We use a planetary albedo model to investigate variations in visible wavelength phase curves of exoplanets. The presence of clouds on these exoplanets significantly alters their planetary albedo spectra. We confirm that non-uniform cloud coverage on the dayside of tidally locked exoplanets will manifest as changes to the magnitude and shift of the phase curve. In this work, we first investigate a test case of our model using a Jupiter-like planet, at temperatures consistent to 2.0 AU insolation from a solar type star, to consider the effect of H2O clouds. We then extend our application of the model to the exoplanet Kepler-7b and consider the effect of varying cloud species, sedimentation efficiency, particle size, and cloud altitude. We show that, depending on the observational filter, the largest possible shift of the phase curve maximum will be 2-10 deg for a Jupiter-like planet, and up to 30 deg (0.08 in fractional orbital phase) for hot-Jupiter exoplanets at visible wavelengths as a function of dayside cloud distribution with a uniformly averaged thermal profile. Finally, we tailor our model for comparison with, and confirmation of, the recent optical phase-curve observations of Kepler-7b with the Kepler space telescope. The average planetary albedo can vary between 0.1-0.6 for the 1300 cloud scenarios that were compared to the observations. We observe that smaller particle size and increasing cloud altitude have a strong effect on increasing albedo. In particular, we show that a set of models where Kepler-7b has roughly half of its dayside covered in small-particle clouds high in the atmosphere, made of bright minerals like MgSiO3 and Mg2SiO4, provide the best fits to the observed offset and magnitude of the phase-curve, whereas Fe clouds are found to have too dark to fit the observations.
Giant exoplanets located >1 AU away from their parent stars have atmospheric environments cold enough for water and/or ammonia clouds. We have developed a new equilibrium cloud and reflected light spectrum model, ExoREL, for widely separated giant exoplanets. The model includes the dissolution of ammonia in liquid water cloud droplets, an effect studied for the first time for exoplanets. While preserving the causal relationship between temperature and cloud condensation, ExoREL is simple and fast to enable efficient exploration of parameter space. Using the model, we find that the mixing ratio…
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 acro…
Here we present the first open-source radiative transfer model for computing the reflected light of exoplanets at any phase geometry, called PICASO: Planetary Intensity Code for Atmospheric Scattering Observations. This code, written in Python, has heritage from a decades old, well-known Fortran model used for several studies of planetary objects within the Solar System and beyond. We have adopted it to include several methodologies for computing both direct and diffuse scattering phase functions, and have added several updates including the ability to compute Raman scattering spectral feature…
The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this paper, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points ($δ$-maps)…
New observational facilities are becoming increasingly capable of observing reflected light from transiting and directly imaged extrasolar planets. In this study, we provide an analytic framework to interpret observed phase curves, geometric albedos, and polarization of giant planet atmospheres. We compute the observables for non-conservative Rayleigh scattering in homogeneous semi-infinite atmospheres using both scalar and vector formalisms. In addition, we compute phase curves and albedos for Lambertian, isotropic, and anisotropic scattering phase functions. We provide analytic expressions f…
In order to recognize a habitable exoplanet from future observed spectra, we present new model reflected spectra and geometric albedo for modern and prebiotic (3.9 Ga) Earth-like exoplanets orbiting within the habitable zone of stars of spectral types F, G, K and M. We compute this for various atmospheric and surface compositions of the planets. Molecules that are potential biosignatures and act as greenhouse agents are incorporated in our model atmosphere. Various combinations of solid and liquid materials such as ocean, coast, land consisting of trees, grass, sand or rocks determine the surf…
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 $η$ 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…
A space telescope capable of high-contrast imaging has been recognized as the avenue toward finding terrestrial planets around nearby Sun-like stars and characterizing their potential habitability. It is thus essential to quantify the capability of reflected light spectroscopy obtained through direct imaging for terrestrial exoplanets, and existing work focused on planetary analogs of modern Earth. Here we go beyond Earth analogs and use a Bayesian retrieval algorithm, ExoReL$^\Re$, to determine what we could learn about terrestrial exoplanets from their reflected light spectra. Recognizing th…
Photosynthesis offers a convenient means of sustaining biospheres. We quantify the constraints for photosynthesis to be functional on the permanent nightside of tidally locked rocky exoplanets via reflected light from their exomoons. We show that the exomoons must be at least half the size of Earth's moon in order for conventional oxygenic photosynthesis to operate. This scenario of photosynthesis is unlikely for exoplanets around late-type M-dwarfs due to the low likelihood of large exomoons and their orbital instability over long timescales. Subsequently, we investigate the prospects for pho…
