Inferring Planetary Obliquity Using Rotational & Orbital Photometry

TL;DR

This paper develops a theoretical framework to infer a planet's obliquity from time-resolved photometry, revealing how the kernel's properties relate to axial tilt and orientation, even with simple albedo patterns.

Contribution

It introduces a convolution-based model linking light curves to planetary obliquity and demonstrates that kernel analysis can uniquely determine a planet's spin axis with limited observations.

Findings

Kernel's width and mean latitude depend on obliquity and orientation.

Perfect kernel knowledge at 2-4 orbital phases suffices for unique obliquity inference.

East-West albedo contrast is more effective than North-South for constraining obliquity.

Abstract

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. However, few studies of more general planets with arbitrary albedo markings have been made and, in particular, a simple theoretical understanding of why it is possible to extract obliquity from light curves is missing. Reflected light seen by a distant observer is the product of a planet's albedo map, its host star's illumination, and the visibility of different regions. It is useful to treat the product of illumination and visibility as the kernel of a convolution. Time-resolved photometry constrains both the albedo map and the kernel, the latter of which sweeps over the planet due to rotational and orbital motion. The kernel's movement distinguishes prograde from retrograde rotation for planets with non-zero obliquity on inclined orbits. We demonstrate that the kernel's longitudinal width and mean latitude are distinct functions of obliquity and axial orientation. Notably, we find that a planet's spin axis affects the kernel -- and hence time-resolved photometry -- even if this planet is East-West uniform or spinning rapidly, or if it is North-South uniform. We find that perfect knowledge of the kernel at 2-4 orbital phases is usually sufficient to uniquely determine a planet's spin axis. Surprisingly, we predict that East-West albedo contrast is more useful for constraining obliquity than North-South contrast.