GJ 1132b, which orbits an M dwarf, is one of the few known Earth-sized planets, and at 12 pc away it is one of the closest known transiting planets. Receiving roughly 19x Earths insolation, this planet is too hot to be habitable but can inform us about the volatile content of rocky planet atmospheres around cool stars. Using Hubble STIS spectra, we search for a transit in the Lyman-alpha line of neutral hydrogen (Ly-alpha). If we were to observe a deep Ly-alpha absorption signature, that would indicate the presence of a neutral hydrogen envelope flowing from GJ 1132b. On the other hand, ruling out deep absorption from neutral hydrogen may indicate that this planet does not have a detectable amount of hydrogen loss, is not losing hydrogen, or lost hydrogen and other volatiles early in the stars life. We do not detect a transit and determine a 2-sigma upper limit on the effective envelope radius of 0.36 R* in the red wing of the Ly-alpha line, which is the only portion of the spectrum we detect after absorption by the ISM. We analyze the Ly-alpha spectrum and stellar variability of GJ1132, which is a slowly-rotating 0.18 solar mass M dwarf with previously uncharacterized UV activity. Our data show stellar variabilities of 5-22%, which is consistent with the M dwarf UV variabilities of up to 41% found by citet{Loyd2014}. Understanding the role that UV variability plays in planetary atmospheres is crucial to assess atmospheric evolution and the habitability of cooler rocky exoplanets.
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