An exoplanet or extrasolar planet is a planet that orbits a star other than the Sun. Starting in 1988, and as of 15 July 2016, there have been 3,472 exoplanets in 2,597 planetary systems and 589 multiple planetary systems confirmed. HARPS (since 2004) has discovered about a hundred exoplanets while the Kepler space telescope (since 2009) has found more than two thousand. Kepler has also detected a few thousand candidate planets, of which about 11% may be false positives. On average, there is at least one planet per star, with a percentage having multiple planets. About 1 in 5 Sun-like stars[a] have an "Earth-sized"[b] planet in the habitable zone,[c] with the nearest expected to be within 12 light-years distance from Earth. Assuming 200 billion stars in the Milky Way,[d] that would be 11 billion potentially habitable Earth-sized planets in the Milky Way, rising to 40 billion if planets orbiting the numerous red dwarfs are included.
The least massive planet known is Draugr (formally PSR B1257+12 A), which is about twice the mass of the Moon. The most massive planet listed on the NASA Exoplanet Archive is DENIS-P J082303.1-491201 b, about 29 times the mass of Jupiter, although according to some definitions of a planet, it is too massive to be a planet and may be a brown dwarf instead. There are planets that are so near to their star that they take only a few hours to orbit and there are others so far away that they take thousands of years to orbit. Some are so far out that it is difficult to tell whether they are gravitationally bound to the star. Almost all of the planets detected so far are within the Milky Way, but there have also been a few possible detections of extragalactic planets.
The discovery of exoplanets has intensified interest in the search for extraterrestrial life. There is special interest in planets that orbit in a star's habitable zone, where it is possible for liquid water, a prerequisite for life on Earth, to exist on the surface. The study of planetary habitability also considers a wide range of other factors in determining the suitability of a planet for hosting life.
Besides exoplanets, there are also rogue planets, which do not orbit any star and which tend to be considered separately, especially if they are gas giants, in which case they are often counted, like WISE 0855−0714, as sub-brown dwarfs. The rogue planets in the Milky Way possibly number in the billions (or more).
- 1 Definition
- 2 History of detection
- 3 Detection methods
- 4 Nomenclature
- 5 Formation and evolution
- 6 Planet-hosting stars
- 7 General features
- 8 Cultural impact
- 9 See also
- 10 Notes
- 11 References
- 12 Further reading
- 13 External links
The official definition of "planet" used by the International Astronomical Union (IAU) only covers the Solar System and thus does not apply to exoplanets. As of April 2011, the only defining statement issued by the IAU that pertains to exoplanets is a working definition issued in 2001 and modified in 2003. That definition contains the following criteria:
- Objects with true masses below the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) that orbit stars or stellar remnants are "planets" (no matter how they formed). The minimum mass/size required for an extrasolar object to be considered a planet should be the same as that used in the Solar System.
- Substellar objects with true masses above the limiting mass for thermonuclear fusion of deuterium are "brown dwarfs", no matter how they formed or where they are located.
- Free-floating objects in young star clusters with masses below the limiting mass for thermonuclear fusion of deuterium are not "planets", but are "sub-brown dwarfs" (or whatever name is most appropriate).
However, the IAU's working definition is not universally accepted. One alternate suggestion is that planets should be distinguished from brown dwarfs on the basis of formation. It is widely thought that giant planets form through core accretion, which may sometimes produce planets with masses above the deuterium fusion threshold; massive planets of that sort may have already been observed. Brown dwarfs form like stars from the direct collapse of clouds of gas and this formation mechanism also produces objects that are below the 13 MJup limit and can be as low as 1 MJup. Objects in this mass range that orbit their stars with wide separations of hundreds or thousands of AU and have large star/object mass ratios likely formed as brown dwarfs; their atmospheres would likely have a composition more similar to their host star than accretion-formed planets which would contain increased abundances of heavier elements. Most directly imaged planets as of April 2014 are massive and have wide orbits so probably represent the low-mass end of brown dwarf formation.
