Looking back at 2013. Part III – The exoplanets of Kepler

The American news channel CNN have selected what they consider to be the ten most important news about natural science and space in 2013. Gladly, planetary systems research top the list, with four different news. Other news concern fundamental physics (two), paleoanthropology and biology (two), cosmology (one) and climate (one). The four planetary news are about a fresh water lake on Mars, the spacecraft Voyager 1 that is leaving the Solar System, the space telescope Kepler looking for exoplanets, and the spectacular meteorite impact in Chelyabinsk, Russia. In four posts I will comment on each of these four top news of 2013.

The idea of planets orbiting other stars is as old as the realization that Earth and the other planets in the Solar System revolve around the Sun. Already Isaac Newton mentions the possibility that other stars are surrounded by planets in his Principia from 1687, and he was not the first to express such ideas. For the generation that grew up with science fiction and imaginative films about events taking place in galaxies far away a long time ago, the thought of other planets than our own is natural. Therefore it is valuable to remember that no known examples of such extrasolar planets (usually called exoplanets) existed twenty years ago – the technology that made it possible to detect them was not developed until the early 1990s.

The first definitive detection of a planet around an ordinary so-called main sequence star was announced in November 1995, when the Swiss astronomers Michel Mayor and Didier Quelos showed that the star 51 Pegasi surrounded itself with a planet that was between half and twice as massive as Jupiter, located only 0.05 AU from the star (one astronomical unit, AU, is the average distance between the Sun and Earth, corresponding to nearly 150 million kilometers). In the following years many discoveries were made, and in early 2009 no less than 334 exoplanets were known, orbiting around 285 different stars. In March that year, NASA launched the Kepler space telescope in orbit around the Sun, whose sole task was to discover new exoplanets. When the telescope became unfit for such observations in May 2013, it had accumulated a database of almost 3800 planet candidates – the Kepler team is currently busy with the time-consuming task of verifying the authenticity of these exoplanets, and at the time of writing (late January 2014) they have confirmed that 242 of the Kepler planets are genuine. Along with all other discoveries, there is now a total of 1070 known and verified exoplanets that orbit 810 different stars, of which 177 stars are home to more than one exoplanet.

I will first describe how Kepler finds planet candidates, how their authenticity is verified, and why Kepler is able to find an extremely interesting type of object that is difficult or impossible to detect with other methods – extrasolar planets that are as small as Earth, and are located far enough from its star not to be scorching hot. I will then use examples of extrasolar planets detected by Kepler to illustrate how different these systems can be compared to our own. Finally, I will write about the reasons why these findings are important and what they can tell us about the process that gives rise to planets.

The Kepler space telescope

Kepler utilizes an idea that is very simple, and that humanity has observed in the form of solar eclipses throughout our existence – if an object gets between us and a distant star, the stellar light fades temporarily. When the Moon gets between us and the Sun, there is a total solar eclipse that will remove all the Sun’s light because the Moon happens to have the same apparent size in the sky as the Sun. When an exoplanet moves between its parent star and Kepler, it will obscure a small fraction of the stellar disk. Kepler can not see the planet or discern the stellar surface, but it can detect a sudden reduction of the stellar brightness, that remains at a lower level until the planet leaves the line of sight and the star returns to its previous brightness. This is called the transit method.

This may sound easy, but there are two substantial technical complications. First, the decrease in brightness of the star due to the planet’s passage is extremely small – one must therefore be able to determine the brightness with extremely high accuracy, so that the slight decrease in signal strength does not drown in various random variations caused by the surroundings or the telescope and the instrument itself. The problem is not the telescope mirror size or the sensitivity of the detector – nowadays, these can fairly easily be manufactured with the required level of performance.The reason that these observations cannot be made from ground is not about the technology itself, but the disturbances caused by Earth’s atmosphere. When light from a star passes through the atmosphere on its way toward a telescope, it will be diffracted in pockets of air having different temperatures and densities, causing the light beam to partially divert from its original path. A telescope on Earth will then measure fairly strong and random changes of the stellar brightness, caused by the atmosphere, which makes it impossible to reach the precision required to detect an eclipse taking place hundreds of light years away. So, the telescope must be sent into space.

The second difficulty has to do with the probability that a randomly selected star would have a planet with such an orbit that it happens to pass right through our line of sight. A planet revolves around a star in a fixed plane, and for us to be able to see an eclipse, we must also be located almost exactly in the same plane. Since this is the case only for a small fraction of the stars, Kepler must observe a huge number of stars to catch the few who actually have planets and are causing eclipses that we can see. Kepler does this by observing about 156,000 different stars. Because it is impossible to tell when an eclipse will take place, Kepler must stare continuously at these stars. This requires Kepler to have a large field of view – it covers a square with a side of 10 degrees, which is 20 times longer than the apparent diameter of the Moon in the sky. It has been staring at the exact same area, located between the constellations Cygnus and Lyra, ever since the first observations began in April 2009 until the telescope lost its full attitude control in May 2013. By then the space telescope had observed for four years – six months more than originally anticipated. The original goal was that Kepler would operate for three and a half years, for two reasons. Firstly, one needs to see the same planet perform at least three or four eclipses in order to be sure that it indeed is a periodic phenomenon. Secondly, the orbital period increases the farther the planet is from its star, and in order to discover planets similar to Earth, whose orbital period is one year, one must observe for at least 3-4 years.


The picture shows an area in the sky between the constellations Cygnus and Lyra
that Kepler has been observing for four years. The boxes shows the areas that the
CCD cameras can survey simultaneously. The original picture can be found at
Image credit: Software Bisque

Transit observations provide two different types of information. The duration of the eclipse shows how fast the planet crosses the stellar disk, providing the orbital period of the planet. Since there is a mathematical relationship between the orbital period, the mass of the star, and the distance between the star and planet, called Kepler’s third law, knowledge about the first two parameters can be used to calculate the average distance between the planet and the star. This relationship was described in 1619 by the German astronomer Johannes Kepler (1571-1630), after whom the space telescope is named.

