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Register a new userAnalytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
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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.
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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
We derive solutions to transit light curves of exoplanets orbiting rapidly-rotating stars. These stars exhibit significant oblateness and gravity darkening, a phenomenon where the poles of the star have a higher temperature and luminosity than the equator. Light curves for exoplanets transiting these stars can exhibit deviations from those of slowly-rotating stars, even displaying significantly asymmetric transits depending on the systems spin-orbit angle. As such, these phenomena can be used as a protractor to measure the spin-orbit alignment of the system. In this paper, we introduce a novel semi-analytic method for generating model light curves for gravity-darkened and oblate stars with transiting exoplanets. We implement the model within the code package starry and demonstrate several orders of magnitude improvement in speed and precision over existing methods. We test the model on a TESS light curve of WASP-33, whose host star displays rapid rotation ($v sin i_* = 86.4$ km/s). We subtract the hosts $delta$-Scuti pulsations from the light curve, finding an asymmetric transit characteristic of gravity darkening. We find the projected spin orbit angle is consistent with Doppler tomography and constrain the true spin-orbit angle of the system as $varphi=108.3^{+19.0}_{-15.4}$~$^{circ}$. We demonstrate the methods uses in constraining spin-orbit inclinations of such systems photometrically with posterior inference. Lastly, we note the use of such a method for inferring the dynamical history of thousands of such systems discovered by TESS.
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.
RefPlanets is a guaranteed time observation (GTO) programme that uses the Zurich IMaging POLarimeter (ZIMPOL) of SPHERE/VLT for a blind search for exoplanets in wavelengths from 600-900 nm. The goals of this study are the characterization of the unprecedented high polarimetic contrast and polarimetric precision capabilities of ZIMPOL for bright targets, the search for polarized reflected light around some of the closest bright stars to the Sun and potentially the direct detection of an evolved cold exoplanet for the first time. For our observations of Alpha Cen A and B, Sirius A, Altair, Eps Eri and Tau Ceti we used the polarimetric differential imaging (PDI) mode of ZIMPOL which removes the speckle noise down to the photon noise limit for angular separations >0.6. We describe some of the instrumental effects that dominate the noise for smaller separations and explain how to remove these additional noise effects in post-processing. We then combine PDI with angular differential imaging (ADI) as a final layer of post-processing to further improve the contrast limits of our data at these separations. For good observing conditions we achieve polarimetric contrast limits of 15.0-16.3 mag at the effective inner working angle of about 0.13, 16.3-18.3 mag at 0.5 and 18.8-20.4 mag at 1.5. The contrast limits closer in (<0.6) depend significantly on the observing conditions, while in the photon noise dominated regime (>0.6), the limits mainly depend on the brightness of the star and the total integration time. We compare our results with contrast limits from other surveys and review the exoplanet detection limits obtained with different detection methods. For all our targets we achieve unprecedented contrast limits. Despite the high polarimetric contrasts we are not able to find any additional companions or extended polarized light sources in the data that has been taken so far.
Neutrinos are a guaranteed signal from supernova explosions in the Milky Way, and a most valuable messenger that can provide us with information about the deepest parts of supernovae. In particular, neutrinos will provide us with physical quantities, such as the radius and mass of protoneutron stars (PNS), which are the central engine of supernovae. This requires a theoretical model that connects observables such as neutrino luminosity and average energy with physical quantities. Here, we show analytic solutions for the neutrino-light curve derived from the neutrino radiation transport equation by employing the diffusion approximation and the analytic density solution of the hydrostatic equation for a PNS. The neutrino luminosity and the average energy as functions of time are explicitly presented, with dependence on PNS mass, radius, the total energy of neutrinos, surface density, and opacity. The analytic solutions provide good representations of the numerical models from a few seconds after the explosion and allow a rough estimate of these physical quantities to be made from observational data.
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