Reflected light curves observed for exoplanets indicate bright clouds at some of them. We estimate how the light curve and total stellar heating of a planet depend on forward and backward scattering in the clouds based on Pioneer and Cassini spacecraft images of Jupiter and Saturn. We fit analytical functions to the local reflected brightnesses of Jupiter and Saturn depending on the planet's phase. These observations cover broad bands at 0.59-0.72 and 0.39-0.5 μm, and narrow bands at 0.938 (atmospheric window), 0.889 (CH4 absorption band), and 0.24-0.28 μm. We simulate the images of the planet…
There's more to life in reflected light: Simulating the detectability of a range of molecules for high-contrast, high-resolution observations of non-transiting terrestrial exoplanets
The high-contrast imaging technique is meant to provide insight into those planets orbiting several astronomical units from their host star. Space missions such as WFIRST, HabEx, and LUVOIR will measure reflected light spectra of cold gaseous and rocky planets. To interpret these observations we introduce ExoReL$^\Re$ (Exoplanetary Reflected Light Retrieval), a novel Bayesian retrieval framework to retrieve cloud properties and atmospheric structures from exoplanetary reflected light spectra. As a unique feature, it assumes a vertically non-uniform volume mixing ratio profile of water and ammo…
Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure their atmospheric properties, and small and temperate planets will be the focus of the next generation telescopes. In this work, we used our Bayesian retrieval algorithm ExoReL$^{\Re}$ to determine the constraints on the atmospheric properties of sub-Neptune planets from observations taken with a HabEx-like telescope. Small and temperate planets may have a non-H$_2$-dominated atmosphere, and therefore, we introduced the compositional analysis technique in our framework to explore the …
The detectability of planetesimal impacts on imaged exoplanets can be measured using Jupiter during the 1994 comet Shoemaker-Levy 9 events as a proxy. By integrating the whole planet flux with and without impact spots, the effect of the impacts at wavelengths from 2 - 4 microns is revealed. Jupiter's reflected light spectrum in the near-infrared is dominated by its methane opacity including a deep band at 2.3 microns. After the impact, sunlight that would have normally been absorbed by the large amount of methane in Jupiter's atmosphere was instead reflected by the cometary material from the i…
Recent work has shown that sulfur hazes may arise in the atmospheres of some giant exoplanets due to the photolysis of H$_{2}$S. We investigate the impact such a haze would have on an exoplanet's geometric albedo spectrum and how it may affect the direct imaging results of WFIRST, a planned NASA space telescope. For temperate (250 K $<$ T$_{\rm eq}$ $<$ 700 K) Jupiter--mass planets, photochemical destruction of H$_{2}$S results in the production of $\sim$1 ppmv of \seight between 100 and 0.1 mbar, which, if cool enough, will condense to form a haze. Nominal haze masses are found to drastically…
Large Interferometer For Exoplanets (LIFE). X. Detectability of currently known exoplanets and synergies with future IR/O/UV reflected-starlight imaging missions
Reflected starlight measurements will open a new path in the characterization of directly imaged exoplanets. However, we still lack a population study of known targets amenable to this technique. Here, we investigate which of the about 4300 exoplanets confirmed to date are accessible to the Roman Space Telescope's coronagraph (CGI) in reflected starlight at reference wavelengths $λ$=575, 730 and 825 nm. We carry out a population study and also address the prospects for phase-curve measurements. We used the NASA Exoplanet Archive as a reference for planet and star properties, and explored the i…
Polarimetry is about to become a powerful tool for determining the atmospheric properties of exoplanets. To provide the basis for the interpretation of observational results and for predictive studies to guide future observations, sophisticated analysis tools are required. Our goal is to develop a radiative transfer tool that contains all the relevant continuum polarization mechanisms for the comprehensive analysis of the polarized flux resulting from the scattering in the atmosphere of, on the surface of, and in the local planetary environment (e.g., planetary rings, exomoons) of extra-solar …
Similar to the case of solar system planets, reflected starlight from exoplanets is expected to be polarized due to atmospheric scattering and the net disk integrated polarization should be non-zero owing to the asymmetrical illumination of the planetary disk. The computation of the disk-integrated reflected flux and its state of polarization involves techniques for the calculation of the local reflection matrices as well as the numerical recipes for integration over the planetary disks. In this paper, we present a novel approach to calculate the azimuth-dependent reflected intensity vectors a…
Seeing oceans, continents, quasi-static weather, and other surface features on exoplanets may allow us to detect and characterize life outside the solar system. The Proxima b planet resides within the stellar habitable zone allowing for liquid water on its surface, and it may be Earth-like. However, even the largest planned telescopes will not be able to resolve its surface features directly. Here, we demonstrate an inversion technique to image indirectly exoplanet surfaces using observed unresolved reflected light variations over the course of the exoplanets orbital and axial rotation: ExoPla…
