Exoplanet Predictions Based on Harmonic Orbit Resonances

Exoplanet Predictions Based on Harmonic Orbit Resonances

Authors:

Aschenwanden et al

Abstract:
The current exoplanet database includes 5454 confirmed planets and candidate planets observed with the KEPLER mission. We find 932 planet pairs from which we extract distance and orbital period ratios. While earlier studies used the Titius-Bode law or a generalized version with logarithmic spacing, which both lack a physical model, we employ here the theory of harmonic orbit resonances, which contains quantized ratios instead, to explain the observed planet distance ratios and to predict undetected exoplanets. We find that the most prevailing harmonic ratios are (2:1), (3:2), and (5:3), in 73\% of the cases, while alternative harmonic ratios of (5:4), (4:3), (5:2), (3:1) occur in 27\% of the other cases. Our orbital predictions includes 171 exoplanets, 2 Jupiter moons, one Saturn moon, 3 Uranus moons, and 4 Neptune moons. The accuracy of the predicted planet distances amounts to a few percent, which fits the data significantly better than the Titius-Bode law or a logarithmic spacing. This information may be useful for targeted exoplanet searches with Kepler data and to estimate the number of live-carrying planets in habitable zones.

Titus-Bode's Law Seems to Apply to Exoplanetary Systems

Applying Titius-Bode's Law on Exoplanetry Systems

Authors:

Altaie et al

Abstract:

We report the application of Titius-Bode's law on 43 exoplanetary systems containing four or more planets. Due to the fact that most of these systems have their planets located within compact regions extending for less than the semi-major axis of Mercury we found the necessity to scale down the Titius-Bode law in each case. In this short article we present sample calculations for three systems out of the whole set. Results show that all systems studied are verifying the applicability of the law with high accuracy. Consequently our investigation verifies practically the scale invariance of Titius-Bode law. The results of this study buildup the confidence in predicting positions of the exoplanets according to Titius-Bode's law besides enabling diagnosing possible reasons of deviations.

Updating Titus-Bode "Laws" for Observed Exoplanets From Kepler

Using the Inclinations of Kepler Systems to Prioritize New Titius-Bode-Based Exoplanet Predictions

Authors:

Bovaird et al

Abstract:

We analyze a sample of multiple-exoplanet systems which contain at least 3 transiting planets detected by the Kepler mission ("Kepler multiples"). We use a generalized Titius-Bode relation to predict the periods of 228 additional planets in 151 of these Kepler multiples. These Titius-Bode-based predictions suggest that there are, on average, ~2 planets in the habitable zone of each star. We estimate the inclination of the invariable plane for each system and prioritize our planet predictions by their geometric probability to transit. We highlight a short list of 77 predicted planets in 40 systems with a high geometric probability to transit, resulting in an expected detection rate of ~15%, ~3 times higher than the detection rate of our previous Titius-Bode-based predictions.

Testing the Titus-Bode Law for Kepler Exoplanet Systems

Testing the Titius-Bode law predictions for Kepler multi-planet systems

Authors:

Huang et al

Abstract:

We use three and half years of Kepler Long Cadence data to search for the 97 predicted planets of Bovaird & Lineweaver (2013) in 56 of the multi-planet systems, based on a general Titius-Bode relation. Our search yields null results in the majority of systems. We detect five planetary candidates around their predicted periods. We also find an additional transit signal beyond those predicted in these systems. We discuss the possibility that the remaining predicted planets are not detected in the Kepler data due to their non-coplanarity or small sizes. We find that the detection rate is beyond the lower boundary of the expected number of detections, which indicates that the prediction power of the TB relation in general extra solar planetary systems is questionable. Our analysis of the distribution of the adjacent period ratios of the systems suggests that the general Titius-Bode relation may over-predict the presence of planet pairs near the 3:2 resonance.