ABSTRACT The GJ 436 planetary system is an extraordinary system. The Neptune-sized planet that orbits the M3 dwarf revealed in the Ly α line an extended neutral hydrogen atmosphere. This material fills a comet-like tail that obscures the stellar disc for more than 10 h after the planetary transit. Here, we carry out a series of 3D radiation hydrodynamic simulations to model the interaction of the stellar wind with the escaping planetary atmosphere. With these models, we seek to reproduce the ${\sim}56{{\ \rm per\ cent}}$ absorption found in Ly α transits, simultaneously with the lack of absorption in H α transit. Varying the stellar wind strength and the EUV stellar luminosity, we search for a set of parameters that best fit the observational data. Based on Ly α observations, we found a stellar wind velocity at the position of the planet to be around [250–460] km s−1 with a temperature of [3–4] × 105 K. The stellar and planetary mass-loss rates are found to be 2 × 10−15 M⊙ yr−1 and ∼[6–10] × 109 g s−1, respectively, for a stellar EUV luminosity of [0.8–1.6] × 1027 erg s−1. For the parameters explored in our simulations, none of our models present any significant absorption in the H α line in agreement with the observations.
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