Also, the 13-Jupiter-mass cutoff does not have precise physical significance. Deuterium fusion can occur in some objects with a mass below that cutoff. The amount of deuterium fused depends to some extent on the composition of the object. The Extrasolar Planets Encyclopaedia includes objects up to 25 Jupiter masses, saying, "The fact that there is no special feature around 13 MJup in the observed mass spectrum reinforces the choice to forget this mass limit". The Exoplanet Data Explorer includes objects up to 24 Jupiter masses with the advisory: "The 13 Jupiter-mass distinction by the IAU Working Group is physically unmotivated for planets with rocky cores, and observationally problematic due to the sin i ambiguity." The NASA Exoplanet Archive includes objects with a mass (or minimum mass) equal to or less than 30 Jupiter masses. Another criterion for separating planets and brown dwarfs, rather than deuterium fusion, formation process or location, is whether the core pressure is dominated by coulomb pressure or electron degeneracy pressure with the dividing line at around 5 Jupiter masses. Another suggestion, based on mass–density relationships, is that the dividing line should be at 60 Jupiter masses.
History of detection
For centuries philosophers and scientists supposed that extrasolar planets existed, but there was no way of detecting them or of knowing their frequency or how similar they might be to the planets of the Solar System. Various detection claims made in the nineteenth century were rejected by astronomers. The first confirmed detection came in 1992, with the discovery of several terrestrial-mass planets orbiting the pulsar PSR B1257+12. The first confirmation of an exoplanet orbiting a main-sequence star was made in 1995, when a giant planet was found in a four-day orbit around the nearby star 51 Pegasi. Some exoplanets have been imaged directly by telescopes, but the vast majority have been detected through indirect methods such as the transit method and the radial-velocity method.
In the sixteenth century the Italian philosopher Giordano Bruno, an early supporter of the Copernican theory that Earth and other planets orbit the Sun (heliocentrism), put forward the view that the fixed stars are similar to the Sun and are likewise accompanied by planets.
In the eighteenth century the same possibility was mentioned by Isaac Newton in the "General Scholium" that concludes his Principia. Making a comparison to the Sun's planets, he wrote "And if the fixed stars are the centers of similar systems, they will all be constructed according to a similar design and subject to the dominion of One."
In 1952, more than 40 years before the first hot Jupiter was discovered, Otto Struve wrote that there is no compelling reason why planets could not be much closer to their parent star than is the case in the Solar System, and proposed that Doppler spectroscopy and the transit method could detect super-Jupiters in short orbits.
Claims of exoplanet detections have been made since the nineteenth century. Some of the earliest involve the binary star 70 Ophiuchi. In 1855 Capt. W. S. Jacob at the East India Company's Madras Observatory reported that orbital anomalies made it "highly probable" that there was a "planetary body" in this system. In the 1890s, Thomas J. J. See of the University of Chicago and the United States Naval Observatory stated that the orbital anomalies proved the existence of a dark body in the 70 Ophiuchi system with a 36-year period around one of the stars. However, Forest Ray Moulton published a paper proving that a three-body system with those orbital parameters would be highly unstable. During the 1950s and 1960s, Peter van de Kamp of Swarthmore College made another prominent series of detection claims, this time for planets orbiting Barnard's Star. Astronomers now generally regard all the early reports of detection as erroneous.
In 1991 Andrew Lyne, M. Bailes and S. L. Shemar claimed to have discovered a pulsar planet in orbit around PSR 1829-10, using pulsar timing variations. The claim briefly received intense attention, but Lyne and his team soon retracted it.
As of 15 July 2016, a total of 3,472 confirmed exoplanets are listed in the Extrasolar Planets Encyclopaedia, including a few that were confirmations of controversial claims from the late 1980s. The first published discovery to receive subsequent confirmation was made in 1988 by the Canadian astronomers Bruce Campbell, G. A. H. Walker, and Stephenson Yang of the University of Victoria and the University of British Columbia. Although they were cautious about claiming a planetary detection, their radial-velocity observations suggested that a planet orbits the star Gamma Cephei. Partly because the observations were at the very limits of instrumental capabilities at the time, astronomers remained skeptical for several years about this and other similar observations. It was thought some of the apparent planets might instead have been brown dwarfs, objects intermediate in mass between planets and stars. In 1990 additional observations were published that supported the existence of the planet orbiting Gamma Cephei, but subsequent work in 1992 again raised serious doubts. Finally, in 2003, improved techniques allowed the planet's existence to be confirmed.
On 9 January 1992, radio astronomers Aleksander Wolszczan and Dale Frail announced the discovery of two planets orbiting the pulsar PSR 1257+12. This discovery was confirmed, and is generally considered to be the first definitive detection of exoplanets. Follow-up observations solidified these results, and confirmation of a third planet in 1994 revived the topic in the popular press. These pulsar planets are thought to have formed from the unusual remnants of the supernova that produced the pulsar, in a second round of planet formation, or else to be the remaining rocky cores of gas giants that somehow survived the supernova and then decayed into their current orbits.
