How to determine an exomoon's sense of orbital motion

We present two methods to determine an exomoon's sense of orbital motion (SOM), one with respect to the planet's circumstellar orbit and one with respect to the planetary rotation. Our simulations show that the required measurements will be possible with the European Extremely Large Telescope (E-ELT). The first method relies on mutual planet-moon events during stellar transits. Eclipses with the moon passing behind (in front of) the planet will be late (early) with regard to the moon's mean orbital period due to the finite speed of light. This "transit timing dichotomy" (TTD) determines an exomoon's SOM with respect to the circumstellar motion. For the ten largest moons in the solar system, TTDs range between 2 and 12 s. The E-ELT will enable such measurements for Earth-sized moons around nearby stars. The second method measures distortions in the IR spectrum of the rotating giant planet when it is transited by its moon. This Rossiter-McLaughlin effect (RME) in the planetary spectrum reveals the angle between the planetary equator and the moon's circumplanetary orbital plane, and therefore unveils the moon's SOM with respect to the planet's rotation. A reasonably large moon transiting a directly imaged planet like beta Pic b causes an RME amplitude of almost 100 m/s, about twice the stellar RME amplitude of the transiting exoplanet HD209458b. Both new methods can be used to probe the origin of exomoons, that is, whether they are regular or irregular in nature.Comment: accepted by ApJ Letters, 6 pages, 5 figures (2 color

Similarity between two projections

Given two orthogonal projections P and Q, we are interested in all unitary operators U such that UP=QU and UQ=PU. Such unitaries U have previously been constructed by Wang, Du, and Dou and also by one of the authors. One purpose of this note is to compare these constructions. Very recently, Dou, Shi, Cui, and Du described all unitaries U with the required property. Their proof is via the two projections theorem by Halmos. We here give a proof based on the supersymmetric approach by Avron, Seiler, and one of the authors.Comment: 12 page

Orbital Circularization of Hot and Cool Kepler Eclipsing Binaries

The rate of tidal circularization is predicted to be faster for relatively cool stars with convective outer layers, compared to hotter stars with radiative outer layers. Observing this effect is challenging, because it requires large and well-characterized samples including both hot and cool stars. Here we seek evidence for the predicted dependence of circularization upon stellar type, using a sample of 945 eclipsing binaries observed by Kepler. This sample complements earlier studies of this effect, which employed smaller samples of better-characterized stars. For each Kepler binary we measure $e\cos\omega$ based on the relative timing of the primary and secondary eclipses. We examine the distribution of $e\cos\omega$ as a function of period for binaries composed of hot stars, cool stars, and mixtures of the two types. At the shortest periods, hot-hot binaries are most likely to be eccentric; for periods shorter than 4 days, significant eccentricities occur frequently for hot-hot binaries, but not for hot-cool or cool-cool binaries. This is in qualitative agreement with theoretical expectations based on the slower dissipation rates of hot stars. However, the interpretation of our results is complicated by the largely unknown ages and evolutionary states of the stars in our sample.Comment: Accepted for publication in Ap

BANANA IV: Two aligned stellar rotation axes in the young eccentric binary system EP Crucis: primordial orientation and tidal alignment

With observations of the EP Cru system, we continue our series of measurements of spin-orbit angles in eclipsing binary star systems, the BANANA project (Binaries Are Not Always Neatly Aligned). We find a close alignment between the sky projections of the rotational and orbital angular momentum vectors for both stars (beta_p = -1.8+-1.6 deg and |beta_s|<17 deg). We also derive precise absolute dimensions and stellar ages for this system. The EP Cru and DI Her systems provide an interesting comparison: they have similar stellar types and orbital properties, but DI Her is younger and has major spin-orbit misalignments, raising the question of whether EP Cru also had a large misalignment at an earlier phase of evolution. We show that tidal dissipation is an unlikely explanation for the good alignment observed today, because realignment happens on the same timescale as spin-orbit synchronization, and the stars in EP Cru are far from syncrhonization (they are spinning 9 times too quickly). Therefore it seems that some binaries form with aligned axes, while other superficially similar binaries are formed with misaligned axes.Comment: ApJ accepted, 10 pages, 7 figure

ECCENTRICITY FROM TRANSIT PHOTOMETRY: SMALL PLANETS IN KEPLER MULTI-PLANET SYSTEMS HAVE LOW ECCENTRICITIES

Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution, and influences its habitability. We make these measurements using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary transit to its orbital eccentricity, if the stellar density is known. Our sample consists of 28 bright stars with precise asteroseismic density measurements. These stars host 74 planets with an average radius of 2.6 R[subscript ⊕]. We find that the eccentricity of planets in Kepler multi-planet systems is low and can be described by a Rayleigh distribution with σ = 0.049 ± 0.013. This is in full agreement with solar system eccentricities, but in contrast to the eccentricity distributions previously derived for exoplanets from radial velocity studies. Our findings are helpful in identifying which planets are habitable because the location of the habitable zone depends on eccentricity, and to determine occurrence rates inferred for these planets because planets on circular orbits are less likely to transit. For measuring eccentricity it is crucial to detect and remove Transit Timing Variations (TTVs), and we present some previously unreported TTVs. Finally transit durations help distinguish between false positives and true planets and we use our measurements to confirm six new exoplanets.European Research Council (ASTERISK Project Grant Agreement 267864

The influence of job, team and organizational level resources on employee well-being, engagement, commitment and extra-role performance : test of a model

Purpose &ndash; Worker well-being continues to be fundamental to the study of work and a primary consideration for how organizations can achieve competitive advantage and sustainable and ethical work practices (Cartwright and Holmes; Harter, Schmidt and Keyes; Wright and Cropanzano). The science and practice of employee engagement, a key indicator of employee well-being, continues to evolve with ongoing incremental refinements to existing models and measures. This study aims to elaborate the Job Demands-Resources model of work engagement (Bakker and Demerouti) by examining how organizational, team and job level factors interrelate to influence engagement and well-being and downstream outcome variables such as affective commitment and extra-role behaviour.Design/methodology/approach &ndash; Structural equations modelling of survey data obtained from 3,437 employees of a large multi-national mining company was used to test the important direct and indirect influence of organizational focused resources (a culture of fairness and support), team focused resources (team climate) and job level resources (career development, autonomy, supervisor support, and role clarity) on employee well-being, engagement, extra-role behaviour and organizational commitment.Findings &ndash; The fit of the proposed measurement and structural models met criterion levels and the structural model accounted for sizable proportions of the variance in engagement/wellbeing (66 percent), extra-role-behaviour (52 percent) and commitment (69 percent).Research limitations/implications &ndash; Study limitations (e.g. cross-sectional research design) and future opportunities are outlined.Originality/value &ndash; The study demonstrates important extensions to the Job Demands-Resources model and provides researchers and practitioners with a simple but powerful motivational framework, a suite of measures, and a map of their inter-relationships which can be used to help understand, develop and manage employee well-being and engagement and their outcomes

On the rms-radius of the proton

We study the world data on elastic electron-proton scattering in order to determine the proton charge rms-radius. After accounting for the Coulomb distortion and using a parameterization that allows to deal properly with the higher moments we find a radius of 0.895+-0.018 fm, which is significantly larger than the radii used in the past.Comment: 9 pages, 2 figures, submitted to Phys.Lett.