Extrasolar Planets

A complete, up to date listing of all discovered extrasolar planets is found at:

 Extrasolar Planets Catalog
Additional information, including pointers to other interesting sites is found at:
 The Extrasolar Planets Encyclopaedia
A history of the search for and discovery of extrasolar planets is found at:
 The Search for the Extrasolar Planets: A Brief History
Another very valuable site is Goeff Marcy's page
 The Search for Extrasolar Planets


The discovery of the existence of planets around other stars is a profound and important part of modern science. But what do we know and  how do we know it?   Has this field of science been well informed or guided mostly by  speculation?  Have our opinions about the existence of extrasolar planets been guided by good scientific ideas or by  our gut level instincts and philosophy, namely the Copernican Principle, that the Earth-Sun system is not special.

In many ways, the modern debate has been formed by the Copernican principle.  Carl Sagan, quantified the Copernican philosophy when he wrote (Shklovskii, I.S. and Sagan. C. Intelligent Life in the Universe . New York: Dell Publishing, 1966. 509p. Pg. 130):

With 10 to the 11th stars in our galaxy and 10 to the 9th other galaxies, there are at least 10 to the 20th stars in the universe. Most of them may be accompanied by solar systems. If there are 10 to the 20th solar systems in the universe, and the universe is 10 to the 10th years old -- and if, further, solar systems have formed roughly uniformly in time -- then one solar system is formed every 10 to the negative 10 yr = 3 x 10 to the negative 3 seconds. On the average, a million solar systems are formed in the universe each hour.
The counterpoint to this point of view is the Rare Earth hypothesis: planets like Earth and planetary systems like our own might be rare.  At the turn of the 21st century, we have reached the moment in our history of scientific exploration when we will be able to put the Copernican Principle to the test.

Let's start with exactly what we know.  From that, we can decide whether our current knowledge is valuable and important and assess what impact it has or will have on our understanding of planet formation and the regular existence of planets elsewhere in the universe. Then, we will work backwards and try to understand the history of discovery and the physical principles used to make these discoveries.

What do we know now? or
What's a nice planet like Jupiter doing in a place like this?

Let's start with a list of all the planets so far discovered.  These lists (list1 , list2) presents all the known extrasolar planets.


The most obvious patterns found in these data are that


From our current knowledge of extrasolar planets, we need to ask ourselves many questions, among them the following:

How do we know what we know?

How many planets have we "seen"? None.  As of early 2002, we have pictures or images or direct spectra of exactly zero planets around other stars.  The only claim for such a result has been thoroughly and resoundingly discredited.  No one has ever "seen" a planet around another star!  So how can we claim to know of the existence of nearly 80 extrasolar planets?

Gravity.
Actually, several planet detection techniques  (direct link to original document) have been proposed and tried for detecting extrasolar planets, from "pulsar timing" to "astrometry" to "transit photometry" to "doppler spectroscopy."  All of them have potential, but all the planets discovered thus far (except the "pulsar planets") have been found because of the gravitational tug of war between the parent star and the orbiting planet.
A Gravitational Tug of Ward: Center of Mass.
When we think about orbits, we normally think of a relatively low mass object orbiting a much higher mass object, whether this be the space station orbiting Earth, a moon orbiting a planet, or a planet orbiting a star.

Remember, one of Newton's laws says that the forces of attraction between two attracting bodies are equal and opposite:

F1 = F2

m1a1= m2a2

In one extreme case - a spacecraft orbiting a planet - the mass of the spacecraft is completely negligible in comparison to the planet.  Consider: the mass of Earth is nearly 6 x 1024 kg while the mass of the space station is a few hundred tons, or perhaps as much as 106 kg.

a1= (m2/m1) a2

aearth= (106 kg/ 6 x 1024kg ) aspacecraft

aearth= (1.7 x 10-19) aspacecraft

Thus the tug of the space station on Earth is a more than a billion billion times weaker than the tug of the Earth on the space station.  In a case like this, the Earth doesn't budge.

What about the other extreme - two stars of equal mass.  Can we speak of the first orbiting the second or the second orbiting the first? No. These two stars would co-orbit around the center of mass of the binary star system.  If the stars are truly equal in mass, the center of mass would be exactly halfway between the centers of the two stars.
 
 

astar 1= (mstar 2/mstar 1) astar 2

astar 1= astar 2

This leads us to the in between case.  Consider Jupiter. Jupiter's mass is one-thousandth that of the Sun. Thus, Jupiter's tug on the Sun is not negligible; it is one-tenth of one-percent of the strength of the Sun's tug on Jupiter.

asun= (mjupiter/msun) ajupiter
asun= 0.001 x  ajupiter






Given this situation, we can't think of Jupiter orbiting the Sun with the Sun sitting still; instead, me must think of both objects orbiting the center of mass of the system.  To understand the center of mass concept, think of two children on a see-saw.  One child is bigger, one is smaller.  What do they do to keep the see-saw balanced?  They easily figure out the solution: the larger child has to scoot in toward the fulcrum. Why?

