One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

Artist’s impression of the Kepler telescope [credit: Wikipedia]

So said researchers in their 2015 study which had that title. Then a third planet was seen.

In the abstract they say:

Methods. Our search through two separate pipelines led to the independent discovery of K2-19b and c, a two-planet system of Neptune-sized objects (4.2 and 7.2 R⊕), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously owing to their proximity to resonance and the alignment of conjunctions.

A third planet ‘d’ even nearer to the star was later discovered, and since the data had a general update published only a few days ago (see exoplanet.eu) we can give their observations these new orbit numbers:
19 d = 47.6539 days
6 b = 47.5332
4 c = 47.5972

Translating to conjunctions:
6 – 4 = 2 b-c
19 – 6 = 13 d-b
19 – 4 = 15 d-c

2 and 13 are Fibonacci numbers , with 15 being the sum of the two ‘neighbour’ pairs, as it has to be.

K2-19 b, the middle planet in terms of distance from the star, is the heaviest having ~3 times (2.997) the mass of c and slightly more than 3 times that of d, so b:c ratios are 3:1 mass and 3:2 orbits.

The 3:2 resonance referred to in the study is discussed in section 7.3: Hill stability.

In their caption to Figure 9 the authors say:
the 3:2 MMR* might act as a crucial protection mechanism to ensure the system’s long-term stability on the main sequence. [*mean motion resonance]
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Astronomy & Astrophysics: One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c [2015 research article]