A Search for Additional Bodies in the GJ 1132 Planetary System from 21 Ground-based Transits and a 100 Hour Spitzer Campaign

We present the results of a search for additional bodies in the GJ 1132 system through two methods: photometric transits and transit timing variations of the known planet. We collected 21 transit observations of GJ 1132b with the MEarth-South array since 2015. We obtained 100 near-continuous hours of observations with the $Spitzer$ Space Telescope, including two transits of GJ 1132b and spanning 60% of the orbital phase of the maximum period at which bodies coplanar with GJ 1132b would pass in front of the star. We exclude transits of additional Mars-sized bodies, such as a second planet or a moon, with a confidence of 99.7%. When we combine the mass estimate of the star (obtained from its parallax and apparent $K_s$ band magnitude) with the stellar density inferred from our high-cadence $Spitzer$ light curve (assuming zero eccentricity), we measure the stellar radius of GJ 1132 to be $0.2105_{-0.0085}^{+0.0102}{R}_{\odot }$, and we refine the radius measurement of GJ 1132b to $1.130\pm 0.056R_{\oplus }$. Combined with HARPS RV measurements, we determine the density of GJ 1132b to be $6.2\pm 2.0$\ g cm${}^{-3}$, with the mass determination dominating this uncertainty. We refine the ephemeris of the system and find no evidence for transit timing variations, which would be expected if there was a second planet near an orbital resonance with GJ 1132b.