Abundance of Earth Analogs

The original motivation behind NASA’s Kepler mission (and, indeed, the primary driver of the design of its hardware) was to detect Earth-size planets orbiting Sun-like stars in Earth-like orbits. While the ongoing analysis of the huge amount of data from Kepler’s primary mission has uncovered thousands of planets to date including easier-to-detect Earth-size planets in short-period orbits, larger planets in Earth-like orbits and even potentially habitable planets orbiting stars much smaller than the Sun, no true Earth analogs have been found… yet! This is not to say that such planets do not exist. They are just more difficult to detect via the transit method than those already announced and will require more time to tease out of the data set from Kepler’s prime mission.

Diagram of Kepler spacecraft. Kepler’s design was driven by the goal of being able to detect Earth-size planets orbiting Sun-like stars in Earth-like orbits. (NASA/Kepler Mission/Ball Aerospace)

Earth Analogs

In the mean time, there have been enough planets found with a variety of characteristics in Kepler’s data for scientists to begin to make predictions of how many Earth analogs do exist in the galaxy. Last fall, Erik Petigura (University of California – Berkeley/University of Hawaii at Manoa), Andrew Howard (University of Hawaii at Manoa) and famed extrasolar planet hunter, Geoff Marcy (University of California – Berkeley) published a paper based on an extrapolation of Kepler’s current catalog of planetary finds to estimate that 5.7% (+1.7%, -2.2%) of Sun-like stars are orbited by Earth analogs.

One has to be careful not to confuse “Earth analog” with a “habitable planet”. While some Earth analogs might be habitable, not all habitable planets are Earth analogs as defined in this paper. For the purposes of their paper, Petigura et al. defined an Earth analog as a planet with a radius between 1 and 2 times that of the Earth orbiting a G-type dwarf star with a period of 200 to 400 days. By this definition, for example, Venus (which is most certainly not habitable) is an Earth analog. Also included under this definition are potentially non-terrestrial planets such as mini-Neptunes or gas dwarfs. Earlier analyses of the Kepler data set (including two papers that Marcy coauthored) have shown that the transition from terrestrial to non-terrestrial planets seems to occur in the 1.5 to 2.0 Earth-radii range which constitutes the upper half of their definition of Earth analogs (see “Habitable Planet Reality Check: Terrestrial Planet Size Limit“).

As important as the types of planets included in this definition of Earth analog are those that are excluded that could potentially still be habitable. Planets orbiting slightly hotter F-type or slightly cooler K-type dwarf stars, which have generally been considered candidates for harboring habitable planets, are excluded. Planets in more distant orbits that still reside inside a star’s habitable zone by most definitions are also excluded, as are potentially habitable planets smaller than one Earth radii – both being types of planets Kepler and its mission were not designed to detect.

I should point out that this explanation is not meant to be a criticism of the definition of Earth analog chosen by Petigura et al. Their definition was carefully crafted to include the types of planets that Kepler could potentially detect around stars most similar to the Sun once the data analysis is much further along.  Also, this definition includes what can be reasonably extrapolated from the current Kepler extrasolar planet catalog. This work is but the first step towards eventually estimating the prevalence of potentially habitable and even truly Earth-like planets. With that being said, it is time to consider a new estimate for the prevalence of Earth analogs that has recently become available.

A scatter plot of planet radius versus orbital period for Kepler discoveries as of January 2013. Earth analogs would occupy the blank region towards the lower right corner of this plot. (NASA/Kepler Mission)

New Estimate of Abundance of Earth Analogs

A couple of weeks ago, Daniel Foreman-Mackey (New York State University), David Hogg (New York State University/Max Planck Institute for Astronomy) and Timothy Morton (Princeton University) submitted a paper for publication where they make their own estimate of the prevalence of Earth analogs. In this new paper, the author’s make fewer assumptions than Petigura et al. in their extrapolations of the size distribution of planets and the distribution of planets as a function of orbital period derived from the Kepler catalog.  Foreman-Mackey et al., unlike the earlier work, also explicitly take into account the non-trivial measurement uncertainties in values of planet orbital period and especially planet radius present in the data of the Kepler catalog when performing their extrapolations.

When Foreman-Mackey et al. compare Kepler’s current extrasolar planet catalog to synthetic catalogs generated using their results and those of Petigura et al., their results are more accurate but less precise than the earlier work. This lower precision is reflected in larger relative error bars of their results and more realistically represent the uncertainties in the unavoidable extrapolations from the current list of Kepler discoveries to Earth-size planets in Earth-like orbits.

In the end, Foreman-Mackey et al. come up with an occurrence rate of Earth analogs (as originally defined in the earlier paper by Petigura et al.) of 1.6% (+1.1%,-0.7%). This value is less than a third of that derived by Petigura et al.. Based on their calculations, Foreman-Mackey et al. predict that 9.2 (+5.9,-4.0) Earth analogs are likely to be discovered in the Kepler data (with their stated uncertainty ignoring the Poisson sampling variance resulting from the finite sample size of G-type dwarf stars observed during Kepler’s primary mission).

Only a more thorough analysis of the existing Kepler data set will tell whose predictions about the occurrence rate of Earth analogs is correct. And once those Earth analogs are found and these results folded into a fuller analysis of the data set from Kepler’s primary mission, its K2 extended mission currently underway as well as the results from NASA’s upcoming TESS mission (Transit Exoplanet Survey Satellite due for launch in 2017), will scientists be in a much better position to derive more accurate estimates of not only the prevalence of Earth analogs but potentially habitable planets orbiting all types of stars as well.

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Related Reading

“Detecting Habitable Planets: The Next Decade”, SETIQuest, Volume 4, Number 1, pp. 1-6, First Quarter 1998 [Article]

“Habitable Planet Reality Check: Terrestrial Planet Size Limit”, Drew Ex Machina, July 24, 2014 [Post]

“The Transition from Super Earth to Mini Neptune”, Drew Ex Machina, March 29, 2014 [Post]

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

General References

Geoffrey W. Marcy et al., “Masses, Radii, and Orbits of Small Kepler Planets: The Transition from Gaseous to Rocky Planets”, The Astrophysical Journal Supplement, Vol. 210, No. 2, Article id. 20, February 2014

Daniel Foreman-Mackey, David W. Hogg, Timothy D. Morton, “Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs”, arXiv:1406.3020, Submitted June 11, 2014 [Preprint]

Erik A. Petigura, Andrew W. Howard and Geoffrey W. Marcy, “Prevalence of Earth-size planets orbiting Sun-like stars”, Proceedings of the National Academy of Sciences of the United States, Vol. 110, No. 48, pp. 19273-19278, November 26, 2013 [Abstract & Paper Access]

Lauren M. Weiss and Geoffrey W. Marcy, “The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii”, The Astrophysical Journal Letters, Vol. 783, No. 1, Article id. L6, March 2014