Evolution of Stellar Activity and Habitable zone: I. Ultraviolet Emission of Dwarfs in Open Clusters and Field Stars

Near-ultraviolet (NUV) radiation from dwarf stars plays a critical role in shaping the habitability of planetary systems, yet its long-term evolution across different spectral types remains poorly investigated. Based on GALEX NUV observations, we study the evolution of stellar NUV emission for a sample of 386,500 A- to M-type dwarfs spanning ages from 3 Myr to 10 Gyr, drawn from both open clusters and the field. The normalized NUV emission ($f_{\mathrm{N}\mathrm{U}\mathrm{V}}\mathrm{/}{f}_{\mathrm{J}}$) is used to trace the evolutionary trends. Our results reveal distinct evolutionary pathways after considering the distance completeness: A and early-F dwarfs show a weak decline in NUV emission during the main-sequence phase; late-F to G dwarfs exhibit a clear decrease, consistent with continuous spin-down driven by magnetic braking; late-K and M-dwarfs undergo a rapid decline in NUV emission when they evolve from young stellar objects to main-sequence stars. Furthermore, we construct the evolutionary tracks of stellar ultraviolet habitable zone (UHZ). By comparing stellar circumstellar habitable zone (CHZ) and UHZ, we find that G- and K-type stars offer the most stable overlap between thermal and UV habitability over long-term evolution.