View Full Version : Excess of only one observed planet?

2017-May-14, 05:18 AM
This excess Sarah Ballard and some other exoplanetologists have called the "Kepler Dichotomy", from it appearing in Kepler's planets. I decided to check on whether it exists, so I got data from an exoplanet catalog.

I used a download of the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/) database that I did on 2017 April 24, 5:07 PM PDT, and I found these numbers:

Kepler: 1645 -- 1198, 286, 103, 39, 16, 2, 1
NK Transit: 376 -- 340, 27, 5, 2, 1, 0, 1
NK Radial: 484 -- 384, 74, 15, 6, 3, 2
NK Imaging: 40 -- 38, 1, 0, 1
NK Lensing: 42 -- 40, 2

Kepler = main mission, with K2 discoveries folded into NK Transit
NK = Non-Kepler, everything but Kepler's main mission

There were too few planets discovered with direct imaging or gravitational microlensing to make their numbers a good test, so I focused on the first three. I fit a power-series planet count, N systems with n planets with parameters N0 and r: N = N0 * rn

Kepler: N0 = 2453.88, r = 0.344304, excess = 353.119, ratio = 1.41795
NK Transit: N0 = 457.63, r = 0.23868, excess = 230.773, ratio = 3.11278
NK Radial: N0 = 984.067, r = 0.268019, excess = 120.251, ratio = 1.45593

So the Kepler spacecraft found over 40% more single-planet systems that one would expect from the multiplanet systems that it found. For Kepler's transits, this power law is consistent with multiplanet systems following a Bode-like power law of distance and being viewed from different angles. For non-Kepler transits and for radial-velocity measurements, different observation time ranges and detection limits. That's what makes Kepler's discoveries good for doing such statistics: the main mission had one observation time range and one detection limit.

The excess suggests systems with different compositions, like additional planets having high relative inclinations. Sarah Ballard and others have suggested that this could be from going through a phase of instability, like an inspiraling Jovian planet catching up with another such planet. A near-collision could cause very eccentric orbits, like the sorts of orbits seen for some exoplanets with radial-velocity detection. Such a planet would then clear out all the space from its closest distance to its farthest distance, thus greatly reducing the number of planets that are present.