  Stellar rotation at early ages plays a crucial role in the survival of
primordial atmospheres around Earth-mass exoplanets. Earth-like planets
orbiting fast-rotating stars may undergo complete photoevaporation within the
first few hundred Myr driven by the enhanced stellar XUV radiation, while
planets orbiting slow-rotating stars are expected to experience difficulty to
lose their primordial envelopes. Besides the action of stellar radiation,
stellar winds induce additional erosion on these primordial atmospheres,
altering their morphology, extent, and causing supplementary atmospheric
losses. In this paper, we study the impact of activity-dependent stellar winds
on primordial atmospheres to evaluate the extent at which the action of these
winds can be significant in the whole planetary evolution at early evolutionary
stages. We performed 3D magnetohydrodynamical (MHD) simulations of the
interaction of photoevaporating atmospheres around unmagnetized Earth-mass
planets in the time-span between 50 and 500 Myr, analyzing the joint evolution
of stellar winds and atmospheres for both fast- and slow-rotating stars. Our
results reveal substantial changes in the evolution of primordial atmospheres
when influenced by fast-rotating stars, with a significant reduction in extent
at early ages. In contrast, atmospheres embedded in the stellar winds from
slow-rotating stars remain largely unaltered. The interaction of the magnetized
stellar winds with the ionized upper atmospheres of these planets allows to
evaluate the formation and evolution of different MHD structures, such as
double-bow shocks and induced magnetospheres. This work will shed light to the
first evolutionary stages of Earth-like exoplanets, that are of crucial
relevance in terms of planet habitability.
