Testing the Theory: Other Planetary Systems

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Some 455 planets have been found orbiting other stars---exoplanets (sometimes also called extrasolar planets)---in 388 exoplanet systems at the time of the last update of this webpage. This section will first look at how we find exoplanets and then I will draw some preliminary conclusions based on the statistics of the orbits and masses of the exoplanets.

Finding Exoplanets

Detecting planets around other stars (exoplanets) is a difficult project requiring very careful observations. At first finding planets might seem a simple thing to do---take pictures of stars and look for small faint things orbiting them. A planet would indeed be a faint: a billion or more times fainter than a star in the visible band---the glare of the starlight would wash out the feeble light of a planet. The direct imaging technique of finding planets would be better accomplished in the infrared band because the planet's thermal spectrum would have maximum emission in the infrared band. Also, stars produce less infrared energy than visible band energy---a planet would only be ten to a hundred thousand times fainter than the star. The planet would still be very faint, but at least the contrast ratio is improved by many thousands of times. The direct imaging technique is able to find jovian planets far from their parent stars. Twenty-four planets (as of early-June 2011) have been found this way.

less contrast in the infrared

Some of the planets imaged are very young and still quite warm from their formation. Therefore, the young planets are quite bright in the infrared and easier to detect. Some planets have been imaged by blocking the light from the much brighter star with a device called a coronograph so that the feeble light from the planet can be detected. Use of a coronograph was essential to create the first visible light (optical) image of a planet: that orbiting the very bright star, Fomalhaut, shown below. The black area in the center is the coronograph, the white dot shows the location of the star, the ring is a dusty debris disk analogous to our solar system's Kuiper Belt (but much further out), the small white box shows the location of the planet some 115 AU from its star, and the inset shows its motion over two years of its entire 872-year orbit. Its motion proved it was an object orbiting the star.

Fomalhaut B discovery image

Astronomers have detected disks of dust and gas around young stars using sensitive infrared detectors on the largest telescopes in the world. An equivalent amount of material locked up into a single object will have a smaller total surface area than if it was broken up into many tiny particles. The disks have a lot of surface area and, therefore, can emit a lot of infrared energy. Some bright stars in our sky have dust around them: Vega, Beta Pictoris, and Fomalhaut. These are systems possibly in the beginning stages of forming planets. One disk around the star HR 4796A appears to be in between the dust disk stage and a fully-fledged planet system. The inner part of the disk has been cleared away. Presumably, the dust material has now coalesced into larger things like planets. The planets would have a smaller surface area than if the material was still in tiny particles form, so the planets will be much fainter. The Hubble Space Telescope has also detected disks of gas and dust around 50% of the stars still forming in the Orion Nebula. It appears that the formation of planet systems is a common process in the universe.

Another way to look for exoplanets is to notice their gravitational effect on the stars they orbit. One signature of a planet would be that the star would appear to wobble about as the star and the planet orbit a point situated between them, proportionally closer to the more massive star, called the center of mass. This technique is called the astrometric technique. Our Sun wobbles because of the gravity of the planets orbiting it. Most of the wobble is due to Jupiter which contains more mass than all of the other planets combined. However, the wobble is tiny! Because the Sun is over a thousand times more massive than Jupiter, the center of mass is over a thousand times closer to the Sun, or about 47,000 kilometers above the surface of the Sun (this distance is less than 7% the radius of the Sun). Despite the tiny wobble, astronomers on planets orbiting nearby stars could detect this wobble using the same technology we have here on Earth if they observed the Sun's motion very carefully over a couple of decades. The stronger the gravity between the star and planet, the larger will be the wobble of the star and the easier to detect. Therefore, the astrometric technique is well-suited to finding massive jovian exoplanets close to their parent stars. No exoplanets have been found using this technique (at the time of writing). The now-canceled SIM Lite mission was to use this technique and the Gaia mission, scheduled to launch in 2013, will use this technique.

finding planets from the slight motions of the stars they orbit

Sequence on the right side is actually from two different vantage points. The wobbling star is what you would see if the orbit was face-on. The doppler shifting absorption lines is what you would see if the orbit was edge-on from a position to the right of the star-planet system (so the lines shift toward the red end when the star is moving away from the observer and the exoplanet is moving toward the observer).

Another signature of an exoplanet would be doppler shifts in the star's spectral lines as they orbit their common center of mass. The doppler shift technique (also sometimes called the radial velocity technique) has been the easiest and most prolific way to find exoplanets so far. At of the time of writing over 500 exoplanets have been found using the doppler shift technique. The searches have so far focussed on stars similar to the Sun, though two systems have planets orbiting a pulsar (a type of ultra-compact, dead star discussed in the stellar evolution chapter---planets found using a variation of the doppler shift technique called the timing technique), ten systems have M-type red dwarf stars (including one that has a terrestrial-sized planet in its habitable zone), four systems have brown dwarfs, four systems have A-type stars, and three have B-type stars. Like the astrometric technique, the doppler shift technique is well-suited to finding massive jovian planets close to their parent stars. The number of systems discovered and the details about them changes so rapidly that the best place to find up-to-date information on exoplanets is on the internet. Some websites are given at the end of this chapter.

