A More Precise Mass for GJ 1214 b and the Frequency of Multiplanet Systems Around Mid-M Dwarfs

We present an intensive effort to refine the mass and orbit of the enveloped terrestrial planet GJ 1214 b using 165 radial velocity (RV) measurements taken with the HARPS spectrograph over a period of 10 years. We conduct a joint analysis of the RVs with archival Spitzer/IRAC transits and measure a planetary mass and radius of 8.17 ± 0.43 M_⊕ and ${2.742}_{-0.053}^{+0.050}$ R_⊕. Assuming that GJ 1214 b is an Earth-like core surrounded by a H/He envelope, we measure an envelope mass fraction of X_env = ${5.24}_{-0.29}^{+0.30}$ %. GJ 1214 b remains a prime target for secondary eclipse observations of an enveloped terrestrial, the scheduling of which benefits from our constraint on the orbital eccentricity of <0.063 at 95% confidence, which narrows the secondary eclipse window to 2.8 hr. By combining GJ 1214 with other mid-M-dwarf transiting systems with intensive RV follow up, we calculate the frequency of mid-M-dwarf planetary systems with multiple small planets and find that ${90}_{-21}^{+5}$ % of mid-M dwarfs with a known planet with mass ∈ [1, 10] M_⊕ and orbital period ∈ [0.5, 50] days, will host at least one additional planet. We rule out additional planets around GJ 1214 down to 3 M_⊕ within 10 days, such that GJ 1214 is a single-planet system within these limits. This result has a ${44}_{-5}^{+9}$ probability given the prevalence of multiplanet systems around mid-M dwarfs. We also investigate mid-M-dwarf RV systems and show that the probability that all reported RV planet candidates are real planets is <12% at 99% confidence, although this statistical argument is unable to identify the probable false positives.