[Paper Review] Transits and Occultations

Joshua N. Winn|arXiv (Cornell University)|Jan 12, 2010

Stellar, planetary, and galactic studiesPhysics and Astronomy130 references89 citations

TL;DR

This paper reviews how transits and occultations of exoplanets provide critical insights into planetary properties—such as radius, mass, orbital inclination, atmospheric composition, and potential moons—by analyzing photometric light curves. It highlights that eclipse observations enable precise measurements unattainable via radial velocity alone, serving as a 'royal road' to understanding exoplanetary systems with high-precision photometry and orbital dynamics.

ABSTRACT

When we are fortunate enough to view an exoplanetary system nearly edge-on, the star and planet periodically eclipse each other. Observations of eclipses (transits and occultations) provide a bonanza of information that cannot be obtained from radial-velocity data alone, such as the relative dimensions of the planet and its host star, as well as the orientation of the planet's orbit relative to the sky plane and relative to the stellar rotation axis. The wavelength-dependence of the eclipse signal gives clues about the the temperature and composition of the planetary atmosphere. Anomalies in the timing or other properties of the eclipses may betray the presence of additional planets or moons. Searching for eclipses is also a productive means of discovering new planets. This chapter reviews the basic geometry and physics of eclipses, and summarizes the knowledge that has been gained through eclipse observations, as well as the information that might be gained in the future.

Motivation & Objective

• To synthesize the current understanding of how eclipse observations constrain exoplanet and host star properties beyond radial velocity data.
• To explain the geometric and photometric foundations of transit and occultation light curves for exoplanetary systems.
• To identify key scientific insights gained from eclipse data, including atmospheric characterization, orbital inclination, and evidence for additional planets or moons.
• To outline future prospects for discovering transiting planets, especially around bright stars, using ground-based and space-based surveys.
• To emphasize the role of eclipse observations as a primary method for obtaining precise, fundamental planetary parameters in exoplanetary science.

Proposed method

• Uses Keplerian orbital mechanics and sky-plane geometry to model the positions of planets relative to stars during eclipses, with coordinate systems aligned to the observer's line of sight.
• Applies the parameter $ k = R_p/R_\star $ to quantify the depth of transit signals, linking it to the fraction of starlight blocked.
• Derives light curve shapes using equations for projected separation and sky-plane distance, assuming eclipses occur near conjunctions ($X=0$).
• Models the photometric signal during transits (flux drop due to planet blocking starlight) and occultations (flux drop when planet is hidden behind star).
• Incorporates wavelength-dependent flux variations to infer atmospheric temperature and composition through transmission and emission spectroscopy.
• Utilizes timing variations in eclipse events to detect perturbations from additional planets or moons, leveraging gravitational interactions in multi-planet systems.

Experimental results

Research questions

• RQ1 How can transit and occultation light curves be used to determine the radius and orbital inclination of an exoplanet?
• RQ2 What information about planetary atmospheres can be extracted from wavelength-dependent eclipse signals?
• RQ3 How do timing variations in eclipses reveal the presence of additional planets or moons in a system?
• RQ4 What constraints do eclipse observations provide on planetary mass, spin, and internal structure, especially through oblateness and precession?
• RQ5 What future survey strategies can maximize the discovery of transiting planets, particularly around bright stars, to enable detailed follow-up characterization?

Key findings

• Transit and occultation observations allow precise determination of planetary radius and orbital inclination, with the transit depth directly proportional to $ (R_p/R_\star)^2 $.
• Wavelength-dependent eclipse signals enable atmospheric characterization, revealing temperature profiles and molecular constituents such as water vapor.
• Timing variations in eclipses can detect additional planets or moons, with the amplitude and period of variations sensitive to planetary masses and orbital configurations.
• Planetary oblateness due to rotation or rings can be detected in high-precision light curves, with HD 189733b found to be less oblate than Saturn, consistent with spin-synchronization.
• Precession of the orbit due to tidal forces may allow inference of planetary interior structure, particularly for short-period planets.
• Future surveys like TESS and PLATO aim to survey bright stars across the sky, increasing the number of targets amenable to radial velocity and atmospheric follow-up, especially for habitable-zone Earth-sized planets.