Exoplanet Predictions Based on the Generalised Titius-Bode Relation (1304.3341v4)

Abstract: We evaluate the extent to which newly detected exoplanetary systems containing at least four planets adhere to a generalized Titius-Bode (TB) relation. We find that the majority of exoplanet systems in our sample adhere to the TB relation to a greater extent than the Solar System does, particularly those detected by the Kepler mission. We use a generalized TB relation to make a list of predictions for the existence of 141 additional exoplanets in 68 multiple-exoplanet systems: 73 candidates from interpolation, 68 candidates from extrapolation. We predict the existence of a low-radius (R < 2.5 Earth Radii) exoplanet within the habitable zone of KOI-812 and that the average number of planets in the habitable zone of a star is 1-2. The usefulness of the TB relation and its validation as a tool for predicting planets will be partially tested by upcoming Kepler data releases.

• The paper demonstrates that applying a generalized TB relation to multi-planet systems predicts 73 interpolated and 141 overall new exoplanets.
• It analyzes Kepler data from 68 systems with 4+ planets, introducing a γ parameter to quantify improvements in TB relation adherence.
• The findings suggest the TB relation as a cost-effective predictive tool, including identifying planets in potential habitable zones.

Overview of "Exoplanet Predictions Based on the Generalised Titius-Bode Relation"

This paper explores the application of the generalized Titius-Bode (TB) relation to multi-planet exoplanetary systems, specifically those containing at least four known planets. The TB relation historically suggested a pattern in the spacing of planets in the Solar System, contributing to the discovery of celestial objects like the Asteroid Belt. The authors, Timothy Bovaird and Charles H. Lineweaver, aim to determine whether this relation is applicable to exoplanetary systems, consequently utilizing it as a predictive tool for finding undetected planets.

Methodology and Analysis

The authors collected data from 68 exoplanetary systems, using two main criteria: systems detected predominantly via the Kepler mission and those with at least four confirmed or candidate planets. Crucially, the focus is on testing the adherence of these systems to a generalized two-parameter version of the TB relation given by $a_n = aC^n$, where $a_n$ is the semi-major axis of the $n$th planet.

The paper involved calculating the fit of planetary systems to the TB relation and examining whether a tighter configuration of planets (compactness) corresponds to a better fit. They define this compactness through the logarithmic spacing of planet periods within each system. A key feature of their analysis is the introduction of a fitting parameter, $\gamma$, which quantifies the improvement in TB relation adherence with the insertion of predicted planets.

Findings and Predictions

The findings suggest that many exoplanet systems align well with the TB relation, often to a greater extent than our Solar System. Out of the analyzed systems, 29 required additional planets to better fit the TB relation - resulting in the prediction of 73 new exoplanets through interpolation. Moreover, for all 68 systems, the authors predicted the presence of additional planets beyond the currently known outermost planet, totaling 141 predictions when including both interpolations and extrapolations.

The authors apply practical constraints on the predicted planetary masses and radii based on the detection limits established by the current sensitivity of observation data. Interestingly, their analysis also places several predicted planets within the habitable zones of their respective stars, notably for systems like KOI-812.

Implications and Future Prospects

This research suggests considerable potential for the TB relation in aiding the discovery of exoplanets in known multi-planet systems by narrowing down the search space. The authors propose that, if future detections validate a significant number of their predictions, the TB relation could become an essential tool in exoplanetary research.

Their approach implies that other complex and numerical-intensive methods, like N-body simulations, might not always be necessary or practical for systems with a higher number of planets due to computational constraints. Moreover, while the TB relation offers an empirical basis for prediction, it underscores the ongoing need to understand the underlying physics and formation theories better. This could lead, in the future, to the development of more sophisticated models that may account for disparities in period spacing and resonance phenomena within exoplanetary systems.

By contributing to a growing body of evidence supporting regularities in planetary spacing, this research can spur further developments in the modeling of planetary system architectures and enhance our predictions of where undiscovered planets might lie within the Pancake-like disks of stars other than our Sun.