A More Precise Mass for GJ 1214 b and the Frequency of Multiplanet Systems Around Mid-M Dwarfs
Ryan Cloutier, David Charbonneau, Drake Deming, X. Bonfıls, N. Astudillo-Defru
Abstract
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 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>2.742</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.053</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.050</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> 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 = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>5.24</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.29</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.30</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> %. 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>90</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> % 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>44</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>9</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> 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.