Spectropolarimetric signatures of Earth-like extrasolar planets

We present results of numerical simulations of the flux (irradiance), F, and the degree of polarization (i.e. the ratio of polarized to total flux), P, of light that is reflected by Earth-like extrasolar planets orbiting solar-type stars, as functions of the wavelength (from 0.3 to 1.0 micron, with 0.001 micron spectral resolution) and as functions of the planetary phase angle. We use different surface coverages for our model planets, including vegetation and a Fresnel reflecting ocean, and clear and cloudy atmospheres. Our adding-doubling radiative transfer algorithm, which fully includes multiple scattering and polarization, handles horizontally homogeneous planets only; we simulate fluxes and polarization of horizontally inhomogeneous planets by weighting results for homogeneous planets. Like the flux, F, the degree of polarization, P, of the reflected starlight is shown to depend strongly on the phase angle, on the composition and structure of the planetary atmosphere, on the reflective properties of the underlying surface, and on the wavelength, in particular in wavelength regions with gaseous absorption bands. The sensitivity of P to a planet's physical properties appears to be different than that of F. Combining flux with polarization observations thus makes for a strong tool for characterizing extrasolar planets. The calculated total and polarized fluxes will be made available through the CDS.Comment: 31 pages text, 17 figures, 1 table Submitted to A&

Modeled flux and polarisation signals of horizontally inhomogeneous exoplanets, applied to Earth--like planets

We present modeled flux and linear polarisation signals of starlight that is reflected by spatially unresolved, horizontally inhomogeneous planets and discuss the effects of including horizontal inhomogeneities on the flux and polarisation signals of Earth-like exoplanets. Our code is based on an efficient adding--doubling algorithm, which fully includes multiple scattering by gases and aerosol/cloud particles. We divide a model planet into pixels that are small enough for the local properties of the atmosphere and surface (if present) to be horizontally homogeneous. Given a planetary phase angle, we sum up the reflected total and linearly polarised fluxes across the illuminated and visible part of the planetary disk, taking care to properly rotate the polarized flux vectors towards the same reference plane. We compared flux and polarisation signals of simple horizontally inhomogeneous model planets against results of the weighted sum approximation, in which signals of horizontally homogeneous planets are combined. Apart from cases in which the planet has only a minor inhomogeneity, the signals differ significantly. In particular, the shape of the polarisation phase function appears to be sensitive to the horizontal inhomogeneities. The same holds true for Earth-like model planets with patchy clouds above an ocean and a sandy continent. Our simulations clearly show that horizontal inhomogeneities leave different traces in flux and polarisation signals. Combining flux with polarisation measurements would help retrieving the atmospheric and surface patterns on a planet

The influence of forward-scattered light in transmission measurements of (exo)planetary atmospheres

[Abridged] The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan's atmosphere between 2.0 and 2.8 micron and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab.Comment: Icarus, accepted for publicatio

Looking for the rainbow on exoplanets covered by liquid and icy water clouds

Looking for the primary rainbow in starlight that is reflected by exoplanets appears to be a promising method to search for liquid water clouds in exoplanetary atmospheres. Ice water clouds, that consist of water crystals instead of water droplets, could potentially mask the rainbow feature in the planetary signal by covering liquid water clouds. Here, we investigate the strength of the rainbow feature for exoplanets that have liquid and icy water clouds in their atmosphere, and calculate the rainbow feature for a realistic cloud coverage of Earth. We calculate flux and polarization signals of starlight that is reflected by horizontally and vertically inhomogeneous Earth--like exoplanets, covered by patchy clouds consisting of liquid water droplets or water ice crystals. The planetary surfaces are black. On a planet with a significant coverage of liquid water clouds only, the total flux signal shows a weak rainbow feature. Any coverage of the liquid water clouds by ice clouds, however, dampens the rainbow feature in the total flux, and thus the discovery of liquid water in the atmosphere. On the other hand, detecting the primary rainbow in the polarization signal of exoplanets appears to be a powerful tool for detecting liquid water in exoplanetary atmospheres, even when these clouds are partially covered by ice clouds. In particular, liquid water clouds covering as little as 10%-20% of the planetary surface, with more than half of these covered by ice clouds, still create a polarized rainbow feature in the planetary signal. Indeed, calculations of flux and polarization signals of an exoplanet with a realistic Earth--like cloud coverage, show a strong polarized rainbow feature.Comment: accepted for publication in Astronomy & Astrophysic

Scattering matrices and expansion coefficients of Martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of Martian analogue palagonite particles for scattering angles ranging from 3 to 174 degrees and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0 to 180 degrees. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl

Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Exploring the differentials between servant and transformational leadership

Academic and managerial opinion has been divided for years over the respective merits of servant leadership and transformational leadership styles. However, a new study suggests that one can be just as effective as the other

Individual differences as antecedents of leader behavior: Towards an understanding of multi-level outcomes

The leadership research on individual differences is going through a period of revival. However, due to the substantial number of variables in this area and the different knowledge bases they are associated with (e.g., psychology, endocrinology, genetics), the literature is also becoming highly fragmented as it grows. This fragmentation is preventing different literature streams from effectively communicating with each other and synthesizing the rapidly expanding body of knowledge. Consequently, the continued growth of the individual differences literature is at risk. Therefore, we believe that classifying the relevant literature streams and reviewing the key variables in those streams will be beneficial. We do so by organizing this review and research agenda of the leadership literature on individual differences around the recent model developed by Antonakis, Day, and Schyns (2012). In doing so, we hope to unify some of the future research efforts around a recent and recognized conceptual model, and in turn facilitate communication between these different streams of literature. Moreover, insights from this literature also allow us to propose additions and refinements to the model of Antonakis, Day, and Schyns (2012) that may help scholars by indicating other fruitful areas for future research on individual differences

Motivation in words : promotion- and prevention-oriented leader communication in times of crisis.

Research demonstrates that situational uncertainty or crisis strongly influences the endorsement of the more charismatic or decisive leadership styles and that inspirational communication is at the heart of these styles. However, there is currently little understanding of what leaders should convey through their communication to be endorsed in crisis. Based on regulatory focus theory, we argue that times of crisis make leaders who use more promotion-oriented communication more likely to be endorsed and leaders who use more prevention-oriented communication less likely to be endorsed. Results of Study 1, an archival study of U.S. presidents, show that presidents who use more promotion-oriented communication are more endorsed but only if economic growth is low or if inflation is high, while no effects of the use of prevention orientation of communication surfaces. Results of Study 2, a laboratory experiment, show that leaders who communicate a promotion orientation, as compared to a prevention orientation, motivate higher performance in participants in a crisis condition, but that there is no difference in a no-crisis (i.e. control) condition. Finally, results of Study 3, a scenario experiment, demonstrate that organizational leaders that communicate more promotion-oriented (as opposed to more prevention-oriented) have a higher chance of being endorsed but only in times of crisis and that this effect is mediated by followers’ motivation to realize the plans of the leader