The Metallicities of Stars With and Without Transiting Planets

Host star metallicities have been used to infer observational constraints on planet formation throughout the history of the exoplanet field. The giant planet metallicity correlation has now been widely accepted, but questions remain as to whether the metallicity correlation extends to the small terrestrial-sized planets. Here, we report metallicities for a sample of 518 stars in the Kepler field that have no detected transiting planets and compare their metallicity distribution to a sample of stars that hosts small planets (Rp < 1.7 R_Earth). Importantly, both samples have been analyzed in a homogeneous manner using the same set of tools (Stellar Parameters Classification tool; SPC). We find the average metallicity of the sample of stars without detected transiting planets to be [m/H]_SNTP,dwarf = -0.02 +- 0.02 dex and the sample of stars hosting small planets to be [m/H]_STP = -0.02 +- 0.02 dex. The average metallicities of the two samples are indistinguishable within the uncertainties, and the two-sample Kolmogorov-Smirnov test yields a p-value of 0.68 (0.41 sigma), indicating a failure to reject the null hypothesis that the two samples are drawn from the same parent population. We conclude that the homogeneous analysis of the data presented here support the hypothesis that stars hosting small planets have a metallicity similar to stars with no known transiting planets in the same area of the sky.Comment: Accepted for publication in Ap

Thermal Structure and Radius Evolution of Irradiated Gas Giant Planets

We consider the thermal structure and radii of strongly irradiated gas giant planets over a range in mass and irradiating flux. The cooling rate of the planet is sensitive to the surface boundary condition, which depends on the detailed manner in which starlight is absorbed and energy redistributed by fluid motion. We parametrize these effects by imposing an isothermal boundary condition $T \equiv T_{\rm deep}$ below the photosphere, and then constrain $T_{\rm deep}$ from the observed masses and radii. We compute the dependence of luminosity and core temperature on mass, $T_{\rm deep}$ and core entropy, finding that simple scalings apply over most of the relevant parameter space. These scalings yield analytic cooling models which exhibit power-law behavior in the observable age range $0.1-10 {\rm Gyr}$, and are confirmed by time-dependent cooling calculations. We compare our model to the radii of observed transiting planets, and derive constraints on $T_{\rm deep}$. Only HD 209458 has a sufficiently accurate radius measurement that $T_{\rm deep}$ is tightly constrained; the lower error bar on the radii for other planets is consistent with no irradiation. More accurate radius and age measurements will allow for a determination of the correlation of $T_{\rm deep}$ with the equilibrium temperature, informing us about both the greenhouse effect and day-night asymmetries.Comment: submitted to apj. 14 pages, 20 figure

Occurrence and core-envelope structure of 1--4x Earth-size planets around Sun-like stars

Small planets, 1-4x the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R_e planets with orbital periods under 100 days, and 11% have 1-2 R_e planets that receive 1-4x the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 AU, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R_e show that the smallest of them, R < 1.5 R_e, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: rho = 2.32 + 3.19 R/R_e [g/cc]. Larger planets, in the radius range 1.5-4.0 R_e, have densities that decline with increasing radius, revealing increasing amounts of low-density material in an envelope surrounding a rocky core, befitting the appellation "mini-Neptunes." Planets of ~1.5 R_e have the highest densities, averaging near 10 g/cc. The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. One explanation is that the fast formation of rocky cores in protoplanetary disks enriched in heavy elements permits the gravitational accumulation of gas before it vanishes, forming giant planets. But models of the formation of 1-4 R_e planets remain uncertain. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.Comment: 11 pages, 6 figures, accepted for publication Proc. Natl. Acad. Sc