While one of the primary motivations for NASA’s Kepler mission has been the detection of Earth-size planets orbiting Sun-like stars in Earth-like orbits using precision photometry to observe planetary transits, this successful mission’s huge data set also allows the architecture of extrasolar planetary systems to be studied. This has given astronomers their first opportunity to see how system architectures might vary from system to system as well as determine whether or not our own solar system is typical. A number of analyses have already been performed which are just now beginning to reveal that a wide range of planetary arrangements seem to exist with our solar system being just one example in a wide spectrum of possibilities.

The most numerous group of stars in our galaxy are dim red dwarf stars. Unlike many earlier investigations that tended to look at more Sun-like FGK-type stars, Sarah Ballard (NASA Carl Sagan Fellow at the University of Washington) and John Asher Johnson (Harvard-Smithsonian Center for Astrophysics) recently submitted for publication a statistical analysis of M-dwarf planetary systems detected by NASA’s Kepler mission. In total, they selected 167 KOIs (Kepler Objects of Interest – shorthand for a candidate planet that has not been necessarily confirmed) orbiting 106 stars. Out of these stars, which ranged in spectral type from M4V to K7V, 71 host a single KOI, 17 host a pair of KOIs, 12 host three KOIs, four host four KOIs and two host five KOIs including Kepler 186 (see “Habitable Planet Reality Check: Kepler 186f”).

Since KOIs, by definition, are not necessarily confirmed planetary discoveries, Ballard and Johnson calculated the probability of a KOI being a false positive based on the characteristics of the observed transits. They discarded five single KOIs (6.3% of their original sample of singles) as being potentially blended stellar images or eclipsing binaries. They found that 87 of the KOIs in their remaining sample have a false positive probability (FPP) of <0.05 and 104 have an FPP of <0.10. Of the 11 remaining KOIs with an FPP of >0.10, six reside in transiting multi-planet systems and are therefore likely to be bona fide planets. Another was confirmed to be a hot Jupiter (the only one known to orbit a red dwarf) in a separate study while the remaining four KOIs are conservatively assumed to have a 5% chance of being a false positive for the purpose of this analysis.

The analysis of M-dwarf planetary systems by Ballard and Johnson indicates that no one planetary system architecture can explain the observed occurrence rate of single and multi-transit systems. A model with many planets in nearly coplanar orbits (roughly analogous to our own solar system) does not produce enough single-transit systems. A model with multiple planets in orbits with large mutual inclinations (i.e. >7°) does not produce enough multiple-transit systems. This same phenomena was observed in earlier analyses of hotter, more Sun-like stars observed during the Kepler mission and has become known as the “Kepler Dichotomy”.

The simplest solution to the Kepler Dichotomy is to posit that two different types of architectures for planetary systems exists: one with a single planet or multiple planets with large mutual inclinations and another with multiple planets with low mutual inclinations. Ballard and Johnson found that they could reproduce the observed number of multiple-transiting systems if each M-dwarf hosts 6.1±1.9 planets with typical mutual inclinations of 2.0° +4.0°/-2.0°. Since M-dwarf stars are the most common in the galaxy, the authors consider this architecture to be the “typical” multi-planet system in our galaxy. While the planetary systems of M-dwarfs are more compact than ours, these values neatly include our own solar system with its 8 planets whose orbits have an RMS inclination of 1.9° to the solar system’s invariable plane (i.e. the plane defined by the total angular momentum of the solar system). In order to account for the excess number of single-transit systems, Ballard and Johnson found that 55% +23%/-12% of the systems must have just one planet or multiple planets with large mutual inclinations. This approximate 50-50 split between these two different planetary system architectures is consistent with earlier findings.

Ballard and Johnson also found a modestly significant (i.e. at a 95% confidence level) correlation between some of the host star’s properties and which type of planetary system architecture it is likely to have. They found that faster rotating stars located closer to the galactic midplane that are relatively metal poor (i.e. they have lower concentrations of elements heavier than helium which astronomer dub “metals”) are more likely to have coplanar multi-planet systems. In the case of the correlation with metal concentration, this has already been observed in other studies of planetary systems and a potential explanation already exists. It is believed that metal-rich stars would have more massive circumstellar disks out of which larger numbers of more massive giant planet would form. Beyond a certain point of growth, such systems become unstable and the planets scatter into more eccentric orbits with high mutual inclinations. Metal-deficient stars would form less massive planets that would be more likely to remain in stable, low inclination orbits. The fact that the largest planets in this sample of red dwarfs are found in single-transit system seem to lend support to this hypothesis.

The correlations found with stellar rotation and location relative to the galactic midplane are a bit more difficult to explain. Faster rotating stars located closer to the galactic midplane are typical hallmarks of their relative youth hinting that younger stars are more likely to have coplanar multi-planet systems. This could imply that there is a mechanism that can disrupt such systems well after they form. Although not considered by Ballard and Johnson, it might also hint that the nature of planetary systems formed more recently is different than those formed long ago. Additional study will be needed to better determine the correlation between age and planetary system architecture.

Ballard and Johnson also briefly looked into what role stellar binarity might play in the architecture of M-dwarf planetary systems. While the presence of a companion star can certainly affect the formation of a planetary system, they found that the observed occurrence rate of binary M-dwarf systems is insufficient to explain the observed number of single-transit systems. More analysis of a larger sample will be needed to determine the role of a stellar companion plays in planet formation and system architectures.

A fuller discussion of the occurrence rate and architecture of planetary systems for all types of stars based on information not only from NASA’s Kepler mission but a wide range of other detection techniques can be found in a paper recently submitted by Joshua N. Winn (Massachusetts Institute of Technology) and Daniel C. Fabrycky (University of Chicago). This fully referenced review paper is intended to appear in the 2015 issue of The Annual Review of Astronomy & Astrophysics.

Related Reading

“Habitable Planet Reality Check: Kepler 186f”, Drew Ex Machina, April 20, 2014 [Post]

“The Occurrence of Potentially Habitable Planets Around Red Dwarfs”, Drew Ex Machina, January 12, 2015 [Post]

General References

Sarah Ballard and John Asher Johnson, “The Kepler Dichotomy Among the M Dwarfs: Half of Systems Contain Five or More Coplanar Planets”, arXiv: 1410.4192 (submitted to The Astrophysical Journal), October 15, 2014 [Preprint]

Joshua N. Winn and Daniel C. Fabrycky, “The Occurrence and Architecture of Exoplanetary Systems”, arXiv: 1410.4199 (submitted to The Annual Review of Astronomy & Astrophysics), October 15, 2014 [Preprint]