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 

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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 Planets around White Dwarfs

The white dwarf G29-38 (NASA)

Out of all the odd scenarios that might be possible in our Universe, the thought that there might be habitable planets around White Dwarfs is one of the stranger ideas, in my opinion.  Imagine what it would be like to look up to see a White Dwarf dominating the daytime sky.  How close would the planet have to be to the star to receive enough light and energy to support life?  How would a planet find itself within the Habitable Zone around a White Dwarf?

This last question is particularly interesting because White Dwarfs are the remains of a Red Giants.  Red Giants are the last phase of fusion based main sequence stars.  Between White Dwarf, Red Giant and main sequence phases, a star changes so drastically that it is unlikely planets close to the star would survive into the next phase.  Some very interesting things need to happen for a planet to form within the Habitable Zone of a White Dwarf.

With main sequence stars, the Habitable Zone slows moves away from the star because the star slowly gets hotter.  A planet that starts out within the Habitable Zone of a young main sequence stars may not remain within the Habitable Zone for the full length of that star's life-cycle.^[001] [002] Oddly enough, White Dwarfs have the exact opposite problem.  White Dwarfs cool down as they age.^[003]  Habitable Zones around White Dwarfs will shrink until being too small for any sizable planet to exist within it.

The Habitable Zone around a White Dwarf is very small compared to that of Sun.  The Habitable Zone around Sun is roughly between the orbits of Venus and Mars.  The Habitable Zone around a White Dwarf is much closer than even the orbit of Mercury around Sun.^[003]  It seems a planet that close to a White Dwarf cannot exist without some special events.

How do planets get to the Habitable Zone?

A planet could have existed in the previous solar system during the main sequence star phase, but much further out; so far out that it may not have been previously habitable.  When the main sequence star expands to become a Red Giant, then explodes to leave a White Dwarf, the planet would have to move from the outer reaches of the solar system to a stable close orbit.  This sounds incredible, but apparently it is possible since planets have been discovered around Neutron Stars, which go thru even more violence.^[003]

Another possible scenario is it the matter ejected from the exploding Red Giant, or other remaining debris within the solar system somehow creates a new accretion disk around the newly formed White Dwarf, from which new planets could form.^[003]

Water Cycle

Even if either of these scenarios do happen, a water related challenge presents itself.  A lot water must somehow remain or be (re)introduced on these special planets.  Water is likely stripped from any existing planet that moves so close to the White Dwarf.^[004]  Water is also unlikely to be available on any planet that forms so close to any star, White Dwarf or otherwise.  Maybe these planets could gather new water via the same processes as Earth, possibly "delivered to by a barrage of comets."^[003]

If a planet is lucky enough to form around a White Dwarf, what's that White Dwarf going to look like in the sky?  White Dwarfs have a lot of mass, but they are very small in size.  White Dwarfs are about the same size as Earth.^[005]  By my rough calculations, the Habitable Zone around a White Dwarf is about 5 times the distance of Earth to the Moon.  So, I image the White Dwarf would appear several times smaller in the sky as the Earth appears to the Moon.  Maintaining habitability of planet around a White Dwarf might be a bit like trying to keep warm outside on a freezing night next to a slowly fading campfire.

Primary reference:
A Loeb, D Maoz, Monthly Notices of the Royal Astronomical Society: Letters, Volume 432, Issue 1, p.11-15, arXiv:1301.4994 [astro-ph.EP], Detecting bio-markers in habitable-zone earths transiting white dwarfs

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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Small stars may have stable Habitable Zones, but habitable planets might not be common there

Protoplanetary accretion disk around a new star

The previous article Limited lifespan of Habitable Zones around other stars (September 2016) covered the topic of Habitable Zones for planets around other solar systems.  However, Habitable Zones are only one of considerations for finding other stars with habitable planets.  Given the lack of data right now, sometimes science has to fall back on simulations.  These simulations do not replace actual observations.  Instead, they offer clues as to how we may be proceed in our search for hard data.

Habitable Zones appear to be more stable and longer lasting around small stars, such as Red Dwarfs.^[001]  However, what are the chances of habitable planets appearing in these small zones around these small stars?  It turns out that the chances may not be good.

According to the study A Decreased Probability Of Habitable Planet Formation Around Low-Mass Stars, multiple simulations suggest that low-mass stars are unlikely to have terrestrial planets of sufficient size within their Habitable Zones.  This is due to a several factors.  That's not to say it is impossible nor improbable; just not as common as previous thought.^[002]

Other factors

Besides Habitable Zones, another factor to consider is the Habitable Planet Mass Limit.  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 tectonics.^[002]  The lack or presence of global tectonics seems to be a factor in the differences between Venus and Earth.  Though Venus seems to be large enough, its surface heals too quickly to allow for global tectonics.^[003]   The examples within our own solar system suggest that even when planets are large enough, there is no guarantee they will have global tectonics.

Another factor is the Protoplanetary Disk.  During the planet formation phase (accretion), there has to be enough material within the disk of matter that forms around very young stars (Protoplanetary Disk) in order produce larger planets.  Though there are a lot of unknowns regarding this factor, the "ratio of disk mass to stellar mass is roughly constant with stellar mass".  Also, planets seem to form much faster around small stars for various reasons.  With less time to form and less mass within the Protoplanetary Disk, planets around low-mass stars may typically be much smaller.  A second issue with fast forming planets is that they are much less likely to have enough time to collect enough water to support life.^[002]

Exceptions?

Nothing is absolute.  Gliese 581 is a Red Dwarf that has a number of large planets, and also has a debris disk that appears to have tens times amount of comet debris than our own Solar System.  This suggests low-mass stars can have habitable planets.  That said, Gliese 581 may be an outlier.  Other factors are obviously involved that need further study.

Primary reference:
S. N. Raymond, J. Scalo and V. S. Meadows, The Astrophysical Journal 669 (Nov., 2007) 606–614, arXiv:0707.1711 [astro-ph], A Decreased Probability of Habitable Planet Formation around Low-Mass 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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