One can also use the degree of attenuation of the stellar brightness to calculate the diameter of the planet. The larger the planet, the stronger the decrease of the brightness, since a larger fraction of the stellar surface is blocked during eclipse.

Additional observations from Earth

Before one can be sure that a candidate indeed is a planet, other possibilities must be ruled out. For example, it is very common that stars are not alone, but that two revolve around each other at close range. About two-thirds of the stars we see in the sky are in fact such double stars. If we happen to find ourselves being close to the plane in which the two stars move, they will alternately obscure each other as seen from Earth. If one star is slightly fainter than the other, their combined brightness thus undergoes a periodic weakening – they form a so-called eclipsing binary. If such an eclipsing binary happens to be located near the line of sight between Kepler and a bright star that is observed, the fluctuations of the eclipsing binary may be misinterpreted as a planet around the bright star. In order to eliminate the risk of misunderstandings, all candidates – the 3800 objects – must be observed from ground with large telescopes that have much better magnification than Kepler. Thereby, it is possible to see if something undesirable is located very close to the star in question. At the moment, 242 candidates have passed this needle’s eye and are considered real planetary systems. During the process, dozens of candidates turned out to be nothing but eclipsing binaries, showing the necessity of this procedure.

If possible, observers on ground also try to prove the existence of Kepler’s exoplanets in an entirely different way, using the radial velocity method. The method exploits the fact that the star itself will move, if it surrounds itself with planets. Two bodies whose movements are controlled by the gravitational force acting between them, will move around a point in space called the center of mass, which is located somewhere on the line between the bodies. If the bodies have the same mass, as is the case for some double stars, the center of mass is placed midways between them. In such cases, it is possible that the stars both move along the same circle, centered on the center of mass, in each moment being placed on opposite sides of this center. If the mass of one of the bodies is greater than the other, the center of mass will be located closer to the heavier body. The heavier body then moves in a small circle around the center of mass, while the lighter body travels in a wider circle around the center of mass. If the mass difference between the bodies is very large – as is the case for a star and a planet – the center of mass may lie near the surface of the star, or even inside it. In the Solar System, the center of mass, called the barycenter, is located up to a solar diameter outside the center of the Sun. All the planets revolve around this point, but so does the Sun – it therefore follows a path whose size is about as big as the Sun itself. Since all stars that are surrounded by planets wobbles in the same way, the existence of planets is revealed by such movements.

The movement of the star about the center of mass is far too small for us to see – no telescope has such high magnification. What we can observe is instead the stellar radial velocity, i.e., the speed by which the star alternately approaches us and recedes from us. This is done by observing the stellar spectrum. The star emits light at a variety of wavelengths – the shorter the wavelength of a specific beam of light, the more energy the beam carries. When this beam hits a human eye, the energy is used in order to generate a weak electric signal that is transmitted through the optic nerve to the brain. When the brain registers such an electrical signal, we “see” light. The brain does not only tell us that we see light, it also gives us a rough indication of the wavelength of the light. We experience the relatively long wavelength of energy-poor light as red. The relatively short wavelength of high-energy light is perceive as blue. In a similar way, we can build instruments that have the ability to measure exactly how much light there is at different wavelengths. This is called a spectrometer. When a stellar spectrum is observed – i.e., a list of how much light there is at a large number of specific wavelengths – one can see that the intensity of light is severely weakened at certain wavelengths. This is called a spectral line, and it appears since there is a chemical element in the outer parts of the stellar atmosphere that absorbs this type of light and prevents it from leaving the star. The spectral lines of a stellar spectrum therefore tell us what chemical elements are being present. However, they also tell us something more. From laboratory studies, we know that a light source at rest will have its spectral lines at specific wavelengths. But if the light source is set in motion, the spectral lines corresponding to a particular chemical element will shift slightly, by an amount that tells us exactly how fast the light source moves. This is known as Doppler shift. If the light source moves away from us, the spectral lines show up at slightly longer wavelengths compared to rest, and we say that the light is redshifted. If the light source moves toward us, the spectral lines show up at slightly shorter wavelengths than at rest, and we say that the light is blueshifted. Stars that alternately exhibit red- and blueshifted light are therefore performing some sort of wobbling motion, caused by the presence of invisible planets. By measuring the magnitude of these shifts, and the rate by which they increase and decrease, one can calculate both the distance between the star and the planet, and the planetary mass.

The radial velocity method has traditionally been the most important way of detecting exoplanets. For example, the first exoplanet around the star 51 Pegasi was discovered with this method, and by early 2009, 75% of all exoplanets had been discovered in this way. The transit method had been used in only 16% of the cases. The problem with the radial velocity method is that the planet must have a very high mass, and it must be located very close to the parent star, otherwise the Doppler shift will not be large enough to be measurable. Finding a planet similar to Earth – having a relatively small mass and a quite large distance to the star – is extremely difficult with the radial velocity method.

This is exactly what makes Kepler so unique and important. It makes it possible to search for a large number of exoplanets by using the transit method. With the transit method, it is possible to find smaller planets that are farther from their parent star than with the radial velocity method. Kepler was designed with the explicit goal of being able to find planets similar to Earth, both in terms of size and distance to the star.

Kepler has found a large number of planets that are described in terms of their diameters and orbital periods. In order for this information to make sense, it must be compared to something more familiar. Therefore, before examining some of Kepler’s findings, we should first remember how our own planetary system looks like. This is also necessary in order to understand the terminology that has emerged around exoplanets.