On 6 October 1995, Michel Mayor and Didier Queloz of the University of Geneva announced the first definitive detection of an exoplanet orbiting a main-sequence star, namely the nearby G-type star 51 Pegasi. This discovery, made at the Observatoire de Haute-Provence, ushered in the modern era of exoplanetary discovery. Technological advances, most notably in high-resolution spectroscopy, led to the rapid detection of many new exoplanets: astronomers could detect exoplanets indirectly by measuring their gravitational influence on the motion of their host stars. More extrasolar planets were later detected by observing the variation in a star's apparent luminosity as an orbiting planet passed in front of it.
Initially, most known exoplanets were massive planets that orbited very close to their parent stars. Astronomers were surprised by these "hot Jupiters", because theories of planetary formation had indicated that giant planets should only form at large distances from stars. But eventually more planets of other sorts were found, and it is now clear that hot Jupiters are a minority of exoplanets. In 1999, Upsilon Andromedae became the first main-sequence star known to have multiple planets. Kepler-16 contains the first discovered planet that orbits around a binary main-sequence star system.
On 26 February 2014, NASA announced the discovery of 715 newly verified exoplanets around 305 stars by the Kepler Space Telescope. These exoplanets were checked using a statistical technique called "verification by multiplicity". Prior to these results, most confirmed planets were gas giants comparable in size to Jupiter or larger as they are more easily detected, but the Kepler planets are mostly between the size of Neptune and the size of Earth.
As of March 2014, NASA's Kepler mission had identified more than 2,900 planetary candidates, several of them being nearly Earth-sized and located in the habitable zone, some around Sun-like stars.
Planets are extremely faint compared to their parent stars. For example, a Sun-like star is about a billion times brighter than the reflected light from any exoplanet orbiting it. It is difficult to detect such a faint light source, and furthermore the parent star causes a glare that tends to wash it out. It is necessary to block the light from the parent star in order to reduce the glare while leaving the light from the planet detectable; doing so is a major technical challenge which requires extreme optothermal stability. All exoplanets that have been directly imaged are both large (more massive than Jupiter) and widely separated from their parent star.
Specially designed direct-imaging instruments such as Gemini Planet Imager, VLT-SPHERE, and SCExAO will image dozens of gas giants, however the vast majority of known extrasolar planets have only been detected through indirect methods. The following are the indirect methods that have proven useful:
- transits) in front of its parent star's disk, then the observed brightness of the star drops by a small amount. The amount by which the star dims depends on its size and on the size of the planet, among other factors. Because the transit method requires that the planet's orbit intersect a line-of-sight between the host star and Earth, the probability that an exoplanet in a randomly oriented orbit will be observed to transit the star is somewhat small. The Kepler telescope uses this method.
- As a planet orbits a star, the star also moves in its own small orbit around the system's center of mass. Variations in the star's radial velocity—that is, the speed with which it moves towards or away from Earth—can be detected from displacements in the star's spectral lines due to the Doppler effect. Extremely small radial-velocity variations can be observed, of 1 m/s or even somewhat less.
- Transit timing variation (TTV)
- When multiple planets are present, each one slightly perturbs the others' orbits. Small variations in the times of transit for one planet can thus indicate the presence of another planet, which itself may or may not transit. For example, variations in the transits of the planet Kepler-19b suggest the existence of a second planet in the system, the non-transiting Kepler-19c.
- When a planet orbits multiple stars or if the planet has moons, its transit time can significantly vary per transit. Although no new planets or moons have been discovered with this method, it is used to successfully confirm many transiting circumbinary planets.
- Microlensing occurs when the gravitational field of a star acts like a lens, magnifying the light of a distant background star. Planets orbiting the lensing star can cause detectable anomalies in the magnification as it varies over time. Unlike most other methods which have detection bias towards planets with small (or for resolved imaging, large) orbits, microlensing method is most sensitive to detecting planets around 1–10 AU away from Sun-like stars.
- Astrometry consists of precisely measuring a star's position in the sky and observing the changes in that position over time. The motion of a star due to the gravitational influence of a planet may be observable. Because the motion is so small, however, this method has not yet been very productive. It has produced only a few disputed detections, though it has been successfully used to investigate the properties of planets found in other ways.
