Circular polarization signals of cloudy (exo)planets

The circular polarization of light that planets reflect is often neglected because it is very small compared to the linear polarization. It could, however, provide information on a planet's atmosphere and surface, and on the presence of life, because homochiral molecules that are the building blocks of life on Earth are known to reflect circularly polarized light. We compute $P_c$, the degree of circular polarization, for light that is reflected by rocky (exo)planets with liquid water or sulfuric acid solution clouds, both spatially resolved across the planetary disk and, for planets with patchy clouds, integrated across the planetary disk, for various planetary phase angles $\alpha$. The optical thickness and vertical distribution of the atmospheric gas and clouds, the size parameter and refractive index of the cloud particles, and $\alpha$ all influence $P_c$. Spatially resolved, $P_c$ varies between $\pm 0.20\%$ (the sign indicates the polarization direction). Only for small gas optical thicknesses above the clouds do significant sign changes (related to cloud particle properties) across the planets' hemispheres occur. For patchy clouds, the disk--integrated $P_c$ is typically smaller than $\pm 0.025\%$, with maximums for $\alpha$ between $40^\circ$ and $70^\circ$, and $120^\circ$ to $140^\circ$. As expected, the disk--integrated $P_c$ is virtually zero at $\alpha=0^\circ$ and 180$^\circ$. The disk--integrated $P_c$ is also very small at $\alpha \approx 100^\circ$. Measuring circular polarization signals appears to be challenging with current technology. The small atmospheric circular polarization signal could, however, allow the detection of circular polarization due to homochiral molecules. Confirmation of the detectability of such signals requires better knowledge of the strength of circular polarization signals of biological sources.Comment: 15 pages, 11 figures, Accepted for publication in Astronomy and Astrophysic

The O2 A-band in fluxes and polarization of starlight reflected by Earth-like exoplanets

Earth-like, potentially habitable exoplanets are prime targets in the search for extraterrestrial life. Information about their atmosphere and surface can be derived by analyzing light of the parent star reflected by the planet. We investigate the influence of the surface albedo $A_{\rm s}$, the optical thickness $b_{\rm cloud}$ and altitude of water clouds, and the mixing ratio $\eta$ of biosignature O$_2$ on the strength of the O$_2$ A-band (around 760 nm) in flux and polarization spectra of starlight reflected by Earth-like exoplanets. Our computations for horizontally homogeneous planets show that small mixing ratios ($\eta$ < 0.4) will yield moderately deep bands in flux and moderate to small band strengths in polarization, and that clouds will usually decrease the band depth in flux and the band strength in polarization. However, cloud influence will be strongly dependent on their properties such as optical thickness, top altitude, particle phase, coverage fraction, horizontal distribution. Depending on the surface albedo, and cloud properties, different O$_2$ mixing ratios $\eta$ can give similar absorption band depths in flux and band strengths in polarization, in particular if the clouds have moderate to high optical thicknesses. Measuring both the flux and the polarization is essential to reduce the degeneracies, although it will not solve them, in particular not for horizontally inhomogeneous planets. Observations at a wide range of phase angles and with a high temporal resolution could help to derive cloud properties and, once those are known, the mixing ratio of O$_2$ or any other absorbing gas.Comment: 21 pages, 20 figures, accepted for publication in Ap

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

PyMieDAP: a Python--Fortran tool to compute fluxes and polarization signals of (exo)planets

PyMieDAP (the Python Mie Doubling-Adding Programme) is a Python--based tool for computing the total, linearly, and circularly polarized fluxes of incident unpolarized sun- or starlight that is reflected by, respectively, Solar System planets or moons, or exoplanets at a range of wavelengths. The radiative transfer computations are based on an adding--doubling Fortran algorithm and fully include polarization for all orders of scattering. The model (exo)planets are described by a model atmosphere composed of a stack of homogeneous layers containing gas and/or aerosol and/or cloud particles bounded below by an isotropically, depolarizing surface (that is optionally black). The reflected light can be computed spatially--resolved and/or disk--integrated. Spatially--resolved signals are mostly representative for observations of Solar System planets (or moons), while disk--integrated signals are mostly representative for exoplanet observations. PyMieDAP is modular and flexible, and allows users to adapt and optimize the code according to their needs. PyMieDAP keeps options open for connections with external programs and for future additions and extensions. In this paper, we describe the radiative transfer algorithm that PyMieDAP is based on and the code's principal functionalities. And we provide benchmark results of PyMieDAP that can be used for testing its installation and for comparison with other codes. PyMieDAP is available online under the GNU GPL license at http://gitlab.com/loic.cg.rossi/pymiedapComment: 15 pages, 7 figures, 4 tables. Accepted for publication in Astronomy and Astrophysic

Spectral and Temporal Variability of Earth Observed in Polarization

We present a comprehensive set of spectropolarimetric observations of Earthshine as obtained by FORS2 at the VLT for phase angles from 50degree to 135degree (Sun-Earth-Moon angle), covering a spectral range from 430nm to 920nm. The degree of polarization in BVRI passbands, the differential polarization vegetation index, and the equivalent width of the O2A polarization band around 760nm are determined with absolute errors around 0.1 percent in the degree of polarization. Earthshine polarization spectra are corrected for the effect of depolarization introduced by backscattering on the lunar surface, introducing systematic errors of the order of 1 percent in the degree of polarization. Distinct viewing sceneries such as observing the Atlantic or Pacific side in Earthshine yield statistically different phase curves. The equivalent width defined for the O2A band polarization is found to vary from -5nm to +2nm. A differential polarized vegetation index is introduced and reveals a larger vegetation signal for those viewing sceneries that contain larger fractions of vegetated surface areas. We corroborate the observed correlations with theoretical models from the literature, and conclude that the Vegetation Red Edge(VRE) is a robust and sensitive signature in polarization spectra of planet Earth. The overall behaviour of polarization of planet Earth in the continuum and in the O2A band can be explained by existing models. Biosignatures such as the O2A band and the VRE are detectable in Earthshine polarization with a high degree of significance and sensitivity. An in-depth understanding of Earthshines temporal and spectral variability requires improved models of Earths biosphere, as a prerequisite to interpret possible detections of polarised biosignatures in earthlike exoplanets in the future.Comment: 19 pages, 14 figures, 3 table