The Solar System

The Solar System has eight planets, which are divided into three different groups based on size and composition – the terrestrial planets, the gas giants, and the ice giants. The terrestrial planets have relatively small masses, are quite close to the Sun, and are mainly composed of rock and metal. The terrestrial planets are Mercury, Venus, Earth and Mars. Measured in terms of Earth masses, with the symbol M, we have 0.055M for Mercury, 0.815Mfor Venus, 1M for Earth (by definition), and 0.107M for Mars. Mercury and Mars are thus very small, with masses amounting to only 5% and 11% of Earth’s mass. This can be compared to the mass of the Moon, which is only one percent of Earth’s mass. Venus is almost as massive as Earth. Comparing the planetary masses with each other is far more interesting than looking at their sizes – the mass is a direct measure of the amount of material consumed to form the planet. It is also the mass that determines the strength of the planetary gravitational force, thus how strongly the planet affects the motion of nearby bodies.

For a majority of the exoplanets detected by Kepler we do not know their masses, but only their sizes. If we, in a similar way, measure the sizes of the terrestrial planets, using the Earth radius R as a yardstick, Mercury’s size is 0.38R, Venus’ size is 0.95R, Mars’ size is 0.53R, and the size of the Moon is 0.27R♁. These numbers do not differ much from each other – for example, it is not obvious at first glance that the Moon, which is about one third the size of Earth, actually only has a mass that is 1.2% of that of Earth. The reason is that the body volume, and therefore the mass, increases very fast when the radius is increasing. When doubling the radius, the volume increases a factor eight. When tripling the radius, the volume increases 64 times. The Earth has a volume that is about 50 times that of the Moon. However, the difference in mass between the Earth and the Moon is not a factor of 50, but a factor of 80. The reason is that there is yet another property to consider – the density of the celestial body, i.e., how many kilograms of mass that each cubic meter of the planetary material contains. Earth has an average density of 5500 kilograms per cubic meter, which is almost 65% larger than the lunar density – partly because our planet is much richer in iron than the Moon, partly because the enormous gravitational force of Earth is capable of compressing its material to a higher degree than the Moon, which increases the average density. This must be remembered when comparing planets sizes – volume changes strongly with radius, and the density can differ significantly between different types of planets, which can lead to very large differences in mass.

The distances of the terrestrial planets from the Sun are 0.39 AU for Mercury, 0.72 AU for Venus, 1 AU for the Earth by definition, and 1.52 AU for Mars. It would have been easier to compare these distances directly with those between the exoplanets and their parent stars. The problem is that the parameter that we actually measure is the orbital period. The period can be converted to distance by using Kepler’s third law, but only if knowing the stellar mass. These masses are indeed known, but not with very high accuracy. An approximate distance expressed in AU, may gradually have to be adjusted, as the stellar mass becomes more precisely known. It is therefore more convenient to compare the orbital periods, although these numbers may be slightly more difficult to assimilate intuitively. I will therefore refer to planetary orbital periods rather than distances, which are 88 days for Mercury, 225 days for Venus, 365 days for Earth, and 687 days for Mars.

The gas giants consist of Jupiter and Saturn. Their masses amount to 318M and 95M, respectively, while the radii amount to 11.21R and 9.45M♁. These numbers are huge compared to the terrestrial planets, and it is difficult to tell from the radii that Jupiter actually is three times as massive as Saturn. Besides size, the compositions of terrestrial planets and gas giants differ markedly – the former are mostly made up of rock and iron, while 70%-95% of the gas giants is hydrogen and helium. While the density of the Earth is 5500 kilograms per cubic meter, the corresponding values for Jupiter and Saturn are only 1300 and 690. Jupiter is 5.20 AU from the Sun while Saturn has an average distance that is almost twice as high, 9.54 AU. In terms of orbital periods, this corresponds to 11.86 years (4332 days) and 29.46 years (10,760 days).

Finally, we have the ice giants Uranus and Neptune. These planets differ dramatically from the gas giants. Firstly, only 5-15% of their masses are hydrogen and helium, whereas the majority (60-70%) is ice, and the remainder is made up of rock and metal. Secondly, their masses are very modest compared to those of the gas giants – only 14.5M for Uranus and 17.1M for Neptune. Their sizes equal 4.01R and 3.88R, respectively. It may seem paradoxical that the heavier Neptune is actually slightly smaller than the lighter Uranus. This is because the mean density of Neptune is higher due to a somewhat larger fraction of ice and rock. The orbital periods of the ice giants are very long, 84 years for Uranus and 165 years for Neptune.

Some terminology

The planets discovered by Kepler are divided into a number of categories based on size. A planet with radius between 0.8-1.25R is simply called an earth. With such a definition Venus and Earth would qualify as “earths” while Mars, Mercury and the Moon would be too small. The next category is called super-Earths, having radii in the range 1.25-2R. In our Solar System, there are no examples of such celestial bodies. If a “super-Earth” consists of rock and metal, and if it has the same density as Earth, it will have a mass of 2-8M. If it instead is made of ice, the mass can be considerably smaller. The transit method can only be used to show that a “super-Earth” exists – the radial velocity method is needed to determine if a “super-Earth” is indeed a large ball of rock and metal, or if it primarily consists of ice and thus looks like a small Uranus.

If the planet has a radius of 2-4R it is called a small Neptune. For example, both Uranus and Neptune would be typical examples of a “small Neptune”. If the radius is between 4-6R it is called a large Neptune. As was the case with “super-Earths”, this type of planet is missing in our own Solar System. If the radius is between 6-22R it is called a giant planet.

A similar unofficial terminology is used for extrasolar planets detected by the radial velocity method, but is based on the planetary mass. Early on, only objects as large as Jupiter or larger were discovered, and they were located extremely close to their parent stars, often within 0.05 AU where the orbital period is only four days or less (compared to Mercury’s heliocentric distance of 0.39 AU and the orbital period of 88 days). Such objects were therefore called hot Jupiters. Giant planets located slightly farther away from the parent star are sometimes called warm Jupiters. With time, discoveries included objects with smaller mass, and if smaller than a tenth of a Jupiter mass, i.e., less than 30M, they are called exo-Neptunes. Since these often are found close to the star as well, they are often referred to as hot or warm Neptunes. If the mass is less than 10M the planet is called a super-Earth.

