The energetic particle environment of a GJ 436 b-like planet

A key first step to constrain the impact of energetic particles in exoplanet atmospheres is to detect the chemical signature of ionisation 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 $a=0.01-0.2\,$au from GJ$\,$436, including GJ$\,$436$\,$b's orbital distance (0.028$\,$au). For these distances we find that, at top-of-atmosphere, stellar energetic particles ionise molecular hydrogen at a rate of $\zeta_{\rm StEP,H_2} \sim 4\times10^{-10}-2\times10^{-13}\,\mathrm{s^{-1}}$. In comparison, Galactic cosmic rays alone lead to $\zeta_{\rm GCR, H_2}\sim2\times 10^{-20}-10^{-18} \,\mathrm{s^{-1}}$. At 10au we find that ionisation due to Galactic cosmic rays equals that of stellar energetic particles: $\zeta_{\rm GCR,H_2} = \zeta_{\rm StEP,H_2} \sim 7\times10^{-18}\,\rm{s^{-1}}$ for the top-of-atmosphere ionisation 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 $P>10^2\,$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.