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