Kepler’s Planetary Bonanza on SciShow

I meant to post this earlier, but it slipped down the list. If you haven’t seen it yet, SciShow did a segment earlier this month on the bonanza of planets discovered via the Kepler Space Telescope. My article on verification by multiplicity got a special shout-out in the credits on the YouTube page (see the about tab)!




What is Verification by Multiplicity?


There’s been a buzz the last few days about the 715 new planets that NASA has verified, using data from the Kepler Space Telescope. This discovery doubles the number of known planets, and turned up four new planets that could possibly support life.

Beyond the sheer joy of the discovery, one of the interesting aspects of this announcement is the statistical technique that NASA scientists used to winnow out so many planets from the data in bulk: verification by multiplicity. Using this technique, scientists can verify the presence of suspected planets around a star sooner, without having to wait for additional measurements and observations.

I got curious: what is verification by multiplicity? I’m no astronomer, but it’s not too difficult to grasp the basic statistical reasoning behind the method, as described in Lissauer et al. “Almost All of Kepler’s Multiple Planet Candidates Are Planets,” to be published in The Astrophysical Journal on March 10 (a preprint is available at My discussion isn’t exactly what the researchers did, and I stay with a simple case and avoid the actual astrophysics, but it gets the idea across. I’ll use R to work the example, but you should be able to follow the discussion even if you’re not familiar with that programming language.

The need for statistical verification

From what I understand of the introduction to the paper, there are two ways to determine whether or not a planet candidate is really a planet: the first is to confirm the fact with additional measurements of the target star’s gravitational wobble, or by measurements of the transit times of the apparent planets across the face of the star. Getting sufficient measurements can take time. The other way is to “validate” the planet by showing that it’s highly unlikely that the sighting was a false positive. Specifically, the probability that the signal observed was caused by a planet should be at least 100 times larger than the probability that the signal is a false positive. The validation analysis is a Bayesian approach that considers various mechanisms that produce false positives, determines the probability that these various mechanisms could have produced the signal in question, and compares them to the probability that a planet produced the signal.

The basic idea behind verification by multiplicity is that planets are often clustered in multi-planet star systems, while false positive measurements (mistaken identification of potential planets) occur randomly. Putting this another way: if false positives are random, then they won’t tend to occur together near the same star. So if you observe a star with multiple “planet signals,” it’s unlikely that all the signals are false positives. We can use that observation to quantify how much more likely it is that a star with multiple candidates actually hosts a planet. The resulting probability can be used as an improved prior for the planet model when doing the statistical validation described above.

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Goldbach’s Celestial Atlas

Christian Goldbach, Prussian mathematician. Probably most famous for the Goldbach conjecture, one of the oldest unsolved problems in mathematics:

Every even integer greater than 2 can be expressed as the sum of two primes.

The story goes that he scribbled this conjecture in the margin of a letter he wrote to Euler. In fact, he wrote two versions of the conjecture in that letter — one in the body, and one in the margin. The statement above, which is how we know the Goldbach conjecture today, actually came from a subsequent letter, in which he and Euler continued the original conversation.

But less known is the fact that Goldbach also dabbled — very briefly — in astronomy. In 1799 he published Neuester Himmels – Atlas zum Gebrauche für Schul und Akademischen Unterricht, nach Flamsteed … [], in einer neuen Manier, mit doppelten schwarzen Stern-Charten bearbeitet; durchgehends verbessert, und mit den neuesten astronomischen Entdeckungen vermehrt [The Newest Celestial Atlas for the use of School and Academic Education, according to Flamsteed …[], in a new Style, edited with double black Star-Charts; improved and expanded with the latest astronomical Discoveries].

NewImageThe constellation Leo, with figures
Thumbnail image from The Linda Hall Library

The atlas was printed with white stars on a black background in two pressings: the first pressing had the stars only, as you would see them in the night sky. On the second pressing, annotations and figures of the constellations were added, as seems to have been customary with star-charts of the time.

Neuster Himmels was Goldbach’s only astronomical publication. The Linda Hall Library of Science, Engineering, & Technology in Kansas City, Missouri has plates from the first edition of the atlas viewable online. You can see the charts as fairly large images both with and without the figures.