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

Abstract

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 ten years. We conduct a joint analysis of the RVs with archival Spitzer/IRAC transits and measure a planetary mass and radius of $8.17\pm 0.43M_{\oplus }$ and $2.742_{-0.053}^{+0.050}{R}_{\oplus }$. Assuming GJ 1214 b is an Earth-like core surrounded by a H/He envelope, we measure an envelope mass fraction of $X_{\mathrm{env}}=5.24_{-0.29}^{+0.30}$%. GJ 1214 b remains a prime target for secondary eclipse observations of an enveloped terrestrial, the scheduling of which benefits from our tight constraint on the orbital eccentricity of $<0.063$ at 95% confidence, which narrows the secondary eclipse window to 2.8 hours. 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 $\in [1,10]M_{\oplus }$ and orbital period $\in [0.5,50]$ days, will host at least one additional planet. We rule out additional planets around GJ 1214 down to $3M_{\oplus }$ within 10 days such that GJ 1214 is a single-planet system within these limits, a result that has a $44_{-5}^{+9}$% probability given the prevalence of multi-planet 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.

arXiv commentAccepted for publication in AAS journals. 16 pages (main) + 16 pages (appendices), 9 figures (main) + 24 figures (appendix B). Two additional figures in appendix B could not be included due to compilation errors. These figures are included in the source files

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