Authors: Bethlee M. Lindor & Eric Agol
First Author’s Institution: Department of Astronomy, University of Washington, Seattle, WA, USA
Status: Submitted to the Planetary Science Journal [open access]
The Solar System is unique among known planetary systems. The vast majority of exoplanetary systems look nothing like ours: 4 inner rocky planets and 4 outer gas giants (sorry Pluto) orbiting a G-type star, not to mention the intelligent species occupying the planet smack dab in the habitable zone. At the time of writing, we know of only one exoplanetary system with 8 planets: Kepler-90. Moreover, the Solar System contains none of the most commonly found type of exoplanet: Super-Earths and mini-Neptunes.
It is, however, difficult to conclude whether the Solar System is truly unique given the difficulty of detecting exoplanet analogs of Solar System planets. The workhorse methods of exoplanet detection are transits, detecting the shadow of a planet as it passes in front of its star along our line of sight, and radial velocities, detecting the periodic gravitational influence of a planet on its star. Because it is more difficult to detect smaller, less massive planets or planets orbiting at longer orbital periods with these methods, we may obtain a biased view of the exoplanet population.
One exciting method for characterizing multi-planet systems is that of transit-timing variations (TTVs). In a one-star, one-planet system with no complications, we expect transits to happen like clockwork, once every orbital period. However, we sometimes observe transits occurring later or earlier than expected. Causes of this discrepancy could be acceleration towards Earth, apsidal precession, or orbital decay. In multi-planet systems, there are also TTVs associated with the gravitational pull from other planets, as shown in Figure 1. In this paper, the authors imagine how the Solar System would appear to a distant observer viewing the transits of ONLY Venus and Earth and investigating what they could learn about both the transiting (Venus and Earth) and non-transiting (Mercury, Mars, and the outer planets) planets from TTVs.
The authors use observed motions of Earth (really the Earth-Moon Barycenter or EMB to avoid TTV complications from the Moon itself) and Venus to simulate transit times as viewed by a distant observer. They model timing uncertainty due to stellar variability by adding Gaussian noise to each observed transit time. The authors then attempt to fit the observed TTVs with several models, from 2-planets (only Venus + EMB) to 5-planets (Venus, EMB + non-transiting Jupiter, Mars, and Saturn). The other planets contribute only modestly to Venus and EMB TTVs and would be extremely difficult to detect.
The authors investigate what the observer could learn about the Solar System from a modeled 30-year survey including 80 transit observations of Venus and the EMB with 30-second transit timing uncertainty. To compare the various models (2-, 3-, 4-, and 5-planet), the authors invoke the Bayesian Information Criterion (BIC), which prefers simple models with a good fit and penalizes adding additional parameters. A model with a lower BIC is preferred. The 2-planet model does not fit the data extraordinarily well, but, perhaps surprisingly, this incomplete model lacking any other bodies recovers accurate masses and eccentricities for the EMB and Venus.
The authors find that the 3-planet model is strongly preferred over the 2-planet model, with ΔBIC = 116 (a >10σ detection of Jupiter), and the distant observer could easily infer the presence of a gas giant near Jupiter’s actual orbital period, as shown in Figure 2. However, either high timing precision OR the 4-planet model is required to measure Jupiter’s mass accurately. The 4-planet model is preferred over the 3-planet model with ΔBIC = 8 (a marginal 2.8σ detection of Mars). This model yields accurate mass estimates for Venus, the EMB, and Jupiter, but not Mars. Detecting TTVs caused by Saturn would require optimistic timing precision, so the authors do not include a detailed analysis of the 5-planet model.
There are several notable takeaways from this work, such that a distant observer could recover the masses and orbits of Venus and the EMB accurately, without modeling the other planets. This distant observer could easily uncover Jupiter’s existence, even with pessimistic 90-sec transiting timing noise, though better timing precision, better modeling, and a longer survey duration help in constraining its mass and orbital properties. Very high timing precision (10-sec) would enable a >5σ detection of Mars and help constrain the masses and periods of Venus, Earth, Mars, and Jupiter at a level of precision comparable to or better than many known exoplanets in multi-planet systems, as shown in Figure 3.
Characterizing multi-planet systems via TTVs is no small feat: it requires patience and precise timing. This paper provides a clearer view of how our own Solar System, and similarly Solar System analogs, would appear with transits and TTVs. The observer could learn a surprising amount about the architecture and planets within the system with only transits of Venus and Earth, albeit over a decades-long survey duration.
Astrobite edited by Abbe Whitford
Featured image credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington (Mercury), USGS Astrogeology Science Center (Venus, Mars), NASA’s Goddard Space Flight Center/Space Telescope Science Institute (Jupiter), NASA/JPL/Space Science Institute (Saturn) and NASA’s Goddard Space Flight Center (Earth, Jupiter, Uranus)