Most 1.6 Earth-Radius Planets are not Rocky Introduction Sub-Neptune, super-Earth-size exoplanets are a new planet class. They account for 0% of the solar systems planets, and 80% of the planet candidates discovered by Kepler. For most planets, Kepler measures just the planet radius and orbital period. When Kepler finds a planet with radius R p, how likely is that planet to be rocky (with its transit radius defined by a rocky surface) versus a mini- Neptune with a thick envelope of H/He and/or astrophysical ices? Objective: To quantitatively constrain the fraction of planets that are sufficiently dense to be rocky, as a function of planet size, using the sub-sample of Kepler transiting planets with Keck-HIRES radial velocity mass constraints. Which Planets are Rocky? Leslie Rogers, Hubble Fellow, Planet Sample Figure 1: Planet Mass-Radius Diagram. Our sample comprises the transiting Kepler planets with Keck HIRES RV follow-up, highlighted in red (Marcy et al. 2014). Other confirmed transiting sub-Neptune-size planets are indicated with black points. The colored curves are theoretical mass-radius relations for constant planet compositions from Seager et al. (2007). Pure silicate places an extreme lower limit on the mass of a volatile-less rocky planet of specified radius. Less dense planets must have some volatiles (in the form of water or H/He), while more dense planets could potentially be rocky, comprised of iron and silicates alone. Mass- radius pairs that are more density than pure iron are unphysical.. MpMp RpRp y, data) Figure 4: Joint posterior pdf for R mid and  R. The two- parameter linear rocky/non-rocky transition model allows for a range of radii (of width  R centered on R mid ) at which high-mass rocky planets and low-mass non-rocky planets co- exist. The planet mass-radius data are consistent with an abrupt transition (  R =0). P(e) Bayesian Evidence Favors Step Function Model E = E p(data|  )p(  )d  E 1 = 4.9 E 2 = 5.0 E 3 3. Linear Transition Results 1. Step Function Transition Figure 5: The posterior pdf of f rocky conditioned on planet radius, R p. For specified R p, a vertical slice through this figure corresponds to p (f rocky |R p, data), and quantifies how the Kepler+Keck RV planets constrain the fraction of R p -size planets that are dense enough to be rocky. Red values of f rocky are favored by the data, while blue values are disfavored. Figure 3: Posterior pdf of R thresh0 and dR thresh /dlogF. In this two-parameter model, the rocky/non-rocky threshold depends on the amount of irradiation the planet is receiving from its star, F p. The planet mass- radius data are consistent with no incident flux dependence (dR thresh /dlogF=0). R mid = R  < 1.62 R  at 95% conf. (marginalized over  R  RpRp f rocky R mid RR Median 1.48 R  95 th Percentile, 1.59 R  p (R thresh |data) R thresh (R  ) Figure 2: Posterior pdf of R thresh The black curve gives the posterior probability of the rocky/non-rocky threshold in the one- parameter step-function model, wherein all planet larger than R thresh have volatiles, while all planets smaller than R thresh are dense enough to be rocky. dR thresh /dlogF = R  (marginalized over R thresh0  RpRp f rocky R thresh 0 F0F0 F RpRp f rocky R thresh Method A hierarchical bayesian analysis approach is adopted. A flat prior on planet mass and radius is typically assumed when fitting RV and transit data. In the hierarchical analysis, the priors on planet M p and R p are opened to modeling. The underlying population of planets has some intrinsic distribution of properties; some M p -R p pairs are more likely than others. A model is chosen for, f rocky (R p, F p,  ) = fraction of planets dense enough to be rocky  = model parameters (constrained using a resampling approach similar to Hogg et al. 2010) MpMp RpRp RpRp MpMp References Hogg, D. W., Myers, A. D., & Bovy, J. 2010, ApJ, 725, 2166 Marcy, G., Isaacson, H., Howard, A. W., et al. 2014, ApJS, 210, 20 Rogers, L. A. (2014) ApJ, submitted Seager, S., Kuchner, M., Hier-Majumder, C. A., & Militzer, B. 2007, ApJ, 669, 1279 I would like to thank Howard Isaacson and Geoff Marcy for sharing samples from their MCMC fits to the Keck- HIRES RV and Kepler photometry data. I also acknowledge support from support provided by NASA through Hubble Fellowship grant #HF Conclusions Most planets larger than 1.6 R  are not rocky, at 95% statistical confidence. This gives insights into the compositions of the 1000s of Kepler planet candidates without measured masses, and motivates an operational definition of “Earth-like” for calculating the occurrence rate of Earth- analogs,  . f rocky sets an upper bound on the fraction of close-in planets formed after protoplanetary disk dispersal. More planet M p -R p points with smaller error bars are needed to resolve the structure of the transition between rocky and non-rocky planets. MgSiO 3 H2OH2O Fe 2. Flux-Dependent Step Function Transition