  Extreme-ultraviolet and X-ray emissions from stellar coronae drive mass loss
from exoplanet atmospheres, and ultraviolet emission from stellar chromospheres
drives photo-chemistry in exoplanet atmospheres. Comparisons of the spectral
energy distributions of host stars are, therefore, essential for understanding
the evolution and habitability of exoplanets. The large number of stars
observed with the MUSCLES, Mega-MUSCLES, and other recent HST observing
programs has provided for the first time a large sample (79 stars) of
reconstructed Lyman-alpha fluxes that we compare with X-ray fluxes to identify
significant patterns in the relative emission from these two atmospheric
regions as a function of stellar age and effective temperature. We find that as
stars age on the main sequence, the emissions from their chromospheres and
coronae follow a pattern in response to the amount of magnetic heating in these
atmospheric layers. A single trendline slope describes the pattern of X-ray vs.
Lyman-alpha emission for G and K dwarfs, but the different trendlines for M
dwarf stars show that the Lyman-alpha fluxes of M stars are significantly
smaller than warmer stars with the same X-ray flux. The X-ray and Lyman-alpha
luminosities divided by the stellar bolometric luminosities show different
patterns depending on stellar age. The L(Lyman-alpha)/L(bol) ratios increase
smoothly to cooler stars of all ages, but the L(X)/L(bol) ratios show different
trends. For older stars, the increase in coronal emission with decreasing
T(eff) is much steeper than chromospheric emission. We suggest a fundamental
link between atmospheric properties and trendlines relating coronal and
chromospheric heating,
