Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.Comment: 10 pages, 5 figures, accepted to ApJ 6/16/201

Kepler-18b,c, and d: A System of Three Planets Confirmed by Transit Timing Variations, Light Curve Validation, Warm-Spitzer Photometry, and Radial Velocity Measurements

We report the detection of three transiting planets around a Sun-like star, which we designate Kepler-18. The transit signals were detected in photometric data from the Kepler satellite, and were confirmed to arise from planets using a combination of large transit-timing variations (TTVs), radial velocity variations, Warm-Spitzer observations, and statistical analysis of false-positive probabilities. The Kepler-18 star has a mass of 0.97 M_☉, a radius of 1.1 R_☉, an effective temperature of 5345 K, and an iron abundance of [Fe/H] = +0.19. The planets have orbital periods of approximately 3.5, 7.6, and 14.9 days. The innermost planet "b" is a "super-Earth" with a mass of 6.9 ± 3.4 M_⊕, a radius of 2.00 ± 0.10 R_⊕, and a mean density of 4.9 ± 2.4 g cm^3. The two outer planets "c" and "d" are both low-density Neptune-mass planets. Kepler-18c has a mass of 17.3 ± 1.9 M_⊕, a radius of 5.49 ± 0.26 R_⊕, and a mean density of 0.59 ± 0.07 g cm^3, while Kepler-18d has a mass of 16.4 ± 1.4 M_⊕, a radius of 6.98 ± 0.33 R_⊕ and a mean density of 0.27 ± 0.03 g cm^3. Kepler-18c and Kepler-18d have orbital periods near a 2:1 mean-motion resonance, leading to large and readily detected TTVs

The Kepler-454 System: A Small, Not-rocky Inner Planet, a Jovian World, and a Distant Companion

Kepler-454 (KOI-273) is a relatively bright (V = 11.69 mag), Sun-like star that hosts a transiting planet candidate in a 10.6 day orbit. From spectroscopy, we estimate the stellar temperature to be 5687 ± 50 K, its metallicity to be [m/H] = 0.32 ± 0.08, and the projected rotational velocity to be v sin i 10 years and mass >12.1 MJ. The 12 exoplanets with radii <2.7 R_⊕ and precise mass measurements appear to fall into two populations, with those <1.6 R_⊕ following an Earth-like composition curve and larger planets requiring a significant fraction of volatiles. With a density of 2.76 ± 0.73 g cm^(−3), Kepler-454b lies near the mass transition between these two populations and requires the presence of volatiles and/or H/He gas

Fully Point-wise Convolutional Neural Network for Modeling Statistical Regularities in Natural Images

Modeling statistical regularity plays an essential role in ill-posed image processing problems. Recently, deep learning based methods have been presented to implicitly learn statistical representation of pixel distributions in natural images and leverage it as a constraint to facilitate subsequent tasks, such as color constancy and image dehazing. However, the existing CNN architecture is prone to variability and diversity of pixel intensity within and between local regions, which may result in inaccurate statistical representation. To address this problem, this paper presents a novel fully point-wise CNN architecture for modeling statistical regularities in natural images. Specifically, we propose to randomly shuffle the pixels in the origin images and leverage the shuffled image as input to make CNN more concerned with the statistical properties. Moreover, since the pixels in the shuffled image are independent identically distributed, we can replace all the large convolution kernels in CNN with point-wise ($1*1$) convolution kernels while maintaining the representation ability. Experimental results on two applications: color constancy and image dehazing, demonstrate the superiority of our proposed network over the existing architectures, i.e., using 1/10$\sim$1/100 network parameters and computational cost while achieving comparable performance.Comment: 9 pages, 7 figures. To appear in ACM MM 201

Steady-state MreB helices inside bacteria: dynamics without motors

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasi-static evolution of the helical pitch with cell growth, as well as timescales of helix turnover and denovo establishment. We find that while the body of a polarized MreB helix treadmills towards its slow-growing end, the fast-growing tips of laterally associated protofilaments move towards the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.Comment: 7 figures, 1 tabl

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

Orbital Orientations of Exoplanets: HAT-P-4b is Prograde and HAT-14b is Retrograde

We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of λ = –4.9 ± 11.9 deg. In contrast, HAT-P-14b is retrograde, with λ = 189.1 ± 5.1 deg. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tidal dissipation are responsible for the short-period orbits of many exoplanets. In addition, our data revealed a third body in the HAT-P-4 system, which could be a second planet or a companion star

The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced

We have established precise planet radii, semimajor axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. In this sample, we find that planets within a single multi-planet system have correlated sizes: each planet is more likely to be the size of its neighbor than a size drawn at random from the distribution of observed planet sizes. In systems with three or more planets, the planets tend to have a regular spacing: the orbital period ratios of adjacent pairs of planets are correlated. Furthermore, the orbital period ratios are smaller in systems with smaller planets, suggesting that the patterns in planet sizes and spacing are linked through formation and/or subsequent orbital dynamics. Yet, we find that essentially no planets have orbital period ratios smaller than $1.2$, regardless of planet size. Using empirical mass-radius relationships, we estimate the mutual Hill separations of planet pairs. We find that $93\%$ of the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of $\sim20$ mutual Hill radii is most common. We also find that when comparing planet sizes, the outer planet is larger in $65 \pm 0.4\%$ of cases, and the typical ratio of the outer to inner planet size is positively correlated with the temperature difference between the planets. This could be the result of photo-evaporation.Comment: Published in The Astronomical Journal. 15 pages, 17 figure