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

Random walks of molecular motors arising from diffusional encounters with immobilized filaments

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation in two and three dimensions. Results are obtained for the fraction of bound motors, their average velocity and displacement. The diffusion coefficient parallel to the filament becomes anomalously large since detachment and subsequent reattachment, in the presence of directed motion of the bound motors, leads to a broadening of the density distribution. The occurrence of protofilaments on a microtubule is modeled by internal states of the binding sites. After a transient time all protofilaments become equally populated.Comment: 20 pages Phys Rev E format + 11 figure

Long-Period Giant Companions to Three Compact, Multiplanet Systems

Understanding the relationship between long-period giant planets and multiple smaller short-period planets is critical for formulating a complete picture of planet formation. This work characterizes three such systems. We present Kepler-65, a system with an eccentric (e = 0.28 ± 0.07) giant planet companion discovered via radial velocities (RVs) exterior to a compact, multiply transiting system of sub-Neptune planets. We also use precision RVs to improve mass and radius constraints on two other systems with similar architectures, Kepler-25 and Kepler-68. In Kepler-68 we propose a second exterior giant planet candidate. Finally, we consider the implications of these systems for planet formation models, particularly that the moderate eccentricity in Kepler-65\u27s exterior giant planet did not disrupt its inner system

Three Super-Earths Orbiting HD 7924

We report the discovery of two super-Earth mass planets orbiting the nearby K0.5 dwarf HD 7924 which was previously known to host one small planet. The new companions have masses of 7.9 and 6.4 M$_\oplus$, and orbital periods of 15.3 and 24.5 days. We perform a joint analysis of high-precision radial velocity data from Keck/HIRES and the new Automated Planet Finder Telescope (APF) to robustly detect three total planets in the system. We refine the ephemeris of the previously known planet using five years of new Keck data and high-cadence observations over the last 1.3 years with the APF. With this new ephemeris, we show that a previous transit search for the inner-most planet would have covered 70% of the predicted ingress or egress times. Photometric data collected over the last eight years using the Automated Photometric Telescope shows no evidence for transits of any of the planets, which would be detectable if the planets transit and their compositions are hydrogen-dominated. We detect a long-period signal that we interpret as the stellar magnetic activity cycle since it is strongly correlated with the Ca II H and K activity index. We also detect two additional short-period signals that we attribute to rotationally-modulated starspots and a one month alias. The high-cadence APF data help to distinguish between the true orbital periods and aliases caused by the window function of the Keck data. The planets orbiting HD 7924 are a local example of the compact, multi-planet systems that the Kepler Mission found in great abundance.Comment: Accepted to ApJ on 4/7/201

The California-Kepler Survey. IV. Metal-rich Stars Host a Greater Diversity of Planets

Probing the connection between a star's metallicity and the presence and properties of any associated planets offers an observational link between conditions during the epoch of planet formation and mature planetary systems. We explore this connection by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets. After correcting for survey incompleteness, we measure planet occurrence: the number of planets per 100 stars with a given metallicity $M$. Planet occurrence correlates with metallicity for some, but not all, planet sizes and orbital periods. For warm super-Earths having $P = 10-100$ days and $R_P = 1.0-1.7~R_E$, planet occurrence is nearly constant over metallicities spanning $-$0.4 dex to +0.4 dex. We find 20 warm super-Earths per 100 stars, regardless of metallicity. In contrast, the occurrence of warm sub-Neptunes ($R_P = 1.7-4.0~R_E$) doubles over that same metallicity interval, from 20 to 40 planets per 100 stars. We model the distribution of planets as $d f \propto 10^{\beta M} d M$, where $\beta$ characterizes the strength of any metallicity correlation. This correlation steepens with decreasing orbital period and increasing planet size. For warm super-Earths $\beta = -0.3^{+0.2}_{-0.2}$, while for hot Jupiters $\beta = +3.4^{+0.9}_{-0.8}$. High metallicities in protoplanetary disks may increase the mass of the largest rocky cores or the speed at which they are assembled, enhancing the production of planets larger than 1.7 $R_E$. The association between high metallicity and short-period planets may reflect disk density profiles that facilitate the inward migration of solids or higher rates of planet-planet scattering.Comment: 32 pages, 15 figures, 9 tables, accepted for publication in The Astronomical Journa

