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

Response:
Voat.co (backup link)
Reddit

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

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:
Hacker News
Reddit
Twitter

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

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

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

Response:
Hacker News

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

Lack of reproducibility of scientific papers getting attention

A lack of reproducibility of published scientific studies is finally getting recognition by the corporations (that seems to me to that could lose millions from bad research).  Academia seems a bit resist.  Source article:
 Reseach uncovering unreproducibility faces backlash 

U.S. Space & Rocket Center of Huntsville, AL

On a recent trip to Huntsville, AL, I was able to squeeze enough time for myself to visit the world famous U.S. Space & Rocket Center.  When you first walk into the museum, the first couple of exhibits are a little underwhelming, given the grandeur of the purpose of the site.  There is a display of patented inventions, then a tribute to Dr. Wernher von Braun.

It is interesting, but very museum-like.  Where's the rockets?

Well, once you are thru there, you can go outside!  Rockets!  Rockets!  Rockets!  None of them blasting off, but still impressive, nonetheless.

Of course, there is a lot more than just rockets that go into space.  Without giving too much away, here's a few more photos.  This is really a place you should visit just to see the shear scale of these massive machines.

"To good to be true" - Criticism of scientific studies grows

It is almost ironic, the other day I posted this article Reason Why I'm Skeptical of Skepticism which criticized over reliance on many study conclusions without actual supporting or valid data within the studies.  Now, just a few days later, there is a new published "study of studies" which reinforces the idea of being skeptical of scientific study conclusions, Excess Success for Psychology Articles in the Journal Science.  This study exposes that many studies in Psychology have issues, where the declared conclusions are simply "to good to be true" based on the strength of the data.  The inference being that there may be a general problem with all fields of science.

"Not every experiment is methodologically sound, and some experiments (even if methodologically sound) do not clarify the status of a theoretical idea. There is little reason to publish such experimental results, whether they are statistically significant or not. Unfortunately, in day-to-day scientific practice it is quite easy to interpret an unsuccessful outcome as being irrelevant to the theory or as being methodologically flawed and therefore not worth reporting."

In other words, data is cherry-picked in support of the theory rather than attempting to take contrary results into account.  This is basically throwing out the Scientific Method when it doesn't result in data this supports a theory.  In other cases, data collection is just too imprecise to form a suitable theory.  Kind of like garage-in-garbage-out.

I have a feeling a growing criticism of the current system is going to force changes into the process of study publishing and utilization.

Reason why I'm skeptical of Skepticism

There is a plague on modern science and Skepticism.  That plague is over reliance upon research reports.  Research report is a gathering of pre-existing data (the "re" in "research"), repurposed to find patterns.  The problem is that many research reports are created to find correlations in support of predetermined conclusions (assumptions).  Research reports are often formatted as scientific studies and published in science journals along side scientific studies that use the Scientific Method.

What is the Scientific Method?  First, wonder about a phenomenon and ask a question.  Conduct research on that question.  Then, construct a hypothesis (a proposed explanation for the phenomenon). A hypothesis must be formed in such a way to be tested for being  false (falsifiability). The subsequent test must be done in such a way as to try to disprove your hypothesis.  Only after all of this can you analyze your data and form a conclusion from that data.  The final step is to share your results for others to review and check, often in the form of their own studies.  For a study to have value, its results must be replicated by others.¹

The Scientific Method is valuable because it helps eliminate incorrect explanations for a phenomenon.  For example, say someone as a hypothesis that lemons are yellow because someone paints them with yellow paint.  You can test this in any number of ways.  You can go to an orchard and watch the lemons grow, changing color as they mature.  You can buy a lemon at a store and cut it, looking for a layer of paint.  You can peel the lemon and send the skin to a lab to search for significant amounts of paint.  Any of these tests would prove the hypothesis false.  Someone else could create a new hypothesis about why lemons are yellow, knowing that the cause is not paint.

The limitation of an unscientific research report is that it only requires you to visit a grocery store to see that the lemons are yellow in order to confirm your assumption that they've been painted yellow by a person.

Research reports often lack several crucial steps compared to Scientific Method.  First, the purpose of a research report is often to collect data in support of a pre-existing assumption.  An assumption is different than a hypothesis because an assumption is not a proposed explanation for a phenomenon; rather an assumption is that there is a phenomenon ("someone is painting those lemons yellow", instead of asking "why are lemons yellow?").  Second, no test is performed in support of this assumption.  Data is unscientifically collected from different studies, reports and other sources rather than being the results of a direct test.  There is certainly no falsifiability test.  Third, the results of the collected data are often correlated to the original assumption rather than standing on their own within the conclusion.

What's wrong with correlation between data sets?  Correlation is an indicator, but it is not a identifier. The common phrase is "correlation is not causation."  It is extremely easy to correlate unrelated things.  There is a website dedicated to just this.  This is why the Scientific Method requires a falsifiability test.  It eliminates the reliance on correlation.

Now, this is not to say all research reports are bad.  A research report that uses the Scientific Method to analyze data in a way that can be demonstrated with falsifiability does have value.  But, it is very hard tell good reports apart from bad reports using quick Twitter or reddit title links.  You have to read the report to know if it has value or if it is pseudoscience.  You have to read the whole report because the report's title and conclusions often do not even match-up the data within the report.

This is where I run into issues with Skepticism.  Skepticism tends consider any conclusions of a published research report (in support of presumed consensus) to be the same as studies using the Scientific Method.  Opinions regarding concepts outside the presumed consensus are immediately rejected (even if they are published) without regard to the quality of the report or study.  I cannot count how many times I've read a promoted research report, only to find that the evidence in the report is based correlated cherry-picked data.  Blind acceptance of research report conclusions is a big problem with Skepticism, especially as it grows in popularity among Atheists and other non-religious folks.  I've seen seen sources such as "skeptic" magazines that site unscientific research reports as though they are undeniable fact.  It is a problem being exacerbated by the ease with which (mis)information flows on the Internet through various social media and various other media outlets.

Other reading

In researching this topic, I found a very interesting "study of studies" about the flaws in most studies, Why most published research findings are false. Nothing in my article here is based on this study, so take this as a completely different source.  It is worth the read, and more fuel for the fire to be skeptical, not just of Skepticism, but of anyone trying to use a "study" to promote a notion.

Sensless Sunday: Mammoth Star

1. The last pyramids in Egypt where finished before the last of the Woolly Mammoths died out.^{1 2}
2. The World as we know it was designated to end by a Viking myth on 2/22/2014³ and by a modern economist on 3/4/2014.⁴ The quote from War Games rings through my head right now about "We're still here! We're STILL HERE!".
3. Our Solar System is traveling at an average speed of 514,000 mph relative to the Milky Way galactic center.⁵

Remote Stone

Of what world we wonder true?  Our lacking nature holds fast our corporeal soul upon the bosom of thriving abodes that guise the cradled womb.  In this place stand we, me and all others, bound not in chains but yoked hereto nonetheless.  Grand thrusting spears slice through the wondrous  blue veil, floating on the currents of bent universe beyond this round realm, bringing to the helm  fleshless anthropomorphized cold creatures to cast away the dark cloak, thus revealing remote stone for stone’s sake.