Planet Size Distribution from the Kepler Mission and Its Implications for Planet Formation

Lunar and Planetary Science XLVIII (2017) 1576.pdf

PLANET SIZE DISTRIBUTION FROM THE KEPLER MISSION AND ITS IMPLICATIONS FOR PLANET FORMATION. Li Zeng1, Stein B. Jacobsen1, Eugenia Hyung1, Andrew Vanderburg2, Mercedes Lopez- Morales2, Dimitar D. Sasselov2, Juan Perez-Mercader1, Michail I. Petaev1,2, David W. Latham2, Raphaëlle D. Hay- wood2, and Thomas K. R. Mattson3. 1Department of Earth & Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, MA 02138 ([email protected]), 2Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, 3Sandia National Laboratories, PO Box 5800 MS 1189, Albuquerque, NM 87185.

Introduction: The overall size distribution of ex- Bi-Modal Distribution. More careful analysis of oplanets found by the Kepler mission so far appear to plotting 2-D histogram of fluxes received Vs. radii best fit a log-normal distribution, indicative of a popu- reveals a bi-modal distribution on top of the log- lation formed by a material-limited and time-limited normal. The modes are centered around 1.3 R⊕ and 2.3 growth process. Further detailed analysis of their size R⊕, with a gap at 2 R⊕. This seems to be a universal distribution with respect to that of the stellar fluxes feature throughout FGKM stars. These two modes they receive suggests a bimodal modification on top of could correspond to two types of planets in general, the log-normal distribution - a division of planets into independent of the host star type (especially taking into two groups: rocky planets (<2 R⊕) and water-rich plan- account that M-Dwarf radius in Kepler Input Catalog ets (>2 R⊕) with or without gaseous envelopes. (KIC) could be underestimated by ~20% [4]). Planet Size Distribution from Observations: Log-Normal Distribution. Analyzing the overall radius distribution of 5000+ Kepler planet candidates [1], we have obtained the best fit to a log-normal distribution, indicative of growth process, as planets are formed by growing from small bits and pieces. In na- ture, things that grow from small increments where each increment is stochastic follows a log-normal distribution (growth rate proportional to a certain power of its size or mass), such as the size distributions of apples, our finger nails, and pumpkins (yes, pumpkins, Figure 2. Two-dimensional smoothed histogram of as occasionally we find pumpkins that grown really planet radii versus stellar fluxes they receive. big, but those are rare), and the size distribution of Interpretations: cities on Earth [2]. Two types of Planets: rocky and water worlds. These two distinct types of planets are rocky ones (Earths and super-Earths, planets made up of mostly 0.6 silicates and metals with bulk composition similar to 0.5 Earth), and volatile-rich ones. The volatile-rich planets should be water-worlds (made of a significant amount 0.4 (>25%) of H-compounds: H2O, NH3, CH4, in addition 0.3 Density to the silicates/metal and small amount of gas). They Probability 0.2 are NOT gas dwarfs (H2/He-dominated envelope directly on top of a rocky core), because according to 0.1 condensation/evaporation calculations, there is no way 0.0 0 1 2 3 4 5 to deplete the less volatile O, N, C more than H2 and He, in fact they should be enriched. For example, in r (R⊕) Figure 1. One-dimensional histogram of planet radii. our solar system, the Carbon in Uranus and Neptune Our galaxy is an orchard, in which stars and planets [5] is enriched ~50 times solar, and the O, N, C on grow. They grow from small bits and pieces, thus Jupiter and Saturn are enriched a few up to ~10 times obeying a log-normal distribution. Log-normal distri- solar [5]. In three aspects: (1) volatility (characterized bution maximizes the entropy, implying that the by equilibrium condensation temperature in the nebu- growth process is stochastic. Anything that grows by la), (2) density, and (3) cosmic abundance, the refrac- accumulation of random bits and pieces, with each tory elements making up silicates and metals (Si, Fe, increment stochastic, one would get a log-normal dis- etc.), the H-compound forming elements (O, N, C), tribution. There is a completeness correction that may and H2/He always form a ladder or hierarchy, with the

need to be applied to planets <~1.5 R⊕ [3]. Lunar and Planetary Science XLVIII (2017) 1576.pdf

elements O, N, C always falling in the middle of this ets (<2 R⊕, red and yellow ones in the lower-left part) hierarchy: complies very well with that of silicates/metal (2:1 Table 1. Hierachy of Planet-Building Elements weight ratio) composition trend within uncertain- Cosmic Condensation Density ty. This trend was first pointed out by [10] and later Abundance Temperature (solid) followed up by [11].

(by mass) (K) (g/cc) The second group (>2 R⊕, blue and green ones), on H2/He 1000 1~10 0.2 the other hand, complies reasonably well with the fol- O, N, C 6+1+3 100~300 2 lowing formation scenario: Stage (1) accrete met-

Mg-Silicates 2 1300~1400 4 al/silicate materials up to a few M⊕. Stage (2) accrete Fe, Ni metal 1 1300~1400 8 icy materials (H2O, NH3, CH4, i.e., Hydrogen- There seems to be a problem with water line, as to compounds), if they are available, for another few M⊕, whether the water worlds could form so close to the following the trend of the dashed cyan curves, asymp- star. However, recent isotope dating of meteorites sug- totically approaching 100% H2O, NH3, CH4 curve. gests that planetesimals form quickly after the first Stage (3) then accrete H2/He gas, if they are available, condensates from the nebula (<~1 million years), thus following the trend of the dashed purple curves, as- allowing wet accretion directly from the nebula before ymptotically approaching 100% cold H2/He curve. its dissipation [6]. Other evidence. Contaminated white-dwarf spectra Alternative View: photo-evaporation? An alterna- show H2O-rich planet debris. Although, the amount of tive view is that the two populations (bi-modal distri- debris is small compared to 1 Earth mass, it could indi- bution) is a result of photo-evaporation, but there are cate the existence of water worlds out there, if those controversial results in the literature regarding XUV debris come from the breakup of those planets [12, 13]. evaporation models, some predict a bimodal distribu- Conclusion: The planet formation process leads to tion [7], while some do not [8]. three types of planets: rocky, water and gas worlds.