- A pulsar (the small, ultradense remnant of a star that has exploded as a supernova) emits radio waves extremely regularly as it rotates. If planets orbit the pulsar, they will cause slight anomalies in the timing of its observed radio pulses. The first confirmed discovery of an extrasolar planet was made using this method. But as of 2011, it has not been very productive; five planets have been detected in this way, around three different pulsars.
- Like pulsars, there are some other types of stars which exhibit periodic activity. Deviations from the periodicity can sometimes be caused by a planet orbiting it. As of 2013, a few planets have been discovered with this method.
- When a planet orbits very close to the star, it catches a considerable amount of starlight. As the planet orbits around the star, the amount of light changes due to planets having phases from Earth's viewpoint or planet glowing more from one side than the other due to temperature differences.
- Relativistic beaming measures the observed flux from the star due to its motion. The brightness of the star changes as the planet moves closer or further away from its host star.
- Massive planets close to their host stars can slightly deform the shape of the star. This causes the brightness of the star to slightly deviate depending how it is rotated relative to Earth.
- With polarimetry method, a polarized light reflected off the planet is separated from unpolarized light emitted from the star. No new planets have been discovered with this method although a few already discovered planets have been detected with this method.
- Disks of space dust surround many stars, thought to originate from collisions among asteroids and comets. The dust can be detected because it absorbs starlight and re-emits it as infrared radiation. Features in the disks may suggest the presence of planets, though this is not considered a definitive detection method.
The exoplanet naming convention is an extension of the system used for naming multiple-star systems as adopted by the International Astronomical Union (IAU). For exoplanets orbiting a single star, the name is normally formed by taking the name of its parent star and adding a lowercase letter. The first planet discovered in a system is given the designation "b" (the parent star is considered to be "a") and later planets are given subsequent letters. If several planets in the same system are discovered at the same time, the closest one to the star gets the next letter, followed by the other planets in order of orbital size. A provisional IAU-sanctioned standard exists to accommodate the naming of circumbinary planets. A limited number of exoplanets have IAU-sanctioned proper names. Other naming systems exist.
Formation and evolution
Planets form within a few tens of millions of years of their star forming, and there are stars that are forming today and other stars that are ten billion years old, so unlike the planets of the Solar System, which can only be observed as they are today, studying exoplanets allows the observation of exoplanets at different stages of evolution. When planets form they have hydrogen envelopes that cool and contract over time and, depending on the mass of the planet, some or all of the hydrogen is eventually lost to space. This means that even terrestrial planets can start off with large radii. An example is Kepler-51b which has only about twice the mass of Earth but is almost the size of Saturn which is a hundred times the mass of Earth. Kepler-51b is quite young at a few hundred million years old.
Most known exoplanets orbit stars roughly similar to the Sun, i.e. main-sequence stars of spectral categories F, G, or K. Lower-mass stars (red dwarfs, of spectral category M) are less likely to have planets massive enough to be detected by the radial-velocity method. Despite this, several tens of planets around red dwarfs have been discovered by the Kepler spacecraft, which uses the transit method to detect smaller planets.
Some planets orbit one member of a binary star system, and several circumbinary planets have been discovered which orbit around both members of binary star. A few planets in triple star systems are known and one in the quadruple system Kepler-64.
Color and brightness
The apparent brightness (apparent magnitude) of a planet depends on how far away the observer is, how reflective the planet is (albedo), and how much light the planet receives from its star, which depends on how far the planet is from the star and how bright the star is. So, a planet with a low albedo that is close to its star can appear brighter than a planet with high albedo that is far from the star.
The darkest known planet in terms of geometric albedo is TrES-2b, a hot Jupiter that reflects less than 1% of the light from its star, making it less reflective than coal or black acrylic paint. Hot Jupiters are expected to be quite dark due to sodium and potassium in their atmospheres but it is not known why TrES-2b is so dark—it could be due to an unknown chemical.
For gas giants, geometric albedo generally decreases with increasing metallicity or atmospheric temperature unless there are clouds to modify this effect. Increased cloud-column depth increases the albedo at optical wavelengths, but decreases it at some infrared wavelengths. Optical albedo increases with age, because older planets have higher cloud-column depths. Optical albedo decreases with increasing mass, because higher-mass giant planets have higher surface gravities, which produces lower cloud-column depths. Also, elliptical orbits can cause major fluctuations in atmospheric composition, which can have a significant effect.