The period of the star wobble is measured and then the distance (semi-major axis of the orbit) is derived from Kepler's third law. The star's velocity change is measured and then the total mass of the system is derived from Newton's Laws of Motion. We can estimate the mass of the star from its spectral type, estimate the planet velocity from the star wobble period and then derive the exoplanet's mass. However, the doppler effect tells you about the motion along the line of sight only. The exoplanet orbits are undoubtedly inclined, or tipped, to our line of sight and the amount of inclination is uncertain. This introduces an uncertainty in the derived masses of the exoplanets. Usually, astronomers will quote the masses as "mass×sin(orbit inclination angle)", so the actual exoplanet masses could be higher. The star-wobble techniques can also give us the orbit eccentricity if we have observations from the entire orbit.

Astronomers cannot yet determine the diameters of most of the giant exoplanets so their densities, and, therefore, their composition is still unknown. Eighty-one of the giant planets has been observed to move in front of their stars and cause an eclipse or dimming of the starlight. This is called a transit so this means of detecting planets is called the transit technique. A transit means that the planet's orbit is aligned with our line of sight (and the inclination angle is nearly 90 degrees). From the planet transit, astronomers have been able to accurately measure the diameter of the planet. Using the planet mass from the star wobble methods you can then determine the density. Careful observations of the spectrum of the star while the planet is transiting across will enable astronomers to determine the chemical composition of the planet's atmosphere using spectroscopy. In other cases, the planet's spectrum is found from taking the spectrum of the star plus planet, then taking the spectrum of just the star when the planet is behind the star and subtracting it from the star plus planet spectrum. One planet, HD 189733b, has water, methane and carbon dioxide in its atmosphere but the planet is much too hot and massive to support life. It was not until January 2010 that astronomers had been able to take the spectrum of a planet directly---an important step in eventually being able to analyze the spectrum of a terrestrial planet to see if it is supporting life on it.

big planet transitting makes bigger dip in brightness than smaller planet

Most of the transiting planets were first detected via the doppler shift technique, but the transit technique can be another way of searching for planets around other stars. However, most planetary systems do not have their orbits so exquisitely aligned with our line of sight so a lot of stars would need to be looked at to improve the chances of finding even a few transits. One advantage of the transit technique over the star-wobble methods for planet detection is that you would be able to detect terrestrial-diameter planets (i.e., small planets). Small planets like the Earth produce too small a wobble in their parent star because of their small mass to be detected by the star-wobble methods. The COROT mission (ESA) has found a planet less than twice the diameter of the Earth. However, this planet is so close to its star that the planet's surface temperature is 1000 to 1500 deg C! The NASA/JPL spacecraft mission called Kepler is looking at about 156,000 stars simultaneously to search for Earth-sized planets during a 3.5-year period of time. The spacecraft is focussing on planets that could be in the stars' habitable zones (where liquid water could exist on a planet surface). Only 0.5% of the stars are expected to have their planets orbits in the habitable zones properly aligned for detection by Kepler. A terrestrial planet with mass between 0.5 to 10 Earth masses will cause its star to dim by a fractional amount of between 0.00005 to 0.0004, respectively, and the transits will last just a few hours. The 3.5-year time period was determined from the need to verify the repeatability of the planet transiting at least two more times after the first detected transit with the same time interval between transits and depth of transit. Such repeatability of the transits would mean that something was orbiting the star and not just some chance occurrence of an unrelated object passing in front of the star. For a solar-type star with a planet in the habitable zone, the planet would transit the star once a year. However, this assumes that the stars are calm and steady like our Sun. The Kepler team has found that a number of the stars are a bit more active, more variable, than our Sun, so they will need more observations to tease out the dimmings due to transiting planets from those due to the intrinsic variability of the stars themselves. Will NASA have the funds to continue the mission beyond the 3.5-year original mission?

The Kepler team has created some nice interactives showing how the planet detection works as well as how the various planet parameters are derived. As of early 2011, Kepler had found over 1200 planetary candidates with almost 410 of them in 170 planetary systems with multiple planets. Candidate planets are those that have not been verified yet through follow-up observations to make sure the star dimming is not due to another star as in an eclipsing binary system or a dead star called a white dwarf. Sixteen planets have been confirmed, including one that is definitely a rocky planet with a density of 8.8 times that of water called Kepler 10b. However, Kepler 10b orbits less than 0.017 AU from its star (Mercury orbits our Sun at 0.39 AU), so its surface temperature is over 1800 K! Of the candidates (as of early 2011), 68 have diameters less than 1.25 Earth's and 54 candidates reside in their star's habitable zone and have diameters ranging from Earth-size to larger than Jupiter with one having the sought for combination of Earth size in the star's habitable zone (five in the habitable zone have sizes from 0.9 to 2 times the diameter of the Earth). The search continues!

