High-precision eclipse spectrophotometry of transiting terrestrial exoplanets represents a promising path for the first atmospheric characterizations of habitable worlds and the search for life outside our solar system. The detection of terrestrial planets transiting nearby late-type M-dwarfs could make this approach applicable within the next decade, with soon-to-come general facilities. In this context, we previously identified GJ 1214 as a high-priority target for a transit search, as the transit probability of a habitable planet orbiting this nearby M4.5 dwarf would be significantly enhanced by the transiting nature of GJ 1214 b, the super-Earth already known to orbit the star. Based on this observation, we have set up an ambitious high-precision photometric monitoring of GJ 1214 with the Spitzer Space Telescope to probe the inner part of its habitable zone in search of a transiting planet as small as Mars. We present here the results of this transit search. Unfortunately, we did not detect any other transiting planets. Assuming that GJ 1214 hosts a habitable planet larger than Mars that has an orbital period smaller than 20.9 days, our global analysis of the whole Spitzer dataset leads to an a posteriori no-transit probability of ~ 98%. Our analysis allows us to significantly improve the characterization of GJ 1214 b, to measure its occultation depth to be 70+-35 ppm at 4.5 microns, and to constrain it to be smaller than 205ppm (3-sigma upper limit) at 3.6 microns. In agreement with the many transmission measurements published so far for GJ 1214 b, these emission measurements are consistent with both a metal-rich and a cloudy hydrogen-rich atmosphere.
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