Frequency Modulation of Directly Imaged Exoplanets: Geometric Effect as a Probe of Planetary Obliquity

Abstract

We consider the time-frequency analysis of a scattered light curve of a directly imaged exoplanet. We show that the geometric effect due to planetary obliquity and orbital inclination induce the frequency modulation of the apparent diurnal periodicity. We construct a model of the frequency modulation and compare it with the instantaneous frequency extracted from the pseudo-Wigner distribution of simulated light curves of a cloudless Earth. The model provides good agreement with the simulated modulation factor, even for the light curve with Gaussian noise comparable to the signal. Notably, the shape of the instantaneous frequency is sensitive to the difference between the prograde, retrograde, and pole-on spin rotations. While our technique requires the albedo map to be static, it does not need to solve the albedo map of the planet. The time-frequency analysis is complementary to other methods which utilize the amplitude modulation. This paper demonstrates the importance of the frequency domain of the photometric variability for the characterization of directly imaged exoplanets in future research.

11 pages, 10 figures, A typo in Equation (A1) was fixed. The codes are provided at https://github.com/HajimeKawahara/sot and https://github.com/HajimeKawahara/juwvid

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