By using the radial velocity method, mostly large planets located close to their parent stars are discovered. However, thanks to Kepler and the transit method, it has now become possible to detect smaller exoplanets, located farther away from their parent stars. A region known as the habitable zone is particularly interesting. It is a fairly narrow strip where the stellar light is strong enough to melt the ice on an Earth-like planet, but not so strong that the water evaporates. It is an area where liquid water can exist for a long time, which probably is a prerequisite for life to arise and thrive. There are various estimates on the location of the habitable zone boundaries. In a recent investigation, the inner edge was placed at 0.77 AU, just outside the orbit of Venus. The same study showed that the outer edge may lie at 1.18 AU, about midways between Earth and Mars. This corresponds to an orbital period of approximately 250 to 470 days. Stars that are smaller than the Sun radiate less heat and light – in such cases the habitable zone is closer to the star, where the orbital periods are shorter. Stars that are bigger than the Sun radiate more heat and light – in such cases the habitable zone is farther away from the star, where the orbital periods are longer.

One of Kepler’s primary goals is to find an “earth” with radius of 0.8-1.25R and a period of about 250-470 days, orbiting a solar type star – it would be the Earth’s twin, and a place where there possibly is life. We shall now take a closer look at Kepler’s actual discoveries – first some examples of individual systems, then some statistical properties telling us how common the various planetary types are.

Kepler’s discoveries – individual systems

Kepler has discovered various types of planetary systems – some have been seen before, while other types are completely new. Here we shall focus on some examples of planets in the habitable zone, but also “earths” and even smaller planets closer to the star. Furthermore, we look at systems where many planets coexist, but also so-called resonant planets, and double stars that have planets.

Planets in the habitable zone

The search for a planet in the habitable zone around a solar-type star bore fruit in December 2011, when it was announced that Kepler had found a “small Neptune” with a radius of 2.4R called Kepler-22b, which completes one orbit around its parent star, Kepler-22, in 289 days. If this beast has a composition similar to the Earth, its mass is at least 14M – it is then as massive as Uranus. It cannot be ruled out that the planet is dominated by water, which would make it much lighter – in any case, this planet is very different from our own.

An even more interesting finding was published in April 2013. The smallest known planet in the habitable zone of a solar-type star so far had been found – the “super-Earth” Kepler-69c with radius 1.7R and an orbital period of 242 days. Although this corresponds to the orbit of Venus, the planet is still in the habitable zone as the star emits 20% less light and heat than the Sun. The star in question, Kepler-69, also has yet another planet in its possession. This is a “hot small Neptune” called Kepler-69b with radius 2.2R, having a period of only 13 days. This planet is thus at a distance much shorter than the heliocentric distance of Mercury, whose orbital period is as long as 88 days.

The smallest extrasolar planet ever found within the habitable zone, however, is Kepler-62f, a “super-Earth” with a radius of only 1.4R and a period of 267 days. Its parent star, Kepler-62, is not at all similar to the Sun, but is much smaller, cooler, and fainter. Its mass is only 70% of that of the Sun, and it emits only one fifth as much radiation as the Sun. Interestingly, it has yet another “super-Earth” within the habitable zone – Kepler-62e with a radius of 1.6R and a period of 267 days. Hence, this is a system where there are two planets that potentially could be suitable for life. If these two planets would have the same average density as the Earth, their masses would be 2.7M and 4.1M, respectively. If that was not enough, there are also three other planets – the “hot super-Earths” Kepler-62b (1.3R) and Kepler-62d (1.9R), and the planet Kepler-62c (0.54R) which is as small as Mars. The orbital periods of these planets are just 5-18 days, which means they are located extremely close to the star.

Kepler has not yet found an “earth” within the habitable zone of a solar-type star. It remains to see what is hiding among the yet unconfirmed planet candidates.


These drawings show the possible appearances of four of Kepler’s planets that all are located in the habitable zone (plus an image of Earth to the far right). From left; a “small Neptune” named Kepler-22b; the “super-Earth” Kepler-69c; the “super-Earth” Kepler-62e; the “super-Earth” Kepler-62f. The original picture is found at
Image credit: NASA/Ames/JPL-Caltech

“Earths” and even smaller planets

At the time of writing, four of Kepler’s planets have also been detected by the radial velocity method and shown to have masses similar to that of Earth or smaller. The most Earth-like of these, Kepler-42d, has the mass 0.95M and radius 0.57R and is very close to its star – the orbital period amounts to only 1.9 days. The planet has almost the same mass as Earth, but is not much larger than Mars – a sign that it consists of a large iron core covered by a very thin mantle of rock. Another two planets circle the same star. These have much larger masses than Earth, but are noticeably smaller, which also indicates a higher abundance of iron than for Earth – Kepler-42c (1.9M and 0.73R) has the period 11 hours, and Kepler-42b (2.9M and 0.78R) has the period 1.2 days.

The other three low-mass planets are also extremely close to their parent stars – KOI-1843b (0.32M and 0.52R) with period 4.2 hours, Kepler-70c (0.67M and 0.87R) with period 8.2 hours, and KOI-2700b (0.86M and 1.06R) with period 22 hours.

In addition to the six planets with smaller radii than Earth already mentioned, we know of seven others smaller than our planet. The smallest of these is called Kepler-37b and has a radius of only 0.32R, making it almost as small as the Moon. Around the same star revolves another small planet, Kepler-37c, whose radius of 0.75R places it between Mars and Venus in terms of size. There is also Kepler-37d, a “super-Earth” with a radius of 1.94R. These three planets have orbital periods of 13, 21, and 40 days.

