Lyman- \alpha ( Ly \alpha ) emission of neutral hydrogen ( \lambda 1 215.67 Â Ã ) is the main contributor to the ultraviolet flux of low-mass stars such as M dwarfs .
It is also the main light source used in studies of the evaporating upper atmospheres of transiting extrasolar planets with ultraviolet transmission spectroscopy .
However , there are very few observations of the Ly \alpha  emissions of quiet M dwarfs , and none exist for those hosting exoplanets .
Here , we present Ly \alpha  observations of the hot-neptune host star GJ 436 with the Hubble Space Telescope Imaging Spectrograph ( HST /STIS ) .
We detect bright emission in the first resolved and high quality spectrum of a quiet M dwarf at Ly \alpha .
Using an energy diagram for exoplanets and an N -body particle simulation , this detection enables the possible exospheric signature of the hot neptune to be estimated as a \sim 11 \% absorption in the Ly \alpha  stellar emission , for a typical mass-loss rate of 10 ^ { 10 }  g s ^ { -1 } .
The atmosphere of the planet GJÂ 436b is found to be stable to evaporation , and should be readily observable with HST .
We also derive a correlation between X-ray and Ly \alpha  emissions for M dwarfs .
This correlation will be useful for predicting the evaporation signatures of planets transiting other quiet M dwarfs .