Consider two objects with masses m1 and m2.  Measure all distances from the position of the first object, with the separation between the two objects equal to d.  Then the center of mass is located at the distance xcm from the first object:

xcm = m2d/(m1 + m2)


xcm = d/1001
or
d = 1001 xcm

This means that we can think in terms of the 5.2 AU distance from Jupiter to the Sun as divided into 1001 equal steps. The center of mass is at the first step.
At 5.2 AU (7.8 x 108 km) from the Sun, Jupiter is about 1100 solar radii from the Sun (Rsun = 7 x 105 km).  Since (1100 solar radii / 1001)  = 1.1 solar radii, the center of mass of the Jupiter-Sun system is just outside the surface of the Sun.  This means that the Sun actually swings around an imaginary point in space located just above it's surface!

Recall that the law of gravity  is proportional to the masses of the two attracting objects and inversely proportional to the square of the distances between the two objects.  Therefore, if Jupiter were closer to the Sun, Jupiter and the Sun would tug harder on each other.  Similarly, if Jupiter were more massive, Jupiter and the Sun would tug harder on each other.  If it is easiest to detect the planets that tug hardest on their parent stars, it would make sense that

Small planets, even ones in close orbits, and all planets at large distances would be hard to detect. This clearly explains the distribution of masses of planets found - the ones at large distances (1-5 AU) are among the most massive discovered, the smallest ones (Saturn sized) are among those with the very smallest orbits, and no planets smaller than Saturn or as far away as Jupiter is from the Sun have yet been identified.
The Doppler Shift
Light as a wave.  Light is energy that is transmitted through space through what we call radiation, where radiation is simply another word for light.  Physicists, over the last few centuries, have found that the physical universe is describable through mathematics (e.g., gravity) and that movement can either be described as a particle or a wave.  A thrown baseball is a moving particle (well, lots of particles bound together all moving in the same direction to the same place).  The upward and downward motions of water molecules in a pond caused by the passage of a swimming duck is a moving wave.  Light sometimes behaves like a particle and other times like a wave.  This is called the particle-wave duality of light.  In the context of measuring light from distant stars (in order to detect planets), we will treat light according to it's wavelike properties.

The Electromagnetic spectrum.  Light, commonly, is thought of as what our eyes see.  We know, however, that cats have "night vision."  What does this mean?  Our eyes are detectors.  However, they are fairly insensitive detectors compared to photographic film (one can take a long exposure with film to see things too faint for our eye) and they saturate easily (too much light overwhelms us and we become momentarily or permanently blinded).  Eyes have a reasonable response time but we can't use our eyes to detect the winner of an Olympic swimming race in which two swimmers are separated by only thousandths of a second.  In addition to poor sensitivity to amounts of light that are too bright or too faint or to changes in light that are occur too quickly, our eyes also do not see all colors.  The "rainbow" of colors, from violet to red, represent only those to which our eyes are sensitive, the visible light spectrum.  Beyond the violet is the ultraviolet.  Beyond the red is the infrared.  Beyond the ultraviolet is the extreme ultraviolet, then the x-rays, then the gamma-rays.  In the other direction, beyond the infrared is the far-infrared, then the submillimeter, then the millimeter and microwave and radio regimes of the electromagnetic spectrum.

We can quantify the properties of these different forms of light.  Ultraviolet light has more energy and a shorter wavelength than infrared light.  Radio waves have less energy and longer wavelengths than infrared.  For purposes of this discussion, all we are interested in are the wave properties of light; specifically, we note that yellow light occurs in between red and blue, such that red light has a longer wavelength yellow, and blue light a shorter wavelength than yellow.

Motion affects waves.

Imagine a bird, with a moutful of pebbles, flies to the middle of a pond. Hovering still over the center of the pond, the bird drops the pebbles one at a time, one pebble every 10 seconds.  Each dropped pebble generates an expanding circular wave in the pond. Imagine that each wave expands at 2 foot per second so that after 10 seconds, the first wave has a radius of 20 feet. As the pebbles are dropped, a series of concentric waves are generated, with spacings of 20 feet.