Traces of exomoons in computed flux and polarization phase curves of starlight reflected by exoplanets

Context: Detecting moons around exoplanets is a major goal of current and future observatories. Moons are suspected to influence rocky exoplanet habitability, and gaseous exoplanets in stellar habitable zones could harbour abundant and diverse moons to target in the search for extraterrestrial habitats. Exomoons will contribute to exoplanetary signals but are virtually undetectable with current methods. Aims: We identify and analyse traces of exomoons in the temporal variation of total and polarised fluxes of starlight reflected by an Earth-like exoplanet and its spatially unresolved moon across all phase angles, with both orbits viewed in an edge-on geometry. Methods: We compute the total and linearly polarised fluxes, and the degree of linear polarization P of starlight that is reflected by the exoplanet with its moon along their orbits, accounting for the temporal variation of the visibility of the planetary and lunar disks, and including effects of mutual transits and mutual eclipses. Our computations pertain to a wavelength of 450 nm. Results: Total flux F shows regular dips due to planetary and lunar transits and eclipses. Polarization P shows regular peaks due to planetary transits and lunar eclipses, and P can increase and/or slightly decrease during lunar transits and planetary eclipses. Changes in F and P will depend on the radii of the planet and moon, on their reflective properties, and their orbits, and are about one magnitude smaller than the smooth background signals. The typical duration of a transit or an eclipse is a few hours. Conclusions: Traces of an exomoon due to planetary and lunar transits and eclipses show up in F and P of sunlight reflected by planet-moon systems and could be searched for in exoplanet flux and/or polarisation phase functions.Comment: Accepted for publication in Astronomy & Astrophysic

Modelling reflected polarised light from close-in giant exoplanet WASP-96b using PolHEx (Polarisation of Hot Exoplanets)

We present the Polarisation of Hot Exoplanets (PolHEx) code for modelling the total flux (F) and degree of linear polarisation (P) of light spectra reflected by close-in, tidally locked exoplanets. We use the output from a global climate model (GCM) combined with a kinetic cloud model of hot Jupiter WASP-96b as a base to investigate effects of atmospheric longitudinal-latitudinal inhomogeneities on these spectra. We model F and P-spectra as functions of wavelength and planet orbital phase for various model atmospheres. We find different materials and sizes of cloud particles to impact the reflected flux F, and particularly the linear polarisation state P. A range of materials are used to form inhomogeneous mixed-material cloud particles (Al2O3, Fe2O3, Fe2SiO4, FeO, Fe, Mg2SiO4, MgO, MgSiO3, SiO2, SiO, TiO2), with Fe2O3, Fe, and FeO the most strongly absorbing species. The cloud particles near the relatively cool morning terminator are expected to have smaller average sizes and a narrower size distribution than those near the warmer evening terminator, which leads to different reflected spectra at the respective orbital phases .We also find differences in the spectra of F and P as functions of orbital phase for irregularly or spherically shaped cloud particles. This work highlights the importance of including polarisation in models and future observations of the reflection spectra of exoplanets.Comment: Accepted for publication in MNRA

Modelling reflected polarized light from close-in giant exoplanet WASP-96b using PolHEx (Polarisation of hot exoplanets)

Funding: This project has received funding from STFC, under project number ST/V000861/1. ChH further acknowledges funding from the European Union H2020-MSCA-ITN-2019 under grant agreement number 860470 (CHAMELEON). DS acknowledge financial support from the Austrian Academy of Sciences.We present the Polarisation of Hot Exoplanets (PolHEx) code for modelling the total flux (F) and degree of linear polarisation (P) of light spectra reflected by close-in, tidally locked exoplanets. We use the output from a global climate model (GCM) combined with a kinetic cloud model of hot Jupiter WASP-96b as a base to investigate effects of atmospheric longitudinal-latitudinal inhomogeneities on these spectra. We model F and P-spectra as functions of wavelength and planet orbital phase for various model atmospheres. We find different materials and sizes of cloud particles to impact the reflected flux F, and particularly the linear polarisation state P. A range of materials are used to form inhomogeneous mixed-material cloud particles (Al2O3, Fe2O3, Fe2SiO4, FeO, Fe, Mg2SiO4, MgO, MgSiO3, SiO2, SiO, TiO2), with Fe2O3, Fe, and FeO the most strongly absorbing species. The cloud particles near the relatively cool morning terminator are expected to have smaller average sizes and a narrower size distribution than those near the warmer evening terminator, which leads to different reflected spectra at the respective orbital phases. We also find differences in the spectra of F and P as functions of orbital phase for irregularly or spherically shaped cloud particles. This work highlights the importance of including polarisation in models and future observations of the reflection spectra of exoplanets.Publisher PDFPeer reviewe