GJ 1214b revised. Improved trigonometric parallax, stellar parameters, orbital solution, and bulk properties for the super-Earth GJ 1214b

GJ 1214 is orbited by a transiting super-Earth-mass planet. It is a primary target for ongoing efforts to understand the emerging population of super-Earth-mass planets around M dwarfs. We present new precision astrometric measurements, a re-analysis of HARPS radial velocity measurements, and medium-resolution infrared spectroscopy of GJ 1214. We combine these measurements with recent transit follow-up observations and new catalog photometry to provide a comprehensive update of the star-planet properties. The distance is obtained with 0.6% relative uncertainty using CAPScam astrometry. The new value increases the nominal distance to the star by ~10% and is significantly more precise than previous measurements. Updated Doppler measurements combined with published transit observations significantly refine the constraints on the orbital solution. The analysis of the infrared spectrum and photometry confirm that the star is enriched in metals compared to the Sun. Using all this information, combined with empirical mass-luminosity relations for low mass stars, we derive updated values for the bulk properties of the star-planet system. We also use infrared absolute fluxes to estimate the stellar radius and to re-derive the star-planet properties. Both approaches provide very consistent values for the system. Our analysis shows indicates that the favoured mean density of GJ 1214b is 1.6 +/-0.6 g cm^{-3}. We illustrate how fundamental properties of M dwarfs are of paramount importance in the proper characterization of the low mass planetary candidates orbiting them. Given that the distance is now known to better than 1%, interferometric measurements of the stellar radius, additional high precision Doppler observations, and/or or detection of the secondary transit (occultation), are necessary to further improve the constraints on the GJ 1214 star-planet properties.