There is more thermal emission than reflection at some near-infrared wavelengths for massive and/or young gas giants. So, although optical brightness is fully phase-dependent, this is not always the case in the near infrared.
Temperatures of gas giants reduce over time and with distance from their star. Lowering the temperature increases optical albedo even without clouds. At a sufficiently low temperature, water clouds form, which further increase optical albedo. At even lower temperatures ammonia clouds form, resulting in the highest albedos at most optical and near-infrared wavelengths.
In 2014, a magnetic field around HD 209458 b was inferred from the way hydrogen was evaporating from the planet. It is the first (indirect) detection of a magnetic field on an exoplanet. The magnetic field is estimated to be about one tenth as strong as Jupiter's.
Interaction between a close-in planet's magnetic field and a star can produce spots on the star in a similar way to how the Galilean moons produce aurorae on Jupiter. Auroral radio emissions could be detected with radio telescopes such as LOFAR. The radio emissions could enable determination of the rotation rate of a planet which is difficult to detect otherwise.
Earth's magnetic field results from its flowing liquid metallic core, but in super-Earths the mass can produce high pressures with large viscosities and high melting temperatures which could prevent the interiors from separating into different layers and so result in undifferentiated coreless mantles. Magnesium oxide, which is rocky on Earth, can be a liquid metal at the pressures and temperatures found in super-Earths and could generate a magnetic field in the mantles of super-Earths.
Hot Jupiters have been observed to have a larger radius than expected. This could be caused by the interaction between the stellar wind and the planet's magnetosphere creating an electric current through the planet that heats it up causing it to expand. The more magnetically active a star is the greater the stellar wind and the larger the electric current leading to more heating and expansion of the planet. This theory matches the observation that stellar activity is correlated with inflated planetary radii.
In 2007 two independent teams of researchers came to opposing conclusions about the likelihood of plate tectonics on larger super-Earths with one team saying that plate tectonics would be episodic or stagnant and the other team saying that plate tectonics is very likely on super-Earths even if the planet is dry.
If super-Earths have more than 80 times as much water as Earth then they become ocean planets with all land completely submerged. However, if there is less water than this limit, then the deep water cycle will move enough water between the oceans and mantle to allow continents to exist.
The star 1SWASP J140747.93-394542.6 is orbited by an object that is circled by a ring system much larger than Saturn's rings. However, the mass of the object is not known; it could be a brown dwarf or low-mass star instead of a planet.
The brightness of optical images of Fomalhaut b could be due to starlight reflecting off a circumplanetary ring system with a radius between 20 to 40 times that of Jupiter's radius, about the size of the orbits of the Galilean moons.
The rings of the Solar System's gas giants are aligned with their planet's equator. However, for exoplanets that orbit close to their star, tidal forces from the star would lead to the outermost rings of a planet being aligned with the planet's orbital plane around the star. A planet's innermost rings would still be aligned with the planet's equator so that if the planet has a tilted rotational axis, then the different alignments between the inner and outer rings would create a warped ring system.
KIC 12557548 b is a small rocky planet, very close to its star, that is evaporating and leaving a trailing tail of cloud and dust like a comet. The dust could be ash erupting from volcanos and escaping due to the small planet's low surface-gravity, or it could be from metals that are vaporized by the high temperatures of being so close to the star with the metal vapor then condensing into dust.
In June 2015, scientists reported that the atmosphere of GJ 436 b was evaporating, resulting in a giant cloud around the planet and, due to radiation from the host star, a long trailing tail 14×106 km (9×106 mi) long.
Tidally locked planets in a 1:1 spin–orbit resonance would have their star always shining directly overhead on one spot which would be hot with the opposite hemisphere receiving no light and being freezing cold. Such a planet could resemble an eyeball with the hotspot being the pupil. Planets with an eccentric orbit could be locked in other resonances. 3:2 and 5:2 resonances would result in a double-eyeball pattern with hotspots in both eastern and western hemispheres. Planets with both an eccentric orbit and a tilted axis of rotation would have more complicated insolation patterns.
