Orbital Resonance - Mean Motion Resonances Among Extrasolar Planets

Mean Motion Resonances Among Extrasolar Planets

While most extrasolar planetary systems discovered have not been found to have planets in mean motion resonances, some remarkable examples have been uncovered:

• As mentioned above, Gliese 876 e, b and c are in a 1:2:4 orbital resonance, with periods of 124.3, 61.1 and 30.0 days.
• KOI-730 d, b, c and e appear to be in a 3:4:6:8 resonance, with periods of 19.72, 14.79, 9.85 and 7.38 days.
• KOI-500 c, b, e, d and f appear to be in or close to a 20:27:41:62:193 resonance, with periods of 9.522, 7.053, 4.645, 3.072 and 0.9868 days.
• Both KOI-738 and KOI-787 appear to have pairs of planets in a 7:9 resonance.

Cases of extrasolar planets close to a 1:2 mean motion resonance are fairly common. Sixteen percent of systems found by the transit method are reported to have an example of this (with period ratios in the range 1.83-2.18), as well as one sixth of planetary systems characterized by Doppler spectroscopy (with in this case a narrower period ratio range). Due to incomplete knowledge of the systems, the actual proportions are likely to be higher. Overall, about a third of radial velocity characterized systems appear to have a pair of planets close to a commensurability. It is much more common for pairs of planets to have orbital period ratios a few percent larger than a mean motion resonance ratio than a few percent smaller (particularly in the case of first order resonances, in which the integers in the ratio differ by one). This was predicted to be true in cases where tidal interactions with the star are significant.