Prospects of Detecting Rotational Flatness of Exoplanets from Space-based Photometry

In the era of photometry with space-based telescopes, such as CHaracterizing ExOPlanets Satellite, James Webb Space Telescope, PLAnetary Transits and Oscillations of stars, and Atmospheric Remote-sensing Infrared Exoplanet Large-survey, the road has opened for detecting subtle distortions in exoplanet transit light curves-resulting from their non-spherical shape. We investigate the prospects of retrieval of rotational flatness (oblateness) of exoplanets at various noise levels. We present a novel method for calculating the transit light curves based on the Gauss–Legendre quadrature. We compare it in the non-rotating limit to the available analytical models. We conduct injection-and-retrieval tests to assess the precision and accuracy of the retrievable oblateness values. We find that the light curve calculation technique is about 25% faster than a well-known analytical counterpart, while still being precise enough. We show that a 3 σ oblateness detection is possible for a planet orbiting bright enough stars, by exploiting a precise estimate on the stellar density obtained e.g., from asteroseismology. We also show that for noise levels ≥256 ppm (expressed as point-to-point scatter with a 60 s exposure time) detection of planetary oblateness is not reliable.