As more planets are discovered, the field of exoplanetology continues to grow into a deeper study of extrasolar worlds, and will ultimately tackle the prospect of life on planets beyond the Solar System. At cosmic distances, life can only be detected if it is developed at a planetary scale and strongly modified the planetary environment, in such a way that the modifications cannot be explained by classical physico-chemical processes (out of equilibrium processes). For example, molecular oxygen (O
2) in the atmosphere of Earth is a result of photosynthesis by living plants and many kinds of microorganisms, so it can be used as an indication of life on exoplanets, although small amounts of oxygen could also be produced by non-biological means. Furthermore, a potentially habitable planet must orbit a stable star at a distance within which planetary-mass objects with sufficient atmospheric pressure can support liquid water at their surfaces.
On 9 May 2013, a congressional hearing by two United States House of Representatives subcommittees discussed "Exoplanet Discoveries: Have We Found Other Earths?", prompted by the discovery of exoplanet Kepler-62f, along with Kepler-62e and Kepler-62c. A related special issue of the journal Science, published earlier, described the discovery of the exoplanets.
- For the purpose of this 1 in 5 statistic, "Sun-like" means G-type star. Data for Sun-like stars was not available so this statistic is an extrapolation from data about K-type stars
- For the purpose of this 1 in 5 statistic, Earth-sized means 1–2 Earth radii
- For the purpose of this 1 in 5 statistic, "habitable zone" means the region with 0.25 to 4 times Earth's stellar flux (corresponding to 0.5–2 AU for the Sun).
- About 1/4 of stars are GK Sun-like stars. The number of stars in the galaxy is not accurately known, but assuming 200 billion stars in total, the Milky Way would have about 50 billion Sun-like (GK) stars, of which about 1 in 5 (22%) or 11 billion would be Earth-sized in the habitable zone. Including red dwarfs would increase this to 40 billion.
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- Boss, Alan (2009). The Crowded Universe: The Search for Living Planets. Basic Books. ISBN 978-0-465-00936-7 (Hardback); ISBN 978-0-465-02039-3 (Paperback).
- Dorminey, Bruce (2001). Distant Wanderers. Springer-Verlag. ISBN 978-0-387-95074-7 (Hardback); ISBN 978-1-4419-2872-6 (Paperback).
- Jayawardhana, Ray (2011). Strange New Worlds: The Search for Alien Planets and Life beyond Our Solar System. Princeton, NJ: Princeton University Press. ISBN 978-0-691-14254-8 (Hardcover).
- Perryman, Michael (2011). The Exoplanet Handbook. Cambridge University Press. ISBN 978-0-521-76559-6.
- Seager, Sara, ed. (2011). Exoplanets. University of Arizona Press. ISBN 978-0-8165-2945-2.
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Formation and evolution
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Climate and weather
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- New Technique Could Measure Exoplanet Atmospheric Pressure, an Indicator of Habitability, Shannon Hall on 6 March 2014, www.universetoday.com
After hydrogen and helium, oxygen is the most common element in many planetary systems (in some systems carbon is more common than oxygen), and water H2O one of the most common compounds. Gas giants are composed mostly of hydrogen and helium, but most planets are between the size of Earth and Neptune, where many planets will have deep water oceans covering the entire surface in addition to a hydrogen–helium envelope.
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- Are Exoplanets Orbiting Red Dwarf Stars too Dry for Life?, Michael Schirber, Astrobiology Magazine, 27 August 2013
- Carbon-Rich Exoplanets May Lack Surface Water, 26 October 2013
- 'Water-Trapped' Worlds, Adam Hadhazy, Astrobiology Magazine, 18 July 2013
- Lobster-Shaped Extrasolar Oceans, 10 March 2014, Charles Q. Choi, Astrobiology Magazine
- Alien Moons Could Bake Dry from Young Gas Giants' Hot Glow, Adam Hadhazy, Astrobiology Magazine 25 March 2014
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- Spiegel, David S. (2010). "Extreme Climate Variations from Milankovitch-like Eccentricity Oscillations in Extrasolar Planetary Systems". arXiv: [astro-ph.EP].
- Kane, Stephen R.; Raymond, Sean N. (2014). "Orbital Dynamics of Multi-Planet Systems with Eccentricity Diversity". The Astrophysical Journal. 784 (2): 104. arXiv:. Bibcode:2014ApJ...784..104K. doi:10.1088/0004-637X/784/2/104.
- Moorhead, Althea V.; Ford, Eric B. (2009). "Type II migration of planets on eccentric orbits". arXiv: [astro-ph.EP].
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