Now the bird begins to fly directly toward you (on the shore) at a speed of 1 foot per second. Ten seconds after dropping the first pebble, the bird drops a second pebble.  Since the wave moved outwards 20 feet in 10 seconds but the bird flew 10 feet in 10 seconds, the center of the second wave is not concentric with the first. It begins 10 feet from one edge, 30 feet from the other edge.  As the bird continues to fly and drop pebbles, a series of waves are generated. The waves that crest onto the shoreline from which you are watching are separated by 10 feet; at the speed at which the waves propagate, the waves crest onto your shoreline once every 5 seconds, 12 waves per minute. On the opposite shoreline, however, the waves that lap onto the shore are separated by 30 feet and arrive once every 15 seconds, or 4 waves per minute.

This compression and expansion of the waves because of the motion of the object generating the waves (the bird) is called the Doppler shift.  We are more familiar with this effect with sound waves generated by ambulance and fire sirens and train whistles.

If the wave source is moving toward the observer, the waves are closer together so the distance between successive wavecrests (the wavelength) is shorter.  For light, this would be equivalent to making yellow light into blue light (a blueshift).  If the waves are further apart so the distance between successive wavecrests is greater.  For light, this would be equivalent to making yellow light into red light (a redshift).

An on-line illustration of this effect is found at  Doppler Shift.

The Doppler Shift due to a stellar wobble
Assuming two stars, or a star and a large planet, are co-orbiting a center of mass, the star is alternately moving toward us, then sideways to our line of sight, then away from us, and then sideways to our line of sight. Thus, the light from the star changes from blueshifted to normal to redshifted to normal, with the cycle repeating with every orbit of the star.  The planet's motion is similar; however, the light from the planet is so faint that we can only see the light from the star.

There is one other factor we must be aware of: the inclination of the orbit to our line of sight.
If the star's orbit is in the "plane of the sky," then it's motion is never toward or away from us. With no Doppler shift, we would never know that this star was moving.  In this case, the orbit is inclined by 0 degrees.  If the orbit is such that the star comes directly  toward and away from us, we observe the maximum possible motion and we consider the orbit to be inclined by 90 degrees.

An on-line demonstration of the Doppler Wobble can be found at Doppler Wobble.

The Mathematics behind the method
Observe the orbital period to derive the size of the orbit. In practice, an astronomer observes the light from a star and watches certain spectral features, i.e. the fingerprints of the atmospheric contents of the star, move back and forth from redshifted to blueshifted.  By measuring the time period for a complete cycle of motion and measuring the amplitude (the amount of color or wavelength change) of the motion, we can derive the mass of the planet.

The easiest thing to measure is the orbital period P.  We know that P is related to the size of the orbit, to the semi-major axis through Kepler's third law, but we need to use the complete version of Kepler's third law, as derived by Newton:

P2(G[Mstar + Mplanet]/ 4 pi2) = a3

Since we know the mass of the planet will be much smaller than the mass of the star, we can very reasonably approximate this equation as
 
 

P2(GMstar/ 4 pi2) = a3

We have measured P.

G and pi are constants.

And we can determine the mass of the star, Mstar, from other astrophysical information.

Thus, this straightforward measurement of P gives us the size of the orbit, a.

a = P2/3(GMstar/ 4 pi2)1/3

Assume the planet's orbit is a circle to determine the planet's orbital velocity. (we can also assume the orbit is an ellipse, but the math is more complicated).  For any object moving in a circle, we know the equation for the circular velocity:

Vplanet= [GMstar / a]0.5

Since we have determined a, having measured P, and since we know G and Mstar, we have effectively determined the planet's velocity by measuring P!

Observe the orbital velocity of the star.  This is done by measuring the size of the blueshift and redshift in the star's spectrum.  The smallest such velocities that have been measured are about 10 meters per second, and most measured velocities by the planet hunters are in the range of 20 to 100 m/sec.  As a comparison, 3 m/sec would compare to a 33 second speed in the 100 meter dash.  Most children can run this fast!  This is truly a phenomenal measurement.  But remember, we actually observe the quantity called K, which is the velocity of the star (Vstar) multiplied by the factor sin i, where i is the inclination of the orbit. If the orbit is 'in the plane of the sky,' then i = 0; if the orbit is along our line of sight,  i = 90.

If i = 0, then K = Vstar sin i = 0 and if i = 90, K = Vstar sin i = Vstar.  Ultimately, since we measure K but want to know Vstar, we will use:

Vstar = K / sin i

Use the property of momentum conservation.  This property says that the mass of the planet (Mplanet) times the velocity of the planet is equal to the mass of the star times the velocity of the star (Vstar):

MplanetVplanet = MstarVstar

We have already determined Vplanet (from the measured P) and measured Vstar.  Thus, knowing Mstar, we can solve this equation for Mplanet to find the answer we are seeking:

Mplanet  = MstarVstar / Vplanet

Mplanet  = Mstar(K/sin i)/ Vplanet

Mplanet  = (MstarK/ Vplanet) / sin i

Mplanetsin i = MstarK / Vplanet

Ultimately, we only know the mass of the planet to within the unknown factor related to the tilt of the orbit of the system.  The actual mass of the planet is the observed quantity divided by sin i; and clearly, since the maximum value of sin i = 1, the planet's actual mass must be larger than the measured quantity.  Thus, if Mplanet sin i = 1.0 MJupiter, then the actual mass of the planet is larger than 1.0 MJupiter, and might be much larger if i is fairly small.  If i = 10, then this planet would have a mass of 5.8 MJupiter and if i = 4, then this object would have a mass of 14 MJupiter and we wouldn't even consider it a planet!  However, statistically, it is more likely that the inclination is between 5 and 90 than between 0 and 4, so this object is most likely a bona fide planet.

