Here, we study the dichotomy of the escaping atmosphere of the newly discovered close-in exoplanet AU Mic b. On one hand, the high EUV stellar flux is expected to cause a strong atmospheric escape in AU Mic b. On the other hand, the wind of this young star is believed to be very strong, which could reduce or even inhibit the planets atmospheric escape. AU Mic is thought to have a wind mass-loss rate that is up to $1000$ times larger than the solar wind mass-loss rate ($dot{M}_odot$). To investigate this dichotomy, we perform 3D hydrodynamics simulations of the stellar wind--planetary atmosphere interactions in the AU Mic system and predict the synthetic Ly-$alpha$ transits of AU Mic b. We systematically vary the stellar wind mass-loss rate from a `no wind scenario to up to a stellar wind with a mass-loss rate of $1000~dot{M}_odot$. We find that, as the stellar wind becomes stronger, the planetary evaporation rate decreases from $6.5times 10^{10}$ g/s to half this value. With a stronger stellar wind, the atmosphere is forced to occupy a smaller volume, affecting transit signatures. Our predicted Ly-$alpha$ absorption drops from $sim 20%$, in the case of `no wind to barely any Ly-$alpha$ absorption in the extreme stellar wind scenario. Future Ly-$alpha$ transits could therefore place constraints not only on the evaporation rate of AU Mic b, but also on the mass-loss rate of its host star.
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