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Register a new userEffect of Longitudinally Varying Cloud Coverage on Visible Wavelength Reflected-Light Exoplanet Phase Curves
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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.
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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 exoplanets 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 alter a planets geometric albedo spectrum: whereas a clear atmosphere is dark at wavelengths between 0.5 and 1 $mu$m due to molecular absorption, the addition of a sulfur haze boosts the albedo there to $sim$0.7 due to scattering. Strong absorption by the haze shortward of 0.4 $mu$m results in albedos $<$0.1, in contrast to the high albedos produced by Rayleigh scattering in a clear atmosphere. As a result, the color of the planet shifts from blue to orange. The existence of a sulfur haze masks the molecular signatures of methane and water, thereby complicating the characterization of atmospheric composition. Detection of such a haze by WFIRST is possible, though discriminating between a sulfur haze and any other highly reflective, high altitude scatterer will require observations shortward of 0.4 $mu$m, which is currently beyond WFIRSTs design.
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
Time-correlated noise is a significant source of uncertainty when modeling exoplanet light-curve data. A correct assessment of correlated noise is fundamental to determine the true statistical significance of our findings. Here we review three of the most widely used correlated-noise estimators in the exoplanet field, the time-averaging, residual-permutation, and wavelet-likelihood methods. We argue that the residual-permutation method is unsound in estimating the uncertainty of parameter estimates. We thus recommend to refrain from this method altogether. We characterize the behavior of the time averagings rms-vs.-bin-size curves at bin sizes similar to the total observation duration, which may lead to underestimated uncertainties. For the wavelet-likelihood method, we note errors in the published equations and provide a list of corrections. We further assess the performance of these techniques by injecting and retrieving eclipse signals into synthetic and real Spitzer light curves, analyzing the results in terms of the relative-accuracy and coverage-fraction statistics. Both the time-averaging and wavelet-likelihood methods significantly improve the estimate of the eclipse depth over a white-noise analysis (a Markov-chain Monte Carlo exploration assuming uncorrelated noise). However, the corrections are not perfect, when retrieving the eclipse depth from Spitzer datasets, these methods covered the true (injected) depth within the 68% credible region in only $sim$45--65% of the trials. Lastly, we present our open-source model-fitting tool, Multi-Core Markov-Chain Monte Carlo ({MC$^3$}). This package uses Bayesian statistics to estimate the best-fitting values and the credible regions for the parameters for a (user-provided) model. {MC$^3$} is a Python/C code, available at https://github.com/pcubillos/MCcubed.
We carried out a systematic study of full-orbit phase curves for known transiting systems in the northern ecliptic sky that were observed during Year 2 of the TESS primary mission. We applied the same methodology for target selection, data processing, and light-curve fitting as we did in our Year 1 study. Out of the 15 transiting systems selected for analysis, seven - HAT-P-7, KELT-1, KELT-9, KELT-16, KELT-20, Kepler-13A, and WASP-12 - show statistically significant secondary eclipses and day-night atmospheric brightness modulations. Small eastward dayside hotspot offsets were measured for KELT-9b and WASP-12b. KELT-1, Kepler-13A, and WASP-12 show additional phase-curve variability attributed to the tidal distortion of the host star; the amplitudes of these signals are consistent with theoretical predictions. We combined occultation measurements from TESS and Spitzer to compute dayside brightness temperatures, TESS-band geometric albedos, Bond albedos, and phase integrals for several systems. The new albedo values solidify the previously reported trend between dayside temperature and geometric albedo for planets with $1500<T_{mathrm{day}}<3000$ K. For Kepler-13Ab, we carried out an atmospheric retrieval of the full secondary eclipse spectrum, which revealed a non-inverted temperature-pressure profile, significant H$_{2}$O and K absorption in the near-infrared, evidence for strong optical atmospheric opacity due to sodium, and a confirmation of the high geometric albedo inferred from our simpler analysis. We explore the implications of the phase integrals (ratios of Bond to geometric albedos) for understanding exoplanet clouds. We also report updated transit ephemerides for all of the systems studied in this work.
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