Efficient and precise transit light curves for rapidly-rotating, oblate stars

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 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 ($v\sin i_{\ast }=86.4$ km/s). We subtract the host's $\delta$-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 $\phi =108.3_{-15.4}^{+19.0}$~${}^{\circ }$. 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.

arXiv comment33 pages, 9 figures. Submitted to AAS Journals

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• Nodal Precession of WASP-33b for Eleven Years by Doppler Tomographic and Transit Photometric Observations
• Gravity darkening and tidally perturbed stellar pulsation in the misaligned exoplanet system WASP-33
• Discovery of a substellar companion in the TESS light curve of the $\delta$ Scuti/$\gamma$ Doradus hybrid pulsator HD 31221
• Stellar pulsations interfering with the transit light curve: configurations with false positive misalignment
• CHEOPS observations confirm nodal precession in the WASP-33 system
• Atmospheric asymmetries in WASP-121 b revealed by rotational transits detected with JWST