For terrestrial exoplanets with thin atmospheres or no atmospheres, the surface contributes light to the reflected light signal of the planet. Measurement of the variety of disk-integrated brightnesses of bodies in the Solar System and the variation with illumination and wavelength is essential for both planning imaging observations of directly imaged exoplanets and interpreting the eventual datasets. Here we measure the change in brightness of the Galilean satellites as a function of planetocentric longitude, illumination phase angle, and wavelength. The data span a range of wavelengths from …
Observing Earth-like exoplanets orbiting within the habitable zone of Sun-like stars and studying their atmospheres in reflected starlight requires contrasts of $\sim1\mathrm{e}{-10}$ in the visible. At such high contrast, starlight reflected by exozodiacal dust is expected to be a significant source of contamination. Here, we present high-fidelity simulations of coronagraphic observations of a synthetic Solar System located at a distance of 10 pc and observed with a 12 m and an 8 m circumscribed aperture diameter space telescope operating at 500 nm wavelength. We explore different techniques …
Planets in highly eccentric orbits form a class of objects not seen within our Solar System. The most extreme case known amongst these objects is the planet orbiting HD~20782, with an orbital period of 597~days and an eccentricity of 0.96. Here we present new data and analysis for this system as part of the Transit Ephemeris Refinement and Monitoring Survey (TERMS). We obtained CHIRON spectra to perform an independent estimation of the fundamental stellar parameters. New radial velocities from AAT and PARAS observations during periastron passage greatly improve our knowledge of the eccentric n…
Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure atmospheric properties. Previous calculations have shown that a change in the orbital phase would cause a spectral signal, but whether this signal may be used to characterize the atmosphere has not been shown. We simulate starshade-enabled observations of the planet 47 Uma b, using the to-date most realistic simulator SISTER to estimate the uncertainties due to residual starlight, solar glint, and exozodiacal light. We then use the Bayesian retrieval algorithm ExoReL$^\Re$ to determin…
Identifying liquid water on the surface of planets is a high priority, as this traditionally defines habitability. One proposed signature of oceans is specular reflection ("glint"), which increases the apparent albedo of a planet at crescent phases. We post-process a global climate model of an Earth-like planet to simulate reflected lightcurves. Significantly, we obtain glint-like phase variations even though we do not include specular reflection in our model. This false positive is the product of two generic properties: 1) for modest obliquities, a planet's poles receive less orbit-averaged s…
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…
Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface inhomogeneities. Previous research has shown that the light curve of an exoplanet can be inverted to obtain a low-resolution map of the planet, as well as constraints on its spin orientation. Estimating the uncertainty on 2D albedo maps has so far remained elusive. Here we present exocartographer, a flexible open-source Bayesian framework for solving the exo-cartography inverse problem. The map is parameterized …
Simulations of exoplanet albedo profiles are key to planning and interpreting future direct imaging observations. In this paper we demonstrate the use of the Planetary Spectrum Generator to produce simulations of reflected light exoplanet spectra. We use PSG to examine multiple issues relevant to all models of directly imaged exoplanet spectra and to produce sample spectra of the bright, nearby exoplanet $\upsilon$ Andromedae d, a potential direct imaging target for next-generation facilities. We introduce a new, fast, and accurate subsampling technique that enables calculations of disk-integr…
The fine precision of photometric data available from missions like Kepler provide researchers with the ability to measure changes in light on the order of tens of parts per million (ppm). This level of precision allows researchers to measure the loss of light due to exoplanet transits as well as the light emitted by an exoplanet, or planetary photometric emissions. The planetary photometric emissions are due to the thermal emissions of the exoplanet, and reflected stellar light. In many cases it is assumed that the incident stellar light may be modeled as plane parallel rays. For extremely cl…
Context. Clouds have already been detected in exoplanetary atmospheres. They play crucial roles in a planet's atmosphere and climate and can also create ambiguities in the determination of atmospheric parameters such as trace gas mixing ratios. Knowledge of cloud properties is required when assessing the habitability of a planet. Aims. We aim to show that various types of cloud cover such as polar cusps, subsolar clouds, and patchy clouds on Earth-like exoplanets can be distinguished from each other using the polarization and flux of light that is reflected by the planet. Methods. We have comp…
