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The space environment in which planets are embedded depends mainly on thehost star and impacts the evolution of the planetary atmosphere. The quiet Mdwarf GJ 436 hosts a close-in hot Neptune which is known to feature acomet-like tail of hydrogen atoms escaped from its atmosphere due to energeticstellar irradiation. Understanding such star-planet interactions is essentialto shed more light on planet formation and evolution theories, in particularthe scarcity of Neptune-size planets below 3 d orbital period, also known as``Neptune desert''. We aimed at characterising the stellar environment aroundGJ 436, which requires an accurate knowledge of the stellar magnetic field. Thelatter is studied efficiently with spectropolarimetry, since it is possible torecover the geometry of the large-scale magnetic field by applying tomographicinversion on time series of circularly polarised spectra. We usedspectropolarimetric data collected in the optical domain with Narval in 2016 tocompute the longitudinal magnetic field, examine its periodic content viaLomb-Scargle periodogram and Gaussian Process Regression analysis, and finallyreconstruct the large-scale field configuration by means of Zeeman-DopplerImaging. We found an average longitudinal field of -12 G and a stellar rotationperiod of 46.6 d using a Gaussian Process model and 40.1 d using Zeeman-DopplerImaging, both consistent with the literature. The Lomb-Scargle analysis did notreveal any significant periodicity. The reconstructed large-scale magneticfield is predominantly poloidal, dipolar and axisymmetric, with a mean strengthof 16 G. This is in agreement with magnetic topologies seen for other stars ofsimilar spectral type and rotation rate.

The space weather around the exoplanet GJ 436b