We consider the time-frequency analysis of a scattered light curve by 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 with the instantaneous frequency extracted from the pseudo-Wigner distribution of the 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 prograde, retrograde, and pole-on spin rotations. Whereas our technique requires the static property of the albedo map, 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 to the characterization of directly imaged exoplanet in future.
↧