SIMBAD references

A key first step to constrain the impact of energetic particles in exoplanet atmospheres is to detect the chemical signature of ionization due to stellar energetic particles and Galactic cosmic rays. We focus on GJ 436, a well-studied M dwarf with a warm Neptune-like exoplanet. We demonstrate how the maximum stellar energetic particle momentum can be estimated from the stellar X-ray luminosity. We model energetic particle transport through the atmosphere of a hypothetical exoplanet at orbital distances between $a=0.01\text{ and }0.2\,$au from GJ 436, including GJ 436 b's orbital distance (0.028 au). For these distances, we find that, at the top of atmosphere, stellar energetic particles ionize molecular hydrogen at a rate of $\zeta _{\rm StEP,H_2} \sim 4\times 10^{-10}\text{ to }2\times 10^{-13}\, \mathrm{s^{-1}}$. In comparison, Galactic cosmic rays alone lead to $\zeta _{\rm GCR, H_2}\sim 2\times 10^{-20}\!-\!10^{-18} \, \mathrm{s^{-1}}$. At 10 au, we find that ionization due to Galactic cosmic rays equals that of stellar energetic particles: $\zeta _{\rm GCR,H_2} = \zeta _{\rm StEP,H_2} \sim 7\times 10^{-18}\, \rm {s^{-1}}$ for the top-of-atmosphere ionization rate. At GJ 436 b's orbital distance, the maximum ion-pair production rate due to stellar energetic particles occurs at pressure $P\sim 10^{-3}\,$bar, while Galactic cosmic rays dominate for $P\gt 10^2\,$bar. These high pressures are similar to what is expected for a post-impact early Earth atmosphere. The results presented here will be used to quantify the chemical signatures of energetic particles in warm Neptune-like atmospheres.