Technological civilizations may rely upon large-scale photovoltaic arrays to harness energy from their host star. Photovoltaic materials, such as silicon, possess distinctive spectral features, including an "artificial edge" that is characteristically shifted in wavelength shortwards of the "red edge" of vegetation. Future observations of reflected light from exoplanets would be able to detect both natural and artificial edges photometrically, if a significant fraction of the planet's surface is covered by vegetation or photovoltaic arrays respectively. The stellar energy thus tapped can be ut…
The detection of reflected light from an exoplanet is a difficult technical challenge at optical wavelengths. Even though this signal is expected to replicate the stellar signal, not only is it several orders of magnitude fainter, but it is also hidden among the stellar noise. We apply a variant of the cross-correlation technique to HARPS observations of 51 Peg to detect the reflected signal from planet 51 Peg b. Our method makes use of the cross-correlation function of a binary mask with high-resolution spectra to amplify the minute planetary signal that is present in the spectra by a factor …
Future space-based direct imaging missions will perform low-resolution (R$<$100) optical (0.3-1~$μ$m) spectroscopy of planets, thus enabling reflected spectroscopy of cool giants. Reflected light spectroscopy is encoded with rich information about the scattering and absorbing properties of planet atmospheres. Given the diversity of clouds and hazes expected in exoplanets, it is imperative we solidify the methodology to accurately and precisely retrieve these scattering and absorbing properties that are agnostic to cloud species. In particular, we focus on determining how different cloud parame…
We have investigated the information content in reflected-starlight spectra of exoplanets. We specify our analysis to Barnard's Star b candidate super-Earth, for which we assume a radius 0.6 times that of Neptune, an atmosphere dominated by H$_2$-He, and a CH$_4$ volume mixing ratio of 5$\cdot$10$^{-3}$. The main conclusions of our study are however planet-independent. We set up a model of the exoplanet described by seven parameters including its radius, atmospheric methane abundance and basic properties of a cloud layer. We generate synthetic spectra at zero phase (full disk illumination) fro…
An important source of opacity in exoplanet atmospheres at short visible and near-UV wavelengths is Rayleigh scattering of light on molecules. It is accompanied by a related, albeit weaker process -- Raman scattering. We analyze the signatures of Raman scattering imprinted in the reflected light and the geometric albedo of exoplanets, which could provide information about atmospheric properties. Raman scattering affects the geometric albedo spectra of planets in following ways. Firstly, it causes filling-in of strong absorption lines in the incident radiation, thus producing sharp peaks in the…
We report first multicolor polarimetric measurements (UBV bands) for the hot Jupiters HD189733b and confirm our previously reported detection of polarization in the B band (Berdyugina et al. 2008). The wavelength dependence of polarization indicates the dominance of Rayleigh scattering with a peak in the blue B and U bands of ~10^-4+/-10^-5 and at least a factor of two lower signal in the V band. The Rayleigh-like wavelength dependence, detected also in the transmitted light during transits, implies a rapid decrease of the polarization signal toward longer wavelengths. Therefore, the nondetect…
We present a multiple scattering vector radiative transfer model which produces disk integrated, full phase polarized light curves for reflected light from an exoplanetary atmosphere. We validate our model against results from published analytical and computational models and discuss a small number of cases relevant to the existing and possible near-future observations of the exoplanet HD 189733b. HD 189733b is arguably the most well observed exoplanet to date and the only exoplanet to be observed in polarized light, yet it is debated if the planet's atmosphere is cloudy or clear. We model ref…
We recognize the need for the characterization of exoplanets in reflected light in the visible and in the IR termal emission. But for the thermal infrared we also recognize the difficulty of an interferometric nuller We nevertheless endorse the need for future interferometers. We propose a new, realistic, pathway to satisfy both goals, thermal infrared studies and interferometric architectures.
Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the albedo considered over all orbital phase angles, known as the ``spherical albedo". Determining the relationship between the geometric and spherical albedos usually involves complex numerical calculations and closed-form solutions are restricted to simple reflection laws. Here we report the discovery of closed-form solutions for the geometric albedo and integral p…
We present an analysis of the KOI-13.01 candidate exoplanet system included in the September 2011 Kepler data release. The host star is a known and relatively bright $(m_{\rm KP} = 9.95)$ visual binary with a separation significantly smaller (0.8 arcsec) than the size of a Kepler pixel (4 arcsec per pixel). The Kepler light curve shows both primary and secondary eclipses, as well as significant out-of-eclipse light curve variations. We confirm that the transit occurs round the brighter of the two stars. We model the relative contributions from (i) thermal emission from the companion, (ii) plan…
