Blue, white, and red ocean planets - Simulations of orbital variations in flux and polarization colors

An exoplanet's habitability will depend strongly on the presence of liquid water. Flux and/or polarization measurements of starlight that is reflected by exoplanets could help to identify exo-oceans. We investigate which broadband spectral features in flux and polarization phase functions of reflected starlight uniquely identify exo-oceans. We compute total fluxes F and polarized fluxes Q of starlight reflected by cloud-free and (partly) cloudy exoplanets, for wavelengths from 350 to 865 nm. The ocean surface has waves composed of Fresnel reflecting wave facets and whitecaps, and scattering within the water body is included. Total flux F, polarized flux Q, and degree of polarization P of ocean planets change color from blue, through white, to red at phase angles alpha ranging from 134-108 deg for F, and from 123-157 deg for Q, with cloud coverage fraction fc increasing from 0.0 to 1.0 for F, and to 0.98 for Q. The color change in P only occurs for fc ranging from 0.03-0.98, with the color crossing angle alpha ranging from 88-161 deg. The total flux F of a cloudy, zero surface albedo planet can also change color, and for fc=0.0, an ocean planet's F will not change color for surface pressures ps > 8 bars. Polarized flux Q of a zero surface albedo planet does not change color for any fc. The color change of P of starlight reflected by an exoplanet, from blue, through white, to red with increasing alpha above 88 deg, appears to identify a (partly) cloudy exo-ocean. The color change of polarized flux Q with increasing alpha above 123 deg appears to uniquely identify an exo-ocean, independent of surface pressure or cloud fraction. At the color changing phase angle, the angular distance between a star and its planet is much larger than at the phase angle where the glint appears in reflected light. The color change in polarization thus offers better prospects for detecting exo-oceans.Comment: Accepted for publication in Astron. Astrophys; multicolumn versio

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

Renascent Entrepreneurship

Why should individuals that have exited their firm consider re-entering into entrepreneurship, i.e. become renascent entrepreneurs? According to the logic of economic models of firm dynamics there is no reason to re-enter into entrepreneurship following termination of a previous firm. In contrast, research on nascent entrepreneurship has shown the positive effect of entrepreneurial experience on planning a new firm start. Based on the empirical evidence from a database consisting of ex-entrepreneurs, this study shows that renascent entrepreneurship is a pervasive phenomenon in current society. Especially entrepreneurial human and social capital induce renascent entrepreneurship. In addition, the nature of the firm exit also affects the probability of renascent entrepreneurship.Economics of Entrepreneurship;Entrepreneurial Preferences;Entrepreneurial Skills;Firm Exit;Renascent Entrepreneurship

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