The planets Earth and Venus would seem alike to a distant observer looking at our solar system. They have similar radii, masses, bulk compositions and distances from the Sun. But upon closer inspection, these “twins” could not be more dissimilar. Earth is a habitable planet with moderate temperatures, plentiful liquid water and a thriving biosphere while Venus experiences a runaway greenhouse effect with a stiflingly thick atmosphere, virtually no water and a sterile surface. While these two planets might have much in common, they evolved in very different directions probably due to the factor of two difference in the amount of energy they receive from the Sun. Understanding the origins of these different evolutionary paths, and hence the limits of planetary habitability, will require finding examples of not only Earth-like extrasolar planets but Venus-like planets as well.

As astronomers continue to struggle to identify Earth-like planets in Kepler’s database, they have had an easier time finding potentially Venus-like planets. This is not necessarily because Venus-like planets are more common but is due to the fact that such planets are easier to detect by the transit detection method successfully employed by Kepler. Venus-like planets orbit closer to their suns than Earth-like planets which increases the probability of producing an observable transit. Also, Venus-like planets have shorter orbital periods than Earth-like planets so that they will produce more transit events increasing the likelihood of detection by improving the signal-to-noise ratio.

Stephen Kane (San Francisco State University), Ravi Kopparapu (Penn State University) and Shawn Domagal-Goldman (NASA Goddard Space Flight Center) have collaborated in an analysis of Kepler data that takes advantage of the more ready detectability of Venus-like planets to estimate their occurrence rate. The first step was to define the Venusian analog to the habitable zone (HZ) called the Venus zone (VZ) – the range of distances from a sun where a terrestrial planet would have surface conditions like Venus. Based on earlier work by Kopparapu et al., the outer limit of the VZ was defined to be the maximum distance where a runaway greenhouse effect would exist. This distance also corresponds to the conservative inner limit of the HZ which is 0.95 AU for an Earth-mass planet in our solar system. For the inner limit of the VZ, Kane et al. adopted the distance where the effective stellar flux is 25 times what the Earth receives from the Sun – the equivalent of 0.2 AU in our solar system. This stellar flux corresponds roughly to the minimum value required for a Venus-size planet to suffer from severe atmospheric erosion that would make it into an airless world like Mercury. While the precise stellar flux required for a planet to lose its atmosphere would depend on the mass of the planet and a host of other factors, Kane et al. adopted this fixed value for the purposes of calculating their initial estimate for the occurrence rate of Venus analogs.

In order to estimate the occurrence rate of Venus-like planets, Kane et al. limited their search of Kepler planet candidates not only by stellar flux but to planets with radii 0.5 to 1.4 times that of the Earth. No explicit reason is given for this choice in their paper except to state that such planets would be most Venus-like in size. However, the low end of this range would correspond to Mars-size planets that would be most difficult for Kepler to detect. In addition, recent analyses of Kepler data strongly suggests that planets much larger than the upper end of the range chosen by Kane et al. are more likely to be mini-Neptunes or gas dwarfs (see “Habitable Planet Reality Check: Terrestrial Planet Size Limit“).

After combing through the database of Kepler planet candidates, Kane et al. identified 43 potentially Venus-like extrasolar planets. Using results from earlier papers on statistical analyses of the occurrence rates of various size planets and corrections for Kepler’s detection rate, Kane et al. estimate an occurrence rate of Venus analogs of 0.32 (+0.05/-0.07) and 0.45 (+0.06/-0.09) for M dwarf stars and G/K dwarf stars, respectively. If we assume that our galaxy contains 400 billion stars with about 77% being M dwarfs and 20% being G and K dwarfs combined (all ballpark numbers), the occurrence rate derived by Kane et al. implies that there are about 135 billion Venus-like planets in our galaxy, give or take a couple of tens of billion.

One should be careful about directly comparing this estimated occurrence rate of Venus-like planets with recently published values of the occurrence rate of Earth analogs such as the most recent estimate of 0.016 (+0.011/-0.007) by Foreman-Mackey et al.. Foreman-Mackey et al., mirroring the earlier work by Petigura et al., define an Earth analog as being a planet with a radius between 1 and 2 times that of the Earth orbiting a G dwarf with an orbital period of 200 to 400 days regardless of the planet’s stellar flux (see “Abundance of Earth Analogs“). While there is some overlap between these definitions of Venus analogs by Kane et al. and Earth analogs by Petigura et al. (e.g. Venus would be considered an Earth analog by this definition just like the Earth), they are defining boundaries for different parts of planet parameter space. Most notably, the definition of a Venus-like planet by Kane et al. includes much smaller planets than are considered in the definition of Earth analog by Petigura et al.. And since smaller planets are generally expected to be much more numerous than larger planets, one would expect the occurrence rate of Venus-like planets to tend to be higher than that for Earth analogs as both are being defined here. The same argument applies when attempting to use the occurrence rate of Earth analogs to estimate the number of habitable Earth-like planets the latter of which will also include a larger number of smaller planets in more distant orbits than considered by Petigura et al.

The work associated with this initial estimate by Kane et al. on the occurrence rate of Venus-like planets is useful for determining where to look for potentially Venus-like planets in an effort to probe the limits of the HZ. Much more work remains to be done sifting through Kepler’s data in the more difficult task of finding Earth-size planets in more distant Earth-like orbits before a statistically meaningful occurrence rate of potentially habitable Earth-like planets can be estimated.

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Related Reading

“The Prevalence of Earth-Size Planets Around Sun-Like Stars”, Drew Ex Machina, November 3, 2015 [Post]

“Abundance of Earth Analogs”, Drew Ex Machina, June 25, 2014 [Post]

“GJ 832c: Habitable Super Earth or Super Venus?”, Drew Ex Machina, June 27, 2014 [Post]

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

General References

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 (accepted for publication in The Astrophysical Journal), June 11, 2014 [Preprint]

Stephen R. Kane, Ravi Kumar Kopparapu and Shawn D. Domagal-Goldman, “On the Frequency of Potential Venus Analogs from Kepler Data”, arXiv: 1409.2886 (accepted for publication in The Astrophysical Journal Letters), September 9, 2014 [Preprint]

R. K. Kopparapu et al., “Habitable zones around main-sequence stars: new estimates”, The Astrophysical Journal, Vol. 765, No. 2, Article ID. 131, March 10, 2013

Ravi Kumar Kopparapu et al., “Habitable zones around main-sequence stars: dependence on planetary mass”, The Astrophysical Journal Letters, Vol. 787, No. 2, Article ID. L29, June 1, 2014

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]