CKS VIII: Eccentricities of Kepler Planets and Tentative Evidence of a High Metallicity Preference for Small Eccentric Planets

Characterizing the dependence of the orbital architectures and formation environments on the eccentricity distribution of planets is vital for understanding planet formation. In this work, we perform statistical eccentricity studies of transiting exoplanets using transit durations measured via Kepler combined with precise and accurate stellar radii from the California-Kepler Survey and Gaia. Compared to previous works that characterized the eccentricity distribution from transit durations, our analysis benefits from both high precision stellar radii ($\sim$3%) and a large sample of $\sim$1000 planets. We observe that that systems with only a single observed transiting planet have a higher mean eccentricity ($\bar{e} \sim 0.21$) than systems with multiple transiting planets ($\bar{e} \sim 0.05$), in agreement with previous studies. We confirm the preference for high and low eccentricity subpopulations among the singly transiting systems. Finally, we show suggestive new evidence that high $e$ planets in the Kepler sample are preferentially found around high metallicity ([Fe/H] $>0$) stars. We conclude by discussing the implications on planetary formation theories

Constraints on the Obliquities of Kepler Planet-Hosting Stars

Stars with hot Jupiters have obliquities ranging from 0-180 degrees, but relatively little is known about the obliquities of stars with smaller planets. Using data from the California-Kepler Survey, we investigate the obliquities of stars with planets spanning a wide range of sizes, most of which are smaller than Neptune. First, we identify 156 planet hosts for which measurements of the projected rotation velocity (vsini) and rotation period are both available. By combining estimates of v and vsini, we find nearly all the stars to be compatible with high inclination, and hence, low obliquity (less than about 20 degrees). Second, we focus on a sample of 159 hot stars (> 6000K) for which vsini is available but not necessarily the rotation period. We find 6 stars for which vsini is anomalously low, an indicator of high obliquity. Half of these have hot Jupiters, even though only 3% of the stars that were searched have hot Jupiters. We also compare the vsini distribution of the hot stars with planets to that of 83 control stars selected without prior knowledge of planets. The mean vsini of the control stars is lower than that of the planet hosts by a factor of approximately pi/4, as one would expect if the planet hosts have low obliquities. All these findings suggest that the Kepler planet-hosting stars generally have low obliquities, with the exception of hot stars with hot Jupiters.Comment: AJ, in pres

The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets

The size of a planet is an observable property directly connected to the physics of its formation and evolution. We used precise radius measurements from the California-Kepler Survey (CKS) to study the size distribution of 2025 $\textit{Kepler}$ planets in fine detail. We detect a factor of $\geq$2 deficit in the occurrence rate distribution at 1.5-2.0 R$_{\oplus}$. This gap splits the population of close-in ($P$ < 100 d) small planets into two size regimes: R$_P$ < 1.5 R$_{\oplus}$ and R$_P$ = 2.0-3.0 R$_{\oplus}$, with few planets in between. Planets in these two regimes have nearly the same intrinsic frequency based on occurrence measurements that account for planet detection efficiencies. The paucity of planets between 1.5 and 2.0 R$_{\oplus}$ supports the emerging picture that close-in planets smaller than Neptune are composed of rocky cores measuring 1.5 R$_{\oplus}$ or smaller with varying amounts of low-density gas that determine their total sizes.Comment: Paper III in the California-Kepler Survey series, accepted to the Astronomical Journa

Molecular Spiders with Memory

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bound to these altered segments more weakly. Inspired by these experiments we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider) the slowdown does not effect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias towards unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.Comment: 10 pages, 3 figure

Walks of molecular motors in two and three dimensions

Molecular motors interacting with cytoskeletal filaments undergo peculiar random walks consisting of alternating sequences of directed movements along the filaments and diffusive motion in the surrounding solution. An ensemble of motors is studied which interacts with a single filament in two and three dimensions. The time evolution of the probability distribution for the bound and unbound motors is determined analytically. The diffusion of the motors is strongly enhanced parallel to the filament. The analytical expressions are in excellent agreement with the results of Monte Carlo simulations.Comment: 7 pages, 2 figures, to be published in Europhys. Let