Another method of planet detection uses the gravitational lensing effect discussed in the Einstein's Relativity chapter. When a star passes almost in front of another more distant star as seen from the Earth (the stars are not orbiting each other), the light from the distant star can be warped and focussed toward us by the gravity of the nearer star to produce multiple images of the distant star or even a ring of light if they are aligned exactly right. This lensing effect is too small and the resolving powers of telescopes are too small to see the multiple images. The multiple images will blend together into a single blurry blob that is brighter than when the multiple images are not present (a microlens event). As the nearer star moves in front of the distant star, the nearer star's blurry blob will appear to brighten and then dim as the nearer star moves out of alignment. The microlens event for typical stars in our galaxy moving at typical speeds will last a few weeks to a few months and the amount of the brightness magnification will depend on how closely the near and distant stars are aligned with our line of sight.

close up view of microlens event

The animation above shows an extemely-magnified view of two possible microlens events (what you would see if you had an optical telescope several hundred meters across in space). The brightness of the ring and the combined brightness of the two distorted images exceed the distant star's brightness when it is not lensed. This animation is adapted from a figure by Penny Sackett in a talk about the search for planetary systems using microlenses.

If the nearer star has a planetary system with a planet at the right position, a smaller and briefer microlens event will happen superimposed on top of the star's microlens. By looking for brief deviations in the otherwise smooth increase, then smooth decrease of a stellar microlens event, you could detect the presence of a planet. This method is called the microlens technique and is summarized in the figure below—select the image to view the full-size version in another window. The planet's mass and orbit size could be determined from careful measurements of the brief deviations. The microlens event method can be used to detect jovian-mass and terrestrial-mass planets near their parent stars and the parent stars are distant from the Earth. Like the transit method, a lot of stars must be monitored to pick up even a single stellar microlens event. The microlens events are due to chance alignments that are not repeatable. Thirteen planets orbiting stars have been found using the microlens technique at the time of writing.

microlens planet technique geometry

In May 2011, two teams using the microlens technique announced the discovery of several other planets that are not orbiting a star—"free floaters". The teams had observed about 50 million stars in the direction of the Milky Way's bulge every 10 to 50 minutes in 2006 and 2007 looking for those chance alignments. They found a surprisingly large number of brightenings caused by planet mass objects alone. A statistical extrapolation of the results says that the free floater planets could be almost twice as numerous as normal main sequence stars in the Galaxy.

The transit and microlens techniques are not good for looking planets around a particular star of interest. The star-wobble and direct imaging methods are better. However, the transit and microlens methods are useful for determining the statistics of planetary systems in our galaxy, particularly the number of star systems with terrestrial planets in the habitable zones. Another possible exoplanet detection method uses the amount of lithium in a star. A comparison of stars with planets and those stars without planets shows that the stars with planets have about 1% of the lithium in the star than in stars without planets. Such a detection method could offer a much more cost-effective to search for planetary systems than the other techniques being used now.

Results and Testing the Theory

The figure below summarizes the orbit sizes and orbit eccentricities of the 388 other planetary systems known at the time this was written from the Extra Solar Planets Encyclopedia. The figures include exoplanet data that still need to be confirmed. Data for 421 exoplanets with known orbit sizes are plotted on the left and data for 400 exoplanets with known eccentricities are plotted on the right. Most of these exoplanets are Saturn-Jupiter mass or larger and those that transit their star have densities like Saturn-Jupiter or less.

orbit size histogram orbit eccentricity histogram

Two things to notice are how close the large planets are to their stars and the large eccentricities of some of the planet orbits. The exoplanets very close to their stars are called "hot Jupiters" because their temperatures can get up to 1000 deg C in their cloudtops (the clouds would probably be made out of rock-dust minerals instead of the ammonia, ammonium hydrosulfide, and water clouds of the much colder Jupiter and Saturn). The hot Jupiters with low densities have atmospheres puffed out by the extreme solar heating---that inflates their diameter.

The Condensation Model outlined in the previous section predicts that large planets will only form far from the young star. Giant planets start from a core of rock and ices that were able to solidify far from the intense heat of the young star. The rock-ice cores then pull in surrounding gas by their gravity. Near the star, the temperature is too high to form the rock-ice cores.