Multiple systems

As we have seen, there are several stars that surround themselves with more than one planet – these are called multiple systems. So far, Kepler has discovered no less than twelve systems containing four planets or more, which doubles the known number of planet-rich systems. The Kepler star with the largest number of known planets is called Kepler-90 and is home to no less than seven planets. Three of these have periods shorter than Mercury (7-60 days) and consist of an “earth” and two “super-Earths”. At distances corresponding to the region between Mercury and Venus (92-211 day period) are three more planets – two “small Neptunes” and a giant planet with radius 8.1R, which means it is not quite as large as Saturn. Farthest away, with a period of 332 days, which would have placed it just inside Earth in our own solar system, is a giant planet with a radius of 11.3R, meaning it is slightly larger than Jupiter.

Resonant planets

Some of the multiple systems Kepler discovered have very strange properties. They have an outer planet that happens to have an orbital period that is exactly twice as long as the period of an inner planet. This is called a 1:2 resonance. At least five stars have planets with such properties – Kepler-25, -27, -30, -31 and -32. Moreover, there are examples of 2:3 resonances, which means that an outer planet performs three revolutions around the star, while an inner planet makes two revolutions in exactly the same time. The stars Kepler-23, -24, -28 and -32 have planets with such properties.

Planets around binary stars

Kepler has also discovered a class of systems that previously were completely unknown – planets on wide orbits around two stars that are very close together. The first of these, Kepler-16b, was announced in September 2011. The two stars have masses of 69% and 20% of the solar mass, and orbit each other with a period of 41 days. If they were placed in our Solar System, they would both fit inside Mercury’s orbit. The planet has a mass of 106M, which is slightly more than that of Saturn, and a radius of 8.4R, which is less than for the same planet. The planet’s orbital period is 229 days, which roughly corresponds to the orbit of Venus in our own system.

In January 2012, there were two new cases. At a distance of 4900 light years in the constellation of the Swan is Kepler-34, which consists of two solar-type stars that orbit each other with a period of 28 days – around them, the giant planet Kepler-34b (70M) that orbits with a period of 289 days. At a distance of 5400 light years in the same constellation is also Kepler-35 consisting of two stars which are slightly smaller than the Sun. The orbit each other every 21 days. In orbit around the two stars we find the giant planet Kepler-35b (40M) with an orbital period of 131 days.

In August 2012 a system of two stars was revealed to have two planets in orbit around them – a “small Neptune” named Kepler-47b which has period of 50 days, as well as a “large Neptune” named Kepler-47c, with a 303 day period which places it in the habitable zone.

In October 2012, a system of two stars was described, having 1.5 and 0.41 solar masses, circling each other with a period of 20 days. At a greater distance is a giant planet, PHI-Kepler-64b (168M) which has a period of 139 days. Far beyond are two other stars that orbit the first two at a distance of nearly 1000 AU.

Kepler’s discoveries – statistical properties

Kepler’s observations of a large number of stars, combined with the number of actual planet discoveries, makes it possible to calculate the probability that a particular star will have a planet of a given type. One then takes into account that Kepler missed a large number of planets, simply because they do not move in the plane close to our line of sight. The goal is to say what percentage of all stars in the Milky Way that have planets of certain types. We limit ourselves to stars with roughly 0.6-1.5 solar masses – so-called FGK stars. It is only possible to make firm statements about the planets with short orbital periods. The reason is that Kepler only observed for four years, which limits the selection to planets with periods of less than about 400 days, because it is necessary to see at least three consecutive eclipses. To detect planets like Jupiter, whose orbital period is around 11 years, a telescope like Kepler would have to observe for at least thirty years. Even with such limitations, important results have been found.

For example, about half of all FGK-stars should have a planet with a period less than 85 days, thus having the same distance as Mercury or being even closer to the star. This means that the Milky Way is teeming with planets – every second star has one. Among these planets, the “earths”, “super-Earths” and “small Neptunes” are equally common. Together, they account for over 90% of the cases, whereas every tenth planet is either a “large Neptune” or a “giant planet”. We do not yet know the statistics for smaller planets at slightly greater distance from the star. But we do know that about 8% of all FGK stars have a “large Neptune” or a “giant planet” at a distance similar to Earth’s or smaller.

A special study focused exclusively on small, cool, and faint so-called M-stars, whose surface temperature is between 3030°C-3720°C. They have masses of approximately 0.4-0.6 solar masses, and their emitted light and warmth is only 2%-11% of the solar radiation. The benefit of considering these stars is that the habitable zone is located fairly close to the star, in the region where the orbital periods are less than one year. Thus, the habitable zone coincides with the area where it currently is technically possible to detect many planets, if they exist. About 90% of the M-stars turn out to have an “earth”, “super-Earth” or “small Neptune” with an orbital period of 50 days or less. Almost half of these are “earths”. Therefore it is almost twice as likely to find planets close to the cool M-stars compared to the warmer FGK-stars. The smaller and colder the star, the more difficult it is to find a “super-Earth” or “small Neptune”. The presence of “earths” does not follow such a trend – they are equally common in all M-stars. About 15% of the M-stars have an “earth” which is located in the habitable zone.

Another important discovery has to do with the chemical composition of the host star. In a previous post about the interstellar medium, I have described its typical chemical composition, which is also inherited by the stars formed therefrom. About 99% of the mass is hydrogen and helium, while all the other heavier elements make up about 1%. But there are significant differences between the stars, as some very old stars were formed at a time when there was even less heavier elements than today. Such stars are called metal-poor. Previous studies have shown a clear trend regarding the likelihood of finding a giant planet around a normal FGK-star. The metal poorer the star is, the smaller the chance that there will be a giant planet in orbit around it. Now it is possible to extend this type of study to stars hosting smaller planets. The chemical composition of 152 stars having 226 planets within a distance of at most 0.5 AU have been investigated. It turns out that the chance of finding an “earth”, a “super-Earth” or a “small Neptune” does not depend particularly strongly on the chemical composition of the star – small planets are abundant even around relatively metal-poor stars. Some stars in the study have four times less heavy elements than the Sun, and still have managed to form planets. While stars with slightly higher metal content than the Sun statistically has 2.7 planets with radius less than 4R for every giant planet, this number has risen to 5.9 for the metal-poor stars. This is because the giant planets are becoming increasingly rare as the star’s metal content decreases.

