We study the ellipticity of galaxy cluster halos as characterized by the distribution of cluster galaxies and as measured with weak lensing. We use monte-carlo simulations of elliptical cluster density profiles to estimate and correct for Poisson noise bias, edge bias and projection effects. We apply our methodology to 10,428 SDSS clusters identified by the redMaPPer algorithm with richness above 20. We find a mean ellipticity = 0.271 ± 0.002 (stat) ±0.031 (sys) corresponding to an axis ratio = 0.573 ± 0.002 (stat) ±0.039 (sys). We compare this ellipticity of the satellites to the halo shape, through a stacked lensing measurement using optimal estimators of the lensing quadrupole based on Clampitt and Jain (2016). We find a best-fit axis ratio of 0.56 ± 0.09 (stat) ±0.03 (sys), consistent with the ellipticity of the satellite distribution. Thus cluster galaxies trace the shape of the dark matter halo to within our estimated uncertainties. Finally, we restack the satellite and lensing ellipticity measurements along the major axis of the cluster central galaxy's light distribution. From the lensing measurements we infer a misalignment angle with an RMS of 30 • ± 10 • when stacking on the central galaxy. We discuss applications of halo shape measurements to test the effects of the baryonic gas and AGN feedback, as well as dark matter and gravity. The major improvements in signal-to-noise expected with the ongoing Dark Energy Survey and future surveys from LSST, Euclid and WFIRST will make halo shapes a useful probe of these effects.

The radius-period distribution of exoplanets has been characterized by the Kepler survey, and the empirical mass-radius relation by the subset of Kepler planets with mass measurements. We combine the two in order to constrain the joint mass-radius-period distribution of Kepler transiting planets. We employ hierarchical Bayesian modeling and mixture models to formulate four models with varying complexity and fit these models to the data. We find that the most complex models that treat planets with significant gaseous envelopes, evaporated core planets, and intrinsically rocky planets as three separate populations are preferred by the data and provide the best fit to the observed distribution of Kepler planets. We use these models to calculate occurrence rates of planets in different regimes and to predict masses of Kepler planets, revealing the model dependent nature of both. When using models with envelope mass loss to calculate η ⊕ , we find nearly an order of magnitude drop, indicating that many Earth-like planets discovered with Kepler may be evaporated cores which do not extrapolate out to higher orbital periods. This work provides a framework for higher-dimensional studies of planet occurrence and for using mixture models to incorporate different theoretical populations of planets.

The interaction of silver(I) cations with octamolybdate [Mo 8 O 26 ] 4has been investigated by applying the principles of the building-block concept to the well established silver-octamolybdate reaction system. The self-assembly of dimeric {Ag 2 } linkers allows the formation and isolation of chains and networks where [Mo 8 O 26 ] 4clusters are cross-linked by silver(I) cations. The influence of the solvent on the overall topology has been studied, and the role of the counterion on the resulting structure has been highlighted in each assembly. Fine-tuning of the metal-metal distances of the dimeric {Ag 2 } linking units has been achieved by using different coordinating solvents which act as bridges. Five compounds based on silver octamolybdate building blocks have been isolated, including an uncommon intermediate ((Ph 4 P) 2n [Ag 2 (DMF) 2 (Mo 8 O 26 )] n • 2DMF, and (H 2 NMe 2 ) 2n -[Ag 2 (DMF) 2 (Mo 8 O 26 )] n • 2DMF), and a two-dimensional cross-linked network ([(Ag(DMF)) 2 (Ag(DMF) 2 ) 2 Mo 8 O 26 ] n ). Each compound has been characterized by single-crystal X-ray diffraction, elemental analysis, and FT-IR.

Chameleon theories of gravity predict that the gaseous component of isolated dwarf galaxies rotates with a faster velocity than the stellar component. In this paper, we exploit this effect to obtain new constraints on the model parameters using the measured rotation curves of six low surface brightness galaxies. For f (R) theories, we rule out values of fR0 > 10 −6 . For more general theories, we find that the constraints from Cepheid variable stars are currently more competitive than the bounds we obtain here but we are able to rule out self-screening parameters χc > 10 −6 for fifth-force strengths (coupling of the scalar to matter) as low as 0.05 the Newtonian force. This region of parameter space has hitherto been inaccessible to astrophysical probes. We discuss the future prospects for improving these bounds.