Inferring Planetary Obliquity Using Rotational & Orbital Photometry
Schwartz et al
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted to infer obliquity. We extend this approach to single-epoch observations for planets with arbitrary albedo maps. For diffuse reflection, the flux seen by a distant observer is the product of the planet's albedo map, the host star's illumination, and the observer's visibility of different planet regions. It is useful to treat the product of illumination and visibility as the kernel of a convolution; this kernel is unimodal and symmetric. For planets with unknown obliquity, the kernel is not known a priori, but could be inferred by fitting a rotational light curve. We analyze this kernel under different viewing geometries, finding it well described by its longitudinal width and latitudinal position. We use Monte Carlo simulation to estimate uncertainties on these kernel characteristics from variations in a planet's apparent albedo. We demonstrate that the kernel properties are functions of obliquity and axial orientation, which may both be inferred even if planets are A) East-West uniform or spinning rapidly, or B) North-South uniform. We consider degeneracies in these inferences with a case study, and describe how to tell prograde from retrograde rotation for inclined, oblique planets. This approach could be used to estimate obliquities of terrestrial planets with modest time investment from flagship direct-imaging missions.