In another study the properties of planetary systems having large planets at very short distances from the star were explored – how does this affect the existence of other planets at similar distances? This study examined three different groups. The first group, including 63 system, consisted of planets with radii 0.6-2.5 times that of Jupiter, with orbital periods of 1-5 days, i.e., “hot Jupiters.” All attempts to find another planet near the star of these systems failed – a hot Jupiter reigns alone in this inner region.

The second group also had very short orbital periods, only 0.8-6.3 days, but consisted of planets with radii of 1.4-6.7R, roughly equivalent to a “small” or “large Neptune ” – and a very hot one. The study included 222 such systems. When looking for additional planets on somewhat smaller or larger distances from the star in these systems, the outcome is extremely different from the first group. In the second group there are 73 cases of smaller planets with orbits close to the large one, i.e., every third system. The probability of finding two planets close to each other near the star increases dramatically when the larger of the planets is not extremely large.

The third group consists of planets similar to those in the first, i.e. planets about the size of Jupiter, except that they are slightly farther from the host star and thus have slightly longer orbital periods, 6.3-15.8 days. This is what is called a “warm Jupiter.” Here it is also rare with other planets in the vicinity, but three systems where found including a second planet, near the 1:2 resonance. Although the statistics are uncertain because these are so few planetary systems, these results suggest that about 10% of the “warm Jupiters” are not alone.

The significance of Kepler’s results

Kepler’s observations have resulted in the discovery of a series of very remarkable planetary system, which differ significantly from our own Solar System. We are fascinated and amazed by these odd and alien worlds. The press releases by the scientists are spread further by newspapers and TV channels, along with imaginative drawings by artists of how these planets might look like, to a curious and interested public. The discoveries increase people’s knowledge about their environment and lead to conversation, debate, and speculation. They become a part of popular culture and sooner or later become parts of science fiction books or movies. They inspire many young people to study natural science in schools and universities, some of them becoming scientists that will uncover new knowledge about Nature. This situation is not unlike the collection of strange herbs, plants, and animals from all parts of the world, made by European explorers in the 17th and 18th centuries, that were exhibited in museums, botanical gardens, zoological parks or shown in various collections of curiosities, to the amusement of the general public.

All this is fine, but says rather little about how scientists actually use this new knowledge. It says little about the purpose of building a space telescope like Kepler. To understand the real purpose we can return to the botanical and zoological collections – their real significance was to offer such a high degree of information about Nature, and so many concrete examples of its diversity, that it was possible to begin to see patterns, identify connection and strengthen hypotheses, which eventually made it possible to understand how the species have emerged and evolved on Earth. It was this huge amount of concrete information, that made it possible for Charles Darwin and others to begin to understand the processes by which species evolve and the mechanisms that control the evolution. Similarly, Kepler’s observations are not exclusively about revealing one planetary system that is more spectacular than the other, and the final goal is not only to gather facts about these systems that can be stacked in well-ordered tables. Instead, Kepler is there to provide information that helps us understand how planetary systems are formed and how they evolve over time. We want to understand the underlying processes and mechanisms, and this requires detailed information of how the world actually looks like. That is where Kepler comes in, and this is the light in which we have to see its discoveries.

The physical processes and mechanisms responsible for planet formation are described in mathematical terms, but these equations must be solved in some way. Previously, we were forced to solve these equations by hand, which severely limited the complexity of the equations one could study. Today, the equations are solved numerically with the aid of powerful computers, which means that more realistic processes and mechanisms can be studied.

Computer models of planet formation

From observations of very young stars around us, which currently are in the same stage of development as the Solar System was when it formed 4.6 billion years ago, we know that these young stars are surrounded by vast but thin disks. This disk material has the same composition as the interstellar medium, which means that about 99% of the mass consists of hydrogen and helium, while 1% of the mass is dust grains.

There is currently a large number of computer models developed by researchers to describe what happens when these dust grains gradually merge to form larger bodies. There are models that follow the entire chain from grain to planet, but it is more common to study selected sub-problems and specific aspects of the process. Some models focus on the very first period, when small grains build bodies that are at most a few hundred kilometers in size – so-called planetesimals. These models keep track of a large number of positions, velocities and masses of individual particles, follow their motions over time, as the particles feel the gravitational force of the star and are slowed down or dragged along by the gas in the disk, which often is allowed to have turbulent properties. During collisions between grains, decisions are made regarding the outcome – do particles merge into larger units, do they fragment into a variety of smaller particles, or just bounce against each other? These decisions often rely heavily on laboratory experiments, that studies what actually happens when two grains or clusters of grains with specific masses collide with each other at specific speeds. As the model marches forward in time, one can track how particles grow and determine how long it takes to reach a certain particle size.

Other models describe how these planetesimals merge to form embryos – bodies that are as large as the Moon, Mercury and Mars. Yet other models study how embryos are merged in gigantic collisions to form planets like Venus or Earth. Some models focus on the interactions between the planets and the surrounding gas – when will the planet’s gravitational pull become strong enough to absorb large amounts of gas and grow into a gas giant? How does the gas disk properties change by the presence of a gas giant, and how does this in turn modify the ability of the gas giant to grow further? It was models like these, in the mid 1980s, that showed that a gas giant would not remain at its birthplace, but start drifting towards the star, a phenomenon known as migration. It is this type of modeling that is the basis for most of the ideas, thoughts, claims and knowledge regarding planet formation today – the models are invaluable tools for building our understanding of the world.

