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Lyman-alpha (Lya) emission of neutral hydrogen (1215.67 Angstr\"om) is themain contributor to the ultraviolet flux of low-mass stars such as M dwarfs. Itis also the main light source used in studies of the evaporating upperatmospheres of transiting extrasolar planets with ultraviolet transmissionspectroscopy. However, there are very few observations of the Lya emissions ofquiet M dwarfs, and none exist for those hosting exoplanets. Here, we presentLya observations of the hot-neptune host star GJ436 with the Hubble SpaceTelescope Imaging Spectrograph (HST/STIS). We detect bright emission in thefirst resolved and high quality spectrum of a quiet M dwarf at Lya. Using anenergy diagram for exoplanets and an N-body particle simulation, this detectionenables the possible exospheric signature of the hot neptune to be estimated asa ~11% absorption in the Lya stellar emission, for a typical mass-loss rate of10^10 g/s. The atmosphere of the planet GJ436b is found to be stable toevaporation, and should be readily observable with HST. We also derive acorrelation between X-ray and Lya emissions for M dwarfs. This correlation willbe useful for predicting the evaporation signatures of planets transiting otherquiet M dwarfs.

HST/STIS Lyman-alpha observations of the quiet M dwarf GJ436: Predictions for the exospheric transit signature of the hot neptune GJ436b