Effects of the stellar wind on the Ly-alpha transit of close-in planets

We use 3D hydrodynamics simulations followed by synthetic line profile calculations to examine the effect increasing the strength of the stellar wind has on observed Ly-$\alpha$ transits of a Hot Jupiter (HJ) and a Warm Neptune (WN). We find that increasing the stellar wind mass-loss rate from 0 (no wind) to 100 times the solar mass-loss rate value causes reduced atmospheric escape in both planets (a reduction of 65\% and 40\% for the HJ and WN, respectively, compared to the "no wind" case). For weaker stellar winds (lower ram pressure), the reduction in planetary escape rate is very small. However, as the stellar wind becomes stronger, the interaction happens deeper in the planetary atmosphere and, once this interaction occurs below the sonic surface of the planetary outflow, further reduction in evaporation rates is seen. We classify these regimes in terms of the geometry of the planetary sonic surface. "Closed" refers to scenarios where the sonic surface is undisturbed, while "open" refers to those where the surface is disrupted. We find that the change in stellar wind strength affects the Ly-$\alpha$ transit in a non-linear way. Although little change is seen in planetary escape rates ($\simeq 5.5\times 10^{11}$g/s) in the closed to partially open regimes, the Ly-$\alpha$ absorption (sum of the blue [-300, -40 km/s] \& red [40, 300 km/s] wings) changes from 21\% to 6\% as the stellar wind mass-loss rate is increased in the HJ set of simulations. For the WN simulations, escape rates of $\simeq 6.5\times 10^{10}$g/s can cause transit absorptions that vary from 8.8\% to 3.7\%, depending on the stellar wind strength. We conclude that the same atmospheric escape rate can produce a range of absorptions depending on the stellar wind and that neglecting this in the interpretation of Ly-$\alpha$ transits can lead to underestimation of planetary escape rates.