The purpose of the models is to show exactly what type of planetesimals, embryos and planets that form at different distances from the star, and how long it takes. They also show how the end results are altered when the basic conditions of the simulations are changed – such as the stellar mass, gas disc mass, or the amount of dust present in the disc. This is not casual work – computer models of this type is often the result of lifelong work that takes decades to develop, refine, and perfect. Despite all efforts, it is inevitable that such models are based on a wide range of assumptions and simplifications, that are necessary for practical reasons. The difficult question is always – exactly how correct, realistic and relevant are these models? We know that the predictions differ among models – sometimes in a fundamental way. In order to know which models are more accurate than others, and for improving these models further, it is necessary to compare the model predictions with reality.

Our Solar System is of course extremely important in this context. It is the only planetary system we can study up close. Here we can use radiometric dating of meteorites and material from Earth, the Moon and Mars to verify the timescales of formation suggested by the models. It is possible to investigate asteroids and comets – surviving planetesimals – in situ, to see what internal structure they have and compare it to the predictions of the models. At the same time, the Solar System is only one system out of many, and in order to claim with certainty that we understand how our own Solar System formed, it is necessary to explain how other planetary systems form as well. Here, Kepler’s observations constitute an invaluable source of information – the models must conform with this reality.

In order to sketch how Kepler’s observations may improve our understanding of planet formation, it is first necessary to summarize some aspects that are of great importance in planet formation.

The early stages of Solar System evolution

In our own Solar System there are fundamental differences between terrestrial planets, gas giants and ice giants. We have also seen that exoplanet systems have a similar mix of very small planets and extremely large planets. There are essentially two factors that cause these differences – the existence of a snowline and the fact that the gas disc has a limited lifespan.

The snowline exists because the temperature in the disk falls steadily with distance from the heat and warmth of the central star. Within the snowline, located around 4 AU from the star, it is so hot that the abundant water cannot freeze – the water vapor mixes with the other gases of the disk, and the grains consist exclusively of rock, metal and sulfides. Outside the snowline, it is cold enough for the vapor to freeze – outside 4 AU the grains of rock, metal and sulfide are covered with thick layers of ice.

Observations of young stars show that the gas in the disks only survives for about 3-5 million years. The gas simply evaporate, due to the heating from the star at the center of the disk. If gas giants are to form in the disk, they need to develop before the gas takes off. It is a race against time, which does not always lead to victory. We shall now see how these two factors have shaped our own Solar System.

Models of planetesimal growth within the snowline shows that it may have been very slow. Grains of rock, metal and sulfides have difficulties to stick to each other, preventing rapid growth. Radiometric dating of meteorites seem to confirm that planetesimal formation was a sporadic process that took place repeatedly throughout the first 4-5 million years. Once formed, they merged into embryos rather quickly. However, being scattered at large distances from each other, it took a long time, tens of millions of years, for the embryos to unite in collisions. The Earth was not fully formed until 50-150 million years had passed, when the Moon formed in the last giant collision with an embryo that our planet experienced. These time scales are supported by both simulations and radiometric dating. The terrestrial planets therefore grew long after the gas had disappeared. Mercury and Mars can probably be considered surviving embryos that escaped from being devoured by Venus or Earth.

Outside the snowline, in the outer part of the Solar System, the development was completely different. Here the grains were significantly larger, since they largely consisted of ice, in addition to the rock, metal and sulfides. This ice is very sticky, making it easy for the grains to attach to each other. Models show that it is possible to build very large planets of rock, metal, sulfides and ice in just a couple of million years. The models also show that it is extremely difficult for the planet to soak up any gas, unless it is heavier than ten Earth masses. But when the planet reaches a mass of 10M the gravitational force becomes strong enough to absorb cold gas directly from the disk and quickly grow into a gas giant. It is critically important that the growth to 10M has time to occur before the gas disappears 3-5 million years into Solar System history. The ice giants Uranus and Neptune are probably examples of planets not formed fast enough to consume large quantities of gas, unlike the gas giants Saturn and Jupiter. The gas and ice giants were therefore in place long before Venus and Earth had time to form in the inner Solar System.

Kepler helps to answer important questions

Models show that it is not possible to form a gas giant extremely close to a star. There is usually not enough material to reach 10M, the time it takes to build a large body is too long compared to the gas disk lifetime, and even in the unlikely event that a sufficiently massive planet forms before the gas disappears, this gas is so hot and is moving so fast that it cannot easily be collected by the planet. In our Solar System there are no gas giants close to the Sun. But according to Kepler, a tenth of the stars with masses close to the Sun, have a “large Neptune” or a “giant planet”, within a few tenths of an AU from the star.

Such giant planets must have formed outside the snowline, and have moved closer to the star at a later stage. Computer simulations of interaction between a gas giant and the disk, show that migration can be a very common phenomenon – the gas giant gradually drifts towards the star, and may not stop until it reaches the inner edge of the disc, located only a few hundredths of an AU from the stellar surface. But the move may also have happened in an entirely different way. If two or more gas giants formed close to each other outside the snowline, the gravitational perturbations may have been strong enough to give one of the planets a very elliptical orbit, that occasionally brought it very close to its star. During these close encounters with the star it may happen, according to other models, that the star is forcing the planetary orbit to become more circular, so that it eventually is given a permanent residence in the immediate vicinity of the star.

So here we have two interesting questions. Which of the two possible mechanisms – migration or gravitational perturbations followed by circularization of the orbit – is actually responsible for moving the planet? What is it that makes some planetary systems experience extensive movements of their giant planets while others, like our own, did not experience such a strong redecoration? Kepler’s observations are indispensable by addressing this kind of issues.

