Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

The Kepler Mission has discovered thousands of planets with radii $<4\ R_\oplus$, paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that$M/M_\oplus=2.7(R/R_\oplus)^{1.3}$, a scatter in mass of$1.9\ M_\oplus$, and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes ($R_{pl}<4\ R_\oplus$). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.Comment: 14 pages, 5 figures, 2 tables. Accepted to the Astrophysical Journal on April 28, 2016. Select posterior samples and code to use them to compute the posterior predictive mass distribution are available at https://github.com/dawolfgang/MRrelatio

Beyond 2-D Mass-Radius Relationships: A Nonparametric and Probabilistic Framework for Characterizing Planetary Samples in Higher Dimensions

Fundamental to our understanding of planetary bulk compositions is the relationship between their masses and radii, two properties that are often not simultaneously known for most exoplanets. However, while many previous studies have modeled the two-dimensional relationship between planetary mass and radii, this approach largely ignores the dependencies on other properties that may have influenced the formation and evolution of the planets. In this work, we extend the existing nonparametric and probabilistic framework of \texttt{MRExo} to jointly model distributions beyond two dimensions. Our updated framework can now simultaneously model up to four observables, while also incorporating asymmetric measurement uncertainties and upper limits in the data. We showcase the potential of this multi-dimensional approach to three science cases: (i) a 4-dimensional joint fit to planetary mass, radius, insolation, and stellar mass, hinting of changes in planetary bulk density across insolation and stellar mass; (ii) a 3-dimensional fit to the California Kepler Survey sample showing how the planet radius valley evolves across different stellar masses; and (iii) a 2-dimensional fit to a sample of Class-II protoplanetary disks in Lupus while incorporating the upper-limits in dust mass measurements. In addition, we employ bootstrap and Monte-Carlo sampling to quantify the impact of the finite sample size as well as measurement uncertainties on the predicted quantities. We update our existing open-source user-friendly \texttt{MRExo} \texttt{Python} package with these changes, which allows users to apply this highly flexible framework to a variety of datasets beyond what we have shown here.Comment: Accepted in ApJ. Updated MRExo package and sample scripts available here: https://github.com/shbhuk/mrexo/tree/v1.0dev. Package will be released on PyPI (pip) along with full documentation upon publication in Ap

Synthesis and Assembly of Nonspherical Hollow Silica Colloids Under Confinement

Hard peanut-shaped colloids were synthesized and organized into a degenerate crystal (DC), a phase previously observed only in simulations. In this structure, particle lobes tile a triangular lattice while their orientations uniformly populate the three underlying crystalline directions

Urban Moveability and physical activity in children:longitudinal results from the IDEFICS and I.Family cohort

Background: Physical activity (PA) is one of the major protective behaviours to prevent non-communicable diseases. Positive effects of the built environment on PA are well investigated, although evidence of this association is mostly based on cross-sectional studies. The present study aims to investigate the longitudinal effects of built environment characteristics in terms of a moveability index on PA of children in their transition phase to adolescence using data of the IDEFICS/I.Family cohort. Methods: We used data on 3394 accelerometer measurements of 2488 children and adolescents aged 3 to 15 years old from survey centres of three countries, Germany, Italy, and Sweden, who participated in up to three surveys over 6 years. In network-dependent home neighbourhoods, a moveability index was calculated based on residential density, land use mix, street connectivity, availability of public transport and public open spaces such as green spaces and public playgrounds in order to quantify opportunities for PA of children and adolescents. Linear trajectories of light PA (LPA) and moderate-to-vigorous PA (MVPA) were estimated using linear mixed models accounting for repeated measurements nested within individuals. Least squares means were estimated to quantify differences in trajectories over age. Results: LPA and MVPA declined annually with age by approximately 20 min/day and 2 min/day respectively. In girls, the moveability index showed a consistent significantly positive effect on MVPA (β $\hat{\beta}$ = 2.14, 95% CI: (0.11; 4.16)) for all ages, while in boys the index significantly lessened the decline in LPA with age for each year. (β $\hat{\beta}$ = 2.68, 95% CI: (0.46; 4.90)). Availability of public open spaces was more relevant for MVPA in girls and LPA in boys during childhood, whereas in adolescence, residential density and intersection density became more important. Conclusion: Built environment characteristics are important determinants of PA and were found to have a supportive effect that ameliorates the decline in PA during the transition phase from childhood to adolescence. In childhood environmental support for leisure time PA through public open spaces was found to be the most protective factor whereas in adolescence the positive influence of street connectivity and residential density was most supportive of physical activity. © 2019 The Author(s).Export Date: 30 December 2019; Article; Correspondence Address: Buck, C.; Leibniz Institute for Prevention Research and Epidemiology, BIPS, Achterstraße 30, Germany; email: [email protected]; Funding details: Deutsche Forschungsgemeinschaft, DFG, PI 345/7–1; Funding details: Sixth Framework Programme, FP6, 016181; Funding details: 266044, KBBE 2010–14; Funding details: European Commission, EU; Funding details: German-Israeli Foundation for Scientific Research and Development, GIF; Funding text 1: The work of the first author was funded by the German Research Foundation (DFG) under grant PI 345/7–1. Baseline data collection and the first follow-up work as part of the IDEFICS Study [www.idefics.eu] were financially supported by the European Commission within the Sixth RTD Framework Programme Contract No. 016181 (FOOD). The most recent follow-up was conducted in the framework of the I.Family study [www.ifamilystudy.eu] which was funded by the European Commission within the Seventh RTD Framework Programme Contract No. 266044 (KBBE 2010–14). The research presented here incorporates data from both projects.</p

Importance of Sample Selection in Exoplanet Atmosphere Population Studies

Understanding planet formation requires robust population studies, which are designed to reveal trends in planet properties. In this work, we aim to determine if different methods for selecting populations of exoplanets for atmospheric characterization with JWST could influence population-level inferences. We generate three hypothetical surveys of super-Earths/sub-Neptunes, each spanning a similar radius-insolation flux space. The survey samples are constructed based on three different selection criteria (evenly-spaced-by-eye, binned, and a quantitative selection function). Using an injection-recovery technique, we test how robustly individual-planet atmospheric parameters and population-level parameters can be retrieved. We find that all three survey designs result in equally suitable targets for individual atmospheric characterization, but not equally suitable targets for constraining population parameters. Only samples constructed with a quantitative method or that are sufficiently evenly-spaced-by-eye result in robust population parameter constraints. Furthermore, we find that the sample with the best targets for individual atmospheric study does not necessarily result in the best constrained population parameters. The method of sample selection must be considered. We also find that there may be large variability in population-level results with a sample that is small enough to fit in a single JWST cycle ($\sim$12 planets), suggesting that the most successful population-level analyses will be multi-cycle. Lastly, we infer that our exploration of sample selection is limited by the small number of transiting planets with measured masses around bright stars. Our results can guide future development of programs that aim to determine underlying trends in exoplanet atmospheric properties and, by extension, formation and evolution processes.Comment: 16 pages, 7 figures, accepted Ap