Sample calculation (for 51 Peg)

Observed: P = 4.233 days

Observed: K = 56.83 m s-1

1. calculate semi-major axis of planet's orbit:

P2(GMstar / 4 pi2) = a3

a3 = (4.233 days x 86,400 s/day)2 (6.67 x 10-11 N m2 kg-2 x 1.99 x 1030 kg / [4 x 3.14 x 3.14])

a3 = 4.49 x 1029 m3

a3 = 449. x 1027 m3

a = 7.66 x 109 m

or, since 1 AU = 1.5 x 1011 m

a = 0.051 AU

2. calculate velocity of planet's orbit, assuming circular orbit:

Vplanet= [GMstar / a]0.5

Vplanet= [6.67 x 10-11 N m2 kg-2 x 1.99 x 1030 kg / 7.66 x 109 m]0.5

Vplanet= [(6.67 x 1.99 / 7.66) x 10-11+30-9 m2 s-2]0.5

Vplanet= [1.73 x 1010 m2 s-2]0.5

Vplanet= 1.32 x 105 m s-1

3. calculate mass of planet:

Mplanetsin i = MstarK / Vplanet

Mplanetsin i = 1.99 x 1030 kg x 56.83 m s-1 / 1.32 x 105 m s-1

Mplanetsin i = 8.57 x 1026 kg

Mplanetsin i = 8.57 x 1026 kg x (1 Mjupiter / 1.90 x 1027 kg)

Mplanetsin i = 0.45 Mjupiter




4. calculate plausible mass range for planet:

if i = 10 degrees, then sin i = 0.174

thus: Mplanet = (0.45/0.174) Mjupiter = 2.59 Mjupiter

if i = 75 degrees, then sin i = 0.966

thus: Mplanet = (0.45/0.966) Mjupiter = 0.47 Mjupiter

What planets can we detect?
1. Can we detect a Jupiter?  Let's take an example in our own solar system.  Jupiter orbits the sun with a period of 11.8 years; thus, we would have to make observations for at least six years to measure a single period.  Having done so, we find

Vplanet= 13.1 km/s = 1.31 x 104 m s-1

We  also know that the ratio of Jupiter's mass to that of the Sun is 0.001.  Now, from the momentum conservation equation, we solve for Vstar and find that

Vstar =  (Mplanet / Mstar) Vplanet

Vstar = 0.001 x 13,100 m/s = 13.1 m/s.

Could we detect a Jupiter? Can we measure a stellar doppler velocity of only 13.1 m/s?  Yes, provided the orbital plane is inclined at least about 45 degrees (sin 45 = 0.707) so that the observable K has a value of at least

K = Vstar sin i

K = (13.1 m/s) x 0.707

K = 9.3 m/s

and provided we observe carefully for at least 6 years and have absolutely perfect data.  More likely, we would need decades of data to convincingly detect a Jupiter at 5.2 AU.  Since the planet searches have only been capable of this level of accuracy since 1995, such data does not exist, but we're on the margin!

2. Could we detect an Earth?  If we repeat the process in our first example, noting that Earth's orbital velocity is 29.8 km/sec (29,800 m/sec), and that the ratio of Earth's mass to that of the Sun is 0.000003, we find from momentum conservation that

Vstar = 0.000003 x 29,800 m/s = 0.09 m/s.

Could we detect an Earth?  Not a prayer!  This velocity ( 9 cm/s!) is so far from our detection threshold of about 10 m/sec that we would not bother to try the experiment.

For an Earth-Sun system, what would be required to get the stellar velocity up from 0.09 to 9 m/sec?  We know from the above equation that Vstar will increase directly with Vplanet.  So, we need to increase Vplanet by a factor of 100.  How would we do this?

We know from Kepler's third law that P2 = a3.  We also know that the velocity (of anything) is the distance traveled divided by the travel time, so for an orbiting planet, Vplanet = 2 pi a / P.  Thus,

(2 pi a / Vplanet)2 = a3

(Vplanet)2 = (2 pi)2a2 / a3

(Vplanet)2 = 4 pi2 / a

