How many Earth-size planets are orbiting Sun-like stars?

Size and number of Kepler Planet Candidates

In the search for planets that may be habitable outside of our own solar system, one of the elements that should be considered is planet size.  Planet size is important for various reasons. There is evidence that suggests that plate tectonic activity on a global level is a necessary factor for supporting life on a planet similar to Earth.  Planets must be of a particular size in order to allow for global plate tectonics.^[001] Larger planets (between the range of Mars and Earth) may be necessary to maintain an atmosphere with the right composition to support life.^[002] Based on the limited examples available within our own solar system, life may require specific conditions that are associated with Earth's size.

So, how many Earth-size planets exist?  Well, to start with, small terrestrial planets drastically outnumber larger Earth-size and Jupiter-size planets.  That being the case, recent observations suggest that Earth-size planets are fairly common around Sun-like stars.^[003] There are so many such planets, the 2013 study Prevalence of Earth-size planets orbiting Sun-like stars states that (given certain circumstances),

...the nearest such planet is expected to orbit a star that is less than 12 light-years from Earth and can be seen by the unaided eye.^[003]

That's not only a lot of planets, 12 light-years is a distance that seems at least somewhat reachable with technology that is currently being investigated.  Recently, such a planet seems to have been discovered around the closest star to our own, Proxima Centauri.^[004]  Technically, Proxima Centauri cannot be seen with the unaided eye on its own, but rather as part triple star system that appears as one the dot in the Southern Hemisphere sky called Alpha Centauri, but close enough (literally).^[005]

Kepler's Small Habitable Zone Planets

Overall based on Kepler space observatory results, it is calculated that about 22% of all Sun-like stars have an Earth-size planet within its Habitable Zone.  Prevalence of Earth-size planets orbiting Sun-like stars seems well informed in its conclusion (2013),

Future instrumentation to image and take spectra of these Earths need only observe a few dozen nearby stars to detect a sample of Earth-size planets residing in the Habitable Zones of their host stars.^[003]

The number of Sun-like stars in the Milky Way Galaxy is said to be about 10%.*  The number total stars is a matter of debate, but it often stated as 100 billion stars.^[006]  10% of that is 10 billion stars.  Therefore, 22% of 10 billion is 2.2 billion stars.  With that determined, how common are planets that are so similar to Earth that events naturally occur in the right sequence to spark and nurture life?  How likely is that life to evolve to develop the human-level expression of intelligence and curiosity?  What is the likelihood of any of species developing in the same timeframe as us?  Are other species close enough to us to communicate with us?  Should we really trying to reach out to these others?  Some of these questions will be addressed in further articles.

*10% is stated by multiple tertiary sources for "sun-like" stars, and 7.5% is stated for "g-type" stars, but I could not verify these percentages from any original sources.

Primary reference:
E.A. Petigura, A.W. Howard, G.W. Marcya, Proceedings of the National Academy of Sciences of the United States of America, 110 no. 48, (Nov., 2013), 19273-19278, 10.1073/pnas.1319909110,  Prevalence of Earth-size planets orbiting Sun-like stars

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Article Series:

• Limited lifespan of Habitable Zones around other stars [and a loosely held secret finally revealed about me]
• Small stars may have stable Habitable Zones, but habitable planets might not be common there
• Habitable Planets around White Dwarfs
• Habitable Worlds Around Binary Star Systems might not match Sci-fi
• How many Earth-like planets are orbiting Sun-like stars?
• First round of life in the Universe might have been possible extremely early
• Factors a planet needs for suitability of life; perhaps
• "Goldilocks zone of metallicity" on a galactic scale
• Maybe we are the first

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Habitable Worlds Around Binary Star Systems might not match Sci-fi

It's hard to talk about planets in binary (dual) star systems without mentioning Star Wars: A New Hope.  The famous scene of Luke Skywalker standing and looking off into the distance while two suns appear near the horizon is iconic.  However, there's a problem with that iconic scene.  The problem is a not full-fledged error, just an unlikelihood: both suns appear as the same size in the sky in very close proximity to each other.  The reason this is unlikely is due to the two types of planetary orbits in binary star systems: s-type and p-type.  A planet in either type of binary system would rarely see both suns as the same size in the sky and that close to each other, even if the suns are the same size.

S-type is the name for the orbit of a planet that revolves around just one of the two stars within a binary system. P-type is the name for the orbit of a planet that revolves around both stars within a binary system, having a common barycenter (or center of mass) with the suns as the suns orbit around each other.^[001]

S-type orbits are interesting, but for this article, I'll cover P-type because this is more interesting to me when talking about Habitable Zones, particularly where the suns have similar masses.  Of course, even with p-type orbits, there exist many possible varieties for how the suns can orbit each other.

The ability of a planet to maintain liquid water depends on the interaction between stellar radiation and the top of its atmosphere.  Also, that interaction is complicated in a binary system.  There can be substantial difference in energy received by the dual suns.  Sometimes both suns appear side by side in the sky, providing maximum energy.   However, when one sun is eclipsed by the other, the amount of energy is lessened due to the closer sun blocking the stellar radiation from its partner.^[001]

In either case, this variation in stellar radiation can limit how small a planet's orbit can be around the dual suns and still be capable of harboring life.   As stated in Calculating the Habitable Zone of Binary Start Systems II: P-Type Binaries:

This interaction strongly depends on the stellar spectral energy distributions implying that stars with different energy distributions will contribute differently to the absolute incident flux at the top of the planet’s atmosphere.^[001]

Even with all of these factors, planet formation within the Habitable Zone of a binary system would be similar to that of a singular star system.^[001]

Two suns of similar mass with elliptical orbits around a common barycenter

   Two suns of similar mass in the same orbit around a common barycenter

Where two suns are of the same size, their location to the planet can vary greatly depending on the size of their orbit around their common barycenter.  If there is a wide orbit, it is safe to assume that one sun will provide more energy than the other sun which is farther away.  In this case, the further sun would appear smaller in size within the sky, even though both suns are of the same mass.  The graphics above suggest why the iconic Star Wars scene isn't likely accurate.  The scene is possible maybe one or two times per year if the suns are in similar orbits which are tight and circular; or in rare instances where the suns have elliptical orbits and the planet just happens to be in the right place at the right time.

Sidebar

Here's a close up of Alpha Centauri A and B. Their distance from each other can be as much as 11 AU's, which would make a p-type planetary orbit so large, that habitable planets would be unlikely.  Planets have been discovered in s-type orbits around Alpha Centauri B and their sibling Proxima Centauri.

HZ reference:
N. Haghighipour, L. Kaltenegger, The Astrophysical Journal, 777 (Nov., 2013) 166, arXiv:1306.2890 [astro-ph.EP], Calculating the Habitable Zone of Binary Star Systems II: P-Type Binaries 

Response:
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Article Series:

• Limited lifespan of Habitable Zones around other stars [and a loosely held secret finally revealed about me]
• Small stars may have stable Habitable Zones, but habitable planets might not be common there
• Habitable Planets around White Dwarfs
• Habitable Worlds Around Binary Star Systems might not match Sci-fi
• How many Earth-like planets are orbiting Sun-like stars?
• First round of life in the Universe might have been possible extremely early
• Factors a planet needs for suitability of life; perhaps
• "Goldilocks zone of metallicity" on a galactic scale
• Maybe we are the first

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