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Register a new userEfficient and precise transit light curves for rapidly-rotating, oblate stars
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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.
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Reliable estimations of ephemeris errors are fundamental for the follow-up of CoRoT candidates. An equation for the precision of minimum times, originally developed for eclipsing binaries, has been optimized for CoRoT photometry and been used to calculate such errors. It may indicate expected timing precisions for transit events from CoRoT, as well as from Kepler. Prediction errors for transit events may also be used to calculate probabilities about observing entire or partial transits in any given span of observational coverage, leading to an improved reliability in deductions made from follow-up observations.
We present a novel, iterative method using an empirical Bayesian approach for modeling the limb darkened WASP-121b transit from the TESS light curve. Our method is motivated by the need to improve $R_{p}/R_{ast}$ estimates for exoplanet atmosphere modeling, and is particularly effective with the limb darkening (LD) quadratic law requiring no prior central value from stellar atmospheric models. With the non-linear LD law, the method has all the advantages of not needing atmospheric models but does not converge. The iterative method gives a different $R_{p}/R_{ast}$ for WASP-121b at a significance level of 1$sigma$ when compared with existing non-iterative methods. To assess the origins and implications of this difference, we generate and analyze light curves with known values of the limb darkening coefficients (LDCs). We find that non-iterative modeling with LDC priors from stellar atmospheric models results in an inconsistent $R_{p}/R_{ast}$ at 1.5$sigma$ level when the known LDC values are as those previously found when modeling real data by the iterative method. In contrast, the LDC values from the iterative modeling yields the correct value of $R_{p}/R_{ast}$ to within 0.25$sigma$. For more general cases with different known inputs, Monte Carlo simulations show that the iterative method obtains unbiased LDCs and correct $R_{p}/R_{ast}$ to within a significance level of 0.3$sigma$. Biased LDC priors can cause biased LDC posteriors and lead to bias in the $R_{p}/R_{ast}$ of up to 0.82$%$, 2.5$sigma$ for the quadratic law and 0.32$%$, 1.0$sigma$ for the non-linear law. Our improvement in $R_{p}/R_{ast}$ estimation is important when analyzing exoplanet atmospheres.
The Transiting Exoplanet Survey Satellite (TESS) mission measured light from stars in ~75% of the sky throughout its two year primary mission, resulting in millions of TESS 30-minute cadence light curves to analyze in the search for transiting exoplanets. To search this vast data trove for transit signals, we aim to provide an approach that is both computationally efficient and produces highly performant predictions. This approach minimizes the required human search effort. We present a convolutional neural network, which we train to identify planetary transit signals and dismiss false positives. To make a prediction for a given light curve, our network requires no prior transit parameters identified using other methods. Our network performs inference on a TESS 30-minute cadence light curve in ~5ms on a single GPU, enabling large scale archival searches. We present 181 new planet candidates identified by our network, which pass subsequent human vetting designed to rule out false positives. Our neural network model is additionally provided as open-source code for public use and extension.
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 measure the bulk system parameters of the seismically active, rapidly-rotating $delta$-Scuti KOI-976 and constrain the orbit geometry of its transiting binary companion using a combined approach of asteroseismology and gravity-darkening light curve analysis. KOI-976 is a $1.62pm0.2~mathrm{M_odot}$ star with a measured $vsin(i)$ of $120pm2$ km/s and seismically-induced variable signal that varies by $sim$ 0.6% of the stars total photometric brightness. We take advantage of the stars oblate shape and seismic activity to perform three measurements of its obliquity angle relative to the plane of the sky. We first apply rotational splitting theory to the stars variable signal observed in short-cadence emph{Kepler} photometry to constrain KOI-976s obliquity angle, and then subtract off variability from that dataset using the linear algorithm for significance reduction software {tt LASR}. We perform gravity-darkened fits to emph{Kepler} variability-subtracted short-cadence photometry and to emph{Keplers} phase-folded long-cadence photometry to obtain two more measurements of the stars obliquity. We find that the binary system transits in a grazing configuration with measured obliquity values of $36^circpm17^circ$, $46^circpm16^circ$, and $43^circpm20^circ$ respectively for the three measurements. We perform these analyses as a way to demonstrate overcoming the challenges high-mass stars can present to transit light curve fitting and to prepare for the large number of exoplanets emph{TESS} will discover orbiting A/F stars.
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