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Register a new userClosed-formed ab initio solutions of geometric albedos and reflected light phase curves of exoplanets
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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 phase function, which apply to any law of reflection that only depends on the scattering angle. The shape of a reflected light phase curve, quantified by the integral phase function, and the secondary eclipse depth, quantified by the geometric albedo, may now be self-consistently inverted to retrieve globally averaged physical parameters. Fully Bayesian phase curve
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We derive efficient, closed form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of scattered light phase curves of exoplanets, secondary eclipse light curves in the optical, or future measurements of planet-moon and planet-planet occultations, as well as to photometry of solar system bodies. We derive our solutions for Lambertian bodies illuminated by a point source, but extend them to model illumination sources of finite angular size and rough surfaces with phase-dependent scattering. Our algorithm is implemented in Python within the open-source starry mapping framework and is designed with efficient gradient-based inference in mind. The algorithm is 4-5 orders of magnitude faster than direct numerical evaluation methods and about 10 orders of magnitude more precise. We show how the techniques developed here may one day lead to the construction of two-dimensional maps of terrestrial planet surfaces, potentially enabling the detection of continents and oceans on exoplanets in the habitable zone.
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.
There are now many known exoplanets with Msin(i) within a factor of two of Neptunes, including the transiting planets GJ436b and HAT-P-11b. Planets in this mass-range are different from their more massive cousins in several ways that are relevant to their radiative properties and thermal structures. By analogy with Neptune and Uranus, they are likely to have metal abundances that are an order of magnitude or more greater than those of larger, more massive planets. This increases their opacity, decreases Rayleigh scattering, and changes their equation of state. Furthermore, their smaller radii mean that fluxes from these planets are roughly an order of magnitude lower than those of otherwise identical gas giant planets. Here, we compute a range of plausible radiative equilibrium models of GJ436b and HAT-P-11b. In addition, we explore the dependence of generic Neptune-mass planets on a range of physical properties, including their distance from their host stars, their metallicity, the spectral type of their stars, the redistribution of heat in their atmospheres, and the possible presence of additional optical opacity in their upper atmospheres.
The increasing number of transiting exoplanets sparked a significant interest in discovering their moons. Most of the methods in the literature utilize timing analysis of the raw light curves. Here we propose a new approach for the direct detection of a moon in the transit light curves via the so called Scatter Peak. The essence of the method is the valuation of the local scatter in the folded light curves of many transits. We test the ability of this method with different simulations: Kepler short cadence, Kepler long cadence, ground-based millimagnitude photometry with 3-min cadence, and the expected data quality of the planned ESA mission of PLATO. The method requires ~100 transit observations, therefore applicable for moons of 10-20 day period planets, assuming 3-4-5 year long observing campaigns with space observatories. The success rate for finding a 1 R_Earth moon around a 1 R_Jupiter exoplanet turned out to be quite promising even for the simulated ground-based observations, while the detection limit of the expected PLATO data is around 0.4 R_Earth. We give practical suggestions for observations and data reduction to improve the chance of such a detection: (i) transit observations must include out-of-transit phases before and after a transit, spanning at least the same duration as the transit itself; (ii) any trend filtering must be done in such a way that the preceding and following out-of-transit phases remain unaffected.
Highly volcanic exoplanets, which can be variously characterized as lava worlds, magma ocean worlds, or super-Ios are high priority targets for investigation. The term lava world may refer to any planet with extensive surface lava lakes, while the term magma ocean world refers to planets with global or hemispherical magma oceans at their surface. Highly volcanic planets, including super-Ios, may simply have large, or large numbers of, active explosive or extrusive volcanoes of any form. They are plausibly highly diverse, with magmatic processes across a wide range of compositions, temperatures, activity rates, volcanic eruption styles, and background gravitational force magnitudes. Worlds in all these classes are likely to be the most characterizable rocky exoplanets in the near future due to observational advantages that stem from their preferential occurrence in short orbital periods and their bright day-side flux in the infrared. Transit techniques should enable a level of characterization of these worlds analogous to hot Jupiters. Understanding processes on highly volcanic worlds is critical to interpret imminent observations. The physical states of these worlds are likely to inform not just geodynamic processes, but also planet formation, and phenomena crucial to habitability. Volcanic and magmatic activity uniquely allows chemical investigation of otherwise spectroscopically inaccessible interior compositions. These worlds will be vital to assess the degree to which planetary interior element abundances compare to their stellar hosts, and may also offer pathways to study both the very young Earth, and the very early form of many silicate planets where magma oceans and surface lava lakes are expected to be more prevalent. We suggest that highly volcanic worlds may become second only to habitable worlds in terms of both scientific and public long-term interest.
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