  Terrestrial Solar System planets either have high mean molecular weight
atmospheres, as with Venus, Mars, and Earth, or no atmosphere at all, as with
Mercury. We do not have sufficient observational information to know if this is
typical of terrestrial planets or a phenomenon unique to the Solar System. The
bulk of atmospheric exoplanet studies have focused on hot Jupiters and
Neptunes, but recent discoveries of small, rocky exoplanets transiting small,
nearby stars provide targets that are amenable to atmospheric study. GJ 1132b
has a radius of 1.2 Earth radii and a mass of 1.6 Earth masses, and orbits an
M-dwarf 12 parsecs away from the Solar System. We present results from five
transits of GJ 1132b taken with the Magellan Clay Telescope and the LDSS3C
multi-object spectrograph. We jointly fit our five data sets when determining
the best-fit transit parameters both for the white light curve and
wavelength-binned light curves. We bin the light curves into 20 nm wavelength
bands to construct the transmission spectrum. Our results disfavor a clear, 10x
solar metallicity atmosphere at 3.7 sigma confidence and a 10% H2O, 90% H2
atmosphere at 3.5 sigma confidence. Our data are consistent with a featureless
spectrum, implying that GJ 1132b has a high mean molecular weight atmosphere or
no atmosphere at all, though we do not account for the possible presence of
aerosols. This result is in agreement with theoretical work which suggests that
a planet of GJ 1132b's mass and insolation should not be able to retain a H2
envelope.