Over a decade before the discovery of the first exoplanets, astronomers predicted as part of the Condensation Model that large gas/rock clumps would form far from a young star and spiral inward toward the star because of friction with the gas remaining in the disk around the forming star. The gas/rock clumps can also interact with each other sending one into a small orbit while the other is ejected out of the system. Such interactions may also explain the elliptical orbits we see. Some astronomers working on planet formation models are looking for ways to halt the inward spiral of the gas giant planets near the star through tidal interactions between the planet and star. Perhaps the gas giant planets we see are simply the ones that did not have time to spiral completely into the stars before the gas disk was cleared away by the strong T-Tauri winds that accompany the start of nuclear fusion. Perhaps in our solar system other giant planets had formed but did not survive or were ejected. Evidence for the ejection possibility comes from the potentially large number of free floater planets that the microlens surveys are saying must exist in the Galaxy. Recent computer simulations of the dynamical history of our solar system show that the gravity of Saturn helped prevent Jupiter from spiraling into the Sun and that their orbits may have started further out than they are now, then moved closer in than they are now, and then finally moved further out to their present distances. The simulations also show that Uranus' initial orbit might have been larger than Neptune's initial orbit and that both planets' orbits were smaller than they are now. This shuffling of the gas giant planets would also have affected the material forming the terrestrial planets and changed the distributions of various types of asteroids and comets. Observations of other star/planet formation places and other planetary systems along with more sophisticated computer simulations have confirmed various features of the Condensation Model and they have also led to modifications and extensions of the theory in the continual interaction of observation-theory-testing process of error correction of science.

In the next few years, ground-based interferometers will be completed that can image large exoplanets. What about Earth-like planets? It is unlikely that life could arise on a gas giant planet. NASA's proposed Terrestrial Planet Finder (TPF), a space-based mission, should be able to obtain infrared or optical pictures of life-bearing planets. With TPF astronomers will also be able to analyze the spectrum of the planets to determine the composition of their atmospheres. Spectral lines from water would say that a planet has a vital ingredient for life. If oxygen, particularly ozone (a molecule of three oxygen atoms), is found in the atmosphere, then it would be very likely that life is indeed on the planet. Recall from the previous chapter that molecular oxygen quickly disappears if it is not continually replenished by the photosynthesis process of plants and algae. However, it is conceivably possible for a few non-biological processes (e.g., the runaway greenhouse effect with the photodissociation of carbon dioxide and water) to create an atmosphere rich in molecular oxygen and molecular oxygen does not produce absorption lines in the preferred infrared band that would be used in the TPF mission. Ozone does. Ozone existing along with nitrous oxide and methane in particular ratios with carbon dioxide and water, all of which produce absorption lines in the infrared, would be very strong evidence for an inhabited world.

The setup and technologies TPF will employ will be based on the experience gained from previous projects such as the Keck Interferometer, the Large Binocular Telescope Interferometer, Kepler, CoRot, and the Gaia Mission. Unfortunately, there are now no plans to develop TPF for at least the next decade.

Exoplanets Web Sites

The number of stars with detected planets and the details about them changes so rapidly that the best place to find up-to-date information on exoplanets is on the internet. Here are some WWW links (will display in another window):
  1. An excellent starting point is the Extra Solar Planets Encyclopedia This site is maintained by Jean Schneider of Observatorie de Paris (it is in English, though).
  2. Planet Quest: the search for another Earth (NASA-JPL).
  3. The Terrestrial Planet Finder Book.
  4. The California Planet Survey.
  5. How to Find an Extrasolar Planet (ESA).

Section Review

Vocabulary

astrometric technique center of mass direct imaging technique
doppler shift technique exoplanet microlens technique
transit technique    

Review Questions

  1. What are two signatures of a planet in the starlight?
  2. Why is it better to search for planets in the infrared, rather than the optical band?
  3. What sort of planets are the star wobble methods best suited to find? Why?
  4. What planet properties and orbit properties can you find with the star wobble methods?
  5. What planet detection methods could detect Earth-mass or Earth-size planets? Why would the other methods not be able to find small planets like the Earth?
  6. What planet detection methods can give us the diameter, density, and maybe composition of an exoplanet?
  7. If you wanted to search for planets around a particular star, which method(s) should you use? Why is that?
  8. What challenges to the standard condensation model do the other planetary systems give? What is a likely explanation?
  9. What would be a good way to search for Earth-like planets around other stars? How could you tell if life was probably present on an extrasolar planet?

More Solar System References

Introductory Planets Course

The University of Washington Astronomy department has an excellent web page for their introductory planets course, Astronomy 150. If you need more information about the solar system than what I have in my notes, then that is the place to check next.

Tours of the Planets

Starting points for excellent tours of each of the planets and their moons and the solar system ``fluff'' is given on the Planet Links page.

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last updated: September 15, 2011

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel