Abstract
Abstract 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 system’s 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 semianalytic 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−1). We subtract the host’s δ-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 φ = 108.3 − 15.4 + 19.0 °. We demonstrate the method’s 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 (https://github.com/rodluger/starry, https://rodluger.github.io/starry, https://github.com/shashankdholakia/gravity-dark).
Highlights
The exoplanet transit method has led to the discovery of thousands of exoplanet candidates since the first observed transits of the HD 209458 system by Charbonneau et al (2000) and Henry et al (2000)
We found that the subtraction method in von Essen et al (2020) was effective in removing the pulsation signal and reduced the asymmetry in transit due to the subtraction of a standard transit model from the TESS light curve before detrending, which allowed the asymmetry to be removed by the detrending process
We present a new method for the generation of efficient semi-analytic model transit light curves for rapidly rotating stars that exhibit oblateness and gravity darkening
Summary
The exoplanet transit method has led to the discovery of thousands of exoplanet candidates since the first observed transits of the HD 209458 system by Charbonneau et al (2000) and Henry et al (2000). One of the most widely adopted transit models is that of Mandel & Agol (2002), who found an analytic (i.e., closed form) solution to the integral describing the flux blocked by a planet transiting a star with quadratic limb-darkening This analytic model permitted the generation of fast model light curves, allowing thousands of exoplanet candidates to have their best-fitting parameters measured, including orbital period, planet-star radius ratio, and inclination. Despite its applicability to thousands of transiting exoplanets, the Mandel & Agol (2002) model makes some assumptions that break down for certain systems It assumes that the intensity profile across the stellar disk can be modeled using a single quadratic function in the radial parameter μ to capture the effect of limb darkening. We leave most of the details of the integration and the math to the Appendix
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