Exploring the Detectability of Solar System Analogues by Modeling Transit Timing Variations for Venus and Earth

The most effective exoplanet detection method has been transit photometry, wherein we measure the brightness of stars over periods of time. These measurements, or light curves, are later analyzed for dips in brightness caused by objects passing in front of the host star. However, variations in these time series can occur due to numerous factors: including unseen planets, or moons. Planetary systems with multiple transiting planets are highly valuable for understanding planet occurrence rates and system architectures; and although we have yet to detect a solar system analog, future surveys might detect the twins of Venus and Earth transiting a Sun-like star. In anticipation of such a discovery, we simulate transit timing observations based on the actual orbital motions of Venus and Earth — two habitable zone planets which are influenced by the other solar system bodies — with varying noise levels and observation time spans. We then retrieve the system dynamical parameters using TTVFaster, an approximate N-body model for transit time shifts.

By considering the presence of an unseen Jupiter-, Mars-, or Saturn-analogue, and the Moon, we can gauge the detectability and characterization limits of such objects in exoplanetary systems where two planets are known to transit. We demonstrate that with the retrieval applied to simulated transits of Venus and Earth that we can, for example: 1). measure the correct masses of both Earth and Venus (down to 3% error), and constrain their eccentricities; 2). detect Jupiter near the correct orbital period and mass; 3). detect the Moon; and 4). detect Mars (for really high precision). In general, we find that timing precisions of better than 60 seconds and/or survey durations longer than 15 years would be required to meet these goals. Unfortunately, Jupiter's mass is underestimated in most scenarios, and the moon is degenerate with adding a fourth Mars-like planet. The latter of these findings supports dynamical stability tests of multi-planet systems. Ultimately, this work will help to guide future missions in detecting and characterizing exoplanet systems analogous to our solar system.