The Kepler Mission was designed to answer one question: how many planets like Earth are out there?  Are worlds like our own a common outcome of planet formation, or are they rare?

While the Kepler Mission was designed to answer this question about Earth-sized planets in Earth-like orbits, it was also able to answer this question for planets bigger than Earth and for planets closer to their stars than Earth.  We can ask more broadly, what other kinds of planets are out there?  What types of planets are common, and what types of planets are rare?

Kepler answered these questions with the power of statistics.  By staring at 150,000 stars for four years and searching for transiting exoplanets, Kepler allowed scientists to survey what kinds of planets do and do not exist.

The statistical analysis is easy at first.  We begin with counting how many planets of a certain size Kepler found.  How many Jupiter-sized planets?  How many Neptune-sized planets?  How many Earth-sized planets?  What about planets of in-between sizes?  How many of each of these planets do we find at a variety of different orbits?  We can cross-cut and tally up the Kepler planet harvest to get a first glimpse of which planets are common and which are rare.

Kepler planet count
The Kepler team planet candidate count as of January 2013. The heights of the bars (and the numbers on top of the bars) show how many planets of each size Kepler found. The yellow percentages are the percent increase from the previous Kepler team planet count. There are two things worth noting. 1) Kepler found more planets that are “Neptune-sized” and smaller than big planets. 2) Over time, the Kepler telescope’s sensitivity to small planets increased more than its sensitivity to big planets. This is because big planets are easy to find after their first three transits, whereas a small planet might become detectable only after dozens of transits.  For the watchful: the decrease in the number of Jupiter-sized planets from one accounting to the next occurred because some planet candidates of that size were deemed not to be real planets and were discarded.

But there is a twist: some planets are easier for Kepler to find than others.  Planets closer to their stars are more likely to transit than planets farther away, so our simple tally has under-counted the number of far-out planets.  Also, planets that make deep transits are easier to find than planets that make shallow transits, and so our tally has under-counted the number of small planets.  With some robust geometry, algebra, and signal processing, my colleagues Petigura, Howard, and Marcy (2013) corrected for these counting missteps, creating a clearer picture of which planets are common and which are rare.

Prevalence of Earths
Reproduced from Petigura, Howard, & Marcy (2013). Left: The number of planets of various sizes that were actually found around the Kepler stars (gray), and how many should be added to the tally to correct for missed planets (orange). Rather than expressing the tally as the number of planets, the tally is converted to the fraction of stars that have the indicated planet type: for instance, we can add the left two bins to find that 26% of stars have a planet between 1-2 times the size of the Earth. Only planets with orbital periods of 5-100 days were included in this accounting. Right: The tally of planets at various orbital periods, with the same color scheme as the left panel. Kepler found more planets at longer orbital periods, but note that the study only goes as far as 100 days (Mercury’s orbit around the sun is 88 days). Assuming that the number of planets at Earth-like orbital periods is similar to what is counted at 100 days, this study finds that about 1/5 stars should have a planet 1-2 times the size of Earth in an orbit of 100-400 days.

One important caveat to this survey is that planet size does not necessarily correspond to planet composition.  Just because a planet is Earth-sized and in the habitable zone does not mean that it is a rocky world, let alone a world with continents, oceans, and life.  To learn more about these attributes, we will need to design and build new telescopes.

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