0.4 0.60.81 1.5 22.53 4 5 6 789101215 20 30 4050 70 100 200 400 600 1000 2000 4000 They give well-defined fields in the mass-radius dia- 25 25 flux(F/F⊕) T(K) ● K-435 b gram as shown in Figure 4. 20 20 3000 2000 T K-12 b● =1000 ● T=3000 K-7 b● K-447 b K @ 100bar K KOI-13 b● 1000 @ CoRoT-1 b● CoRoT-2 b● CoRoT-12 b● CoRoTK--5K11b-●433b● b● 1400 100 CoRoT-5 bK●-8 b● 15 K-412 b● K2-K34-76b●b● 15 bar EPICK●-6211351816b● ●b● K-CoRoT17 b●-18 b● 14 CoRoTK-26-41b●b CoRoTK2-99-19b b 14 300 K-427 b● ● ● K-43 b● 13 CoRoTK-CoRoT-16423b●b-4 b K-CoRoT40 b●-6 b● 13 1000 K-422 b● K-434 b● K-432 b●K-14 b● 12 CoRoT-25K-b●426 b● K-44K-b●428 b● CoRoT-14 b● 12 100 K2-30CoRoTb● -9 b● CoRoT-23●b● K-75 b● 11 KOI●-94 d● ●● CoRoT-17 b CoRoT-27 b● CoRoT11 K-425 b CoRoTK-77K--28b45●KbK●b-●-7415b●b● CoRoTK-419-10b●b●Cold H 100bar K-420 b● 2/He 10 700 K @ CoRoT-K29CoRoT-424b● b●-13 b● 10 30 T=400 ● ● 9 K-9 c●K-9 b ●● Jupiter CoRoT-20 b 9 ● Saturn K-34 b K-16 b● K-539 b● 8 10 500 K-35K2b-●39 b● 50%H2/He 8 7 ● 7 K-18 d 20%H /He KOI-94 e● ● 2 6 CoRoT-8 b 6 K-18 c● 5%H2/He

) K-25 c● 5 CoRoT-24 c● 100%H O, NH ,CH 5 ⊕ CoRoT-22 b● 2 3 4

R Uranus O ( EPIC 211391664 b● K-413 b● 50%H2 Gas K-11 e● GJ 436 b● r 4 ●● K-4 b● 4 GJ 3470 b● ●● KOI-142 b● ) 3(rock 3.5 K-94 b● Neptune MgSiO 3.5 K-95 b● K-11 d● 3 K-20 c● 50%Fe 3 K-11 c● GJ 1214 b● K-20 d● K-K96-25b●b●K-48 c● K-106 e● 2.5 K-11 ●f K-106 c● 2.5 ●K2-38 c●K-131 b● K-K68-454b●b K-10 c● Fe K-102 e●BD+20 594 b● 100% 2 K-48●d● 2 K-98 b● K-18 b ● K-48 b● 55 CncK-e20 b● 1.8 K-11 b● K-113 b● 1.8 KOI-94 b● 1.6 K-21 b●● 1.6 CoRoT-7 b K2-38 b● KK--10K97-b●93b●b●K-99 b● 1.4 K-406 b● 1.4 Water K-100 b● 1.2 1.2 GJ 1132 b●● K-102 d● K-78 b 1 ●● 1 Earth●● 0.9 Venus 0.9 K-406 c● ● 0.8 K-131 c 0.8 0.4 0.60.81 1.5 22.53 4 5 6 789101215 20 30 4050 70 100 200 400 600 1000 2000 4000 Rock m (M⊕) Figure 3. Mass-radius diagram of planets with RV- determined masses, color-coded by Tequilibrium. “Main-Sequence” of Planets: If we restrict our Figure 4. Mass-radius diagram of the three types of samples to the planets with masses determined by the planets that form in protoplanetary disks. radial-velocity (RV) method (generally more robust References: [1] NASA Exoplanet Archive. [2] than other methods [9]), then the distribution of planets Limpert E. et al. (2001) BioScience, 51, 5. [3] Petigura on the mass-radius diagram form a main-sequence, that E. A. (2015) arXiv:1510.03902 [4] Newton E. R. et al. is a limited width array, similar to that of stars on (2015) ApJ, 800, 85. [5] Atreya S. K. et al. (2016) Hertzsprung–Russell Diagram (Luminosity- arXiv:1606.04510 [6] Kleine et al. (2009) GCA, 73, Temperature Diagram). This is consistent with the 5150-5188. [7] Owen J. E. and Wu Y. (2013) ApJ, picture of a material-limited, stepwise growth process, 775, 105. [8] Lopez E. D. and Fortney J. J. (2013) ApJ, including two kinds of planet building materials – 776, 2. [9] Hadden S. and Lithwick Y. (2016) ApJ, rocky/metallic component and ices. 828, 44. [10] Dressing C. D. et al. (2015) ApJ, 800, In Figure 3, comparing the positions of planets to 135. [11] Zeng L. et al. (2016) ApJ, 819, 127 [12] Fa- the mass-radius curves of various theoretical composi- rihi J. et al. (2013) Science, 342, 218. [13] Farihi J. et tions (color curves as labelled): the first group of plan- al. (2016) MNRAS, 463, 3186-3192.