  Exoplanet atmospheres are known to be vulnerable to mass loss through
irradiation by stellar X-ray and extreme-ultraviolet emission. We investigate
how this high-energy irradiation varies with time by combining an empirical
relation describing stellar X-ray emission with a second relation describing
the ratio of Solar X-ray to extreme-ultraviolet emission. In contrast to
assumptions commonly made when modelling atmospheric escape, we find that the
decline in stellar extreme-ultraviolet emission is much slower than in X-rays,
and that the total extreme-ultraviolet irradiation of planetary atmospheres is
dominated by emission after the saturated phase of high energy emission (which
lasts around 100 Myr after the formation of the star). The extreme-ultraviolet
spectrum also becomes much softer during this slow decline. Furthermore, we
find that the total combined X-ray and extreme-ultraviolet emission of stars
also occurs mostly after this saturated phase. Our results suggest that models
of atmospheric escape that focus on the saturated phase of high-energy emission
are over-simplified, and when considering the evolution of planetary
atmospheres it is necessary to follow EUV-driven escape on Gyr timescales. This
may make it more difficult to use stellar age to separate the effects of
photoevaporation and core-powered mass-loss when considering the origin the
planet radius valley.