Kepler observations show that migration undoubtedly has taken place. The primary proof of that is that resonant systems have been detected. When the migration moves the planet slowly inwards, the resonances of the planet will also drift inwards. The resonances are located at the distances from the star where the gas and dust has an orbital period that is a small integer fraction of the planet’s orbital period. When the planet migrates, its orbital period keeps changing, why the resonances slowly move as well. If such a resonance accidentally passes the orbit of a smaller planet, the planet gets stuck in the resonance. Then the planets move towards the star in formation, while being constantly locked in the resonance. When the gas finally disappears and the migration ceases, the planets remain locked in their common resonances. So far, Kepler has discovered nine resonant systems. Kepler-90 could also be the result of migration – perhaps the six planets located within the 332 day orbit of the giant planet were pushed there by the drifting giant planet? It is possible that planets eventually will detach from the resonances, for example by gravitational perturbations. If so, the absence of resonant planets today, cannot be used to claim that migration has not occurred. It is therefore possible that the “hot Jupiters” that have smaller planets in their vicinity (about 10%), and the “hot Neptunes” that have small neighbors (about 30%), have picked these planets up during their migration.

But if migration is the only mechanism responsible for large-scale relocation of gas giants, how come that the most extreme planets – the “hot Jupiters” – all are alone near their stars? Why have they not also pushed planets in front of them or dragged them along behind? Could it be that they have arrived in a very different way – for example by strong gravitational perturbations followed by circularization?

A second problem concerns the location of the “earths”. About half of the stars with masses similar to the Sun (FGK-stars) have planets within a few tenths of an AU from the star, of which 30% are “earths”. Among the small M-stars 90% have a planet within a few tenths of an AU from the star, half of which are “earths”. Thus it seems to be very common to find Earth-sized planets, at distances no greater than that between the Sun and Mercury. Does that mean that they formed there? Or do they necessarily form at slightly greater distances, where Venus and Earth are located in our own system, and then migrate inwards? If so, why did not Venus and Earth migrate? No matter which model is used to simulate the formation and migration of Earth-like planets emergence, it must result in a statistical distribution of planets with distance from the star that is consistent with observations, for stars with different mass. If we can produce models that closely reproduces reality, we can be fairly sure that they give us a true picture of how our own planet has formed.

A third problem concerns the very earliest stage – the formation of planetesimals. Today this is an intensive field of research, with a number of competing theories, which paint quite different pictures of planetesimal growth. According to the hierarchical agglomeration scenario bodies are built gradually, as small planetesimals merge into larger ones. Here, objects of all sizes, from a few centimeters to hundreds of kilometers are represented, at least at some stage during the simulations. But there are also alternative scenarios, such as streaming instabilities, where the gas is able to sweep up decimeter-sized boulders into huge swarms which later collapse gravitationally and directly form planetesimals that are hundreds of kilometers in diameter, without the formation of objects with intermediate sizes. Hierarchical agglomeration will proceed no matter how little dust there is in a gas disk – but the smaller the amount the dust, the longer it takes to build planetesimals. Streaming instabilities are extremely sensitive to the amount of dust compared to the amount of gas. If planetesimals are to form very early through streaming instabilities, the gas cannot be metal poor – it should be as rich in heavy elements as the Sun, and preferably twice as rich in metals.

It is therefore interesting that stars whose metal content is only a quarter of the solar metallicity, still have been able to form “earths” and “super-Earths” with the same efficiency as the metal-rich stars. It either means that hierarchical agglomeration dominates, or planetesimals begin to form only once the gas is partially dispersed after 3-5 million years. Kepler observations of the presence of planets around stars of different metallicity thus provide important information that helps us understand the mechanisms that are responsible for the formation of planetesimals, and when these mechanisms are active.


The exploration of our planetary system aims at building an image of the world based on natural science, and to be able to describe in detail how the Earth and the other planets formed. This reconstruction of our own history and our attempts to understand the environment in which we live, is a deeply humanistic quest. It is based in the uniquely human urge to understand ourselves, our environment and our origin. Today we have reached a point where only advanced technology can bring us further – space telescopes like Kepler, or the powerful computers used for model calculations are necessary tools for us to change and improve our image of the world. It may not be obvious at first glance, but the truth is that this technology – despite its industrial appearance and mathematical inaccessibility – is actually part of a humanistic cultural project.


Buchhave, L.A., Latham, D.W., Johansen, A., Bizzarro , M., Torres , G., Rowe, J.F., Batalha, N.M., Borucki, W.J., Brugamyer, E., Caldwell, C., Bryson, S.T., Ciardi, D.R., Cochran, W.D., Endl, M., Esquerdo, G.A., Ford, E.B., Geary, J.C., Gilliland, R.L., Hansen, T., Isaacson, H., Laird, J.B., Lucas, P.W., Marcy, G.W., Morse, J.A., Robertson, P., Shporer, A., Stefanik, R.P., Still, M. Quinn, S.N. (2012). An abundance of small exoplanets around stars with a wide range of metallicities. Nature 486, 375-377 .

Dressing, C. D., Charbonneau, D. (2013). The occurrence rate of small planets around small stars. The Astrophysical Journal 767 (1), 95.

Fressin, F., Guillermo, T., Charbonneau, D., Bryson, S.T., Christiansen, J., Dressing, C.D., Jenkins, J.M., Walkowicz, L.M., Batalha, N.M. (2013). The false positive rate of Kepler and the occurrence of planets. The Astrophysical Journal 766 (2), 81.

Steffen, J.H., Ragozzine, D., Fabrycky, D.C., Carter, J.A., Ford, E.B., Holman, M.J., Rowe, J.F., Welsh, W.F., Borucki, W.J., Boss, A.P., Ciardi, D.R., Quinn, S.N. (2012). Kepler constraints on planets near hot Jupiters. Proceedings of the National Academy of Sciences 109 (21), 7982-7987.

NASA’s website about Kepler: http://kepler.nasa.gov/

The Extrasolar Planet Encyclopaedia : http://exoplanet.eu/catalog/

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