra of F, G, K, and M stars provide diagnostics of the stellar chromosphere through the corona, with line and continuum formation temperatures spanning roughly 10⁴-10⁷ K. The EUV stellar spectrum in turn drives atmospheric photochemistry and numerous escape processes on orbiting planets, and is often combined with the stellar X-ray flux to make up the X-ray and ultraviolet (XUV) irradiance. However, very few direct EUV spectra of other stars exist in the archive, and as a result, X-ray scaling relations are often assumed for the XUV evolution of cool stars. In this work, we present a new study of the EUV history of solar-type stars, using scaling relations based on transition region/coronal far-ultraviolet emission lines and differential emission measure-based synthetic spectra to provide a semiempirical estimate of the EUV evolution of the Sun over the ≈10 Myr-10 Gyr age range for the first time. We utilize new and archival Hubble Space Telescope observations of solar analogs (T_⊙ ± 150 K for stars older than 100 Myr) and “Young Suns” (age < 100 Myr) that will evolve into main-sequence early G-type stars to predict the 90-360 Å EUV flux from a sample of 23 stars. We find that the EUV activity evolution for solar-type stars follows a two-component behavior: a saturated L(EUV)/L_bol plateau (at a level of about 10^–4) followed by a power-law decay (α ≈ -1.1) after ages of ≈50-100 Myr. Consequently, the EUV flux incident at 1 au around solar analogs varies over the lifetime of the Sun, ranging from 100× the present-day UV irradiance at 10 Myr to 0.3× the present-day level at 10 Gyr. We find that the EUV luminosity is approximately the same as the soft X-ray luminosity up to approximately 1 Gyr, after which the EUV luminosity of the stars dominates. In comparison to Sun-like stars, the EUV saturation level of early/mid M dwarfs is several times higher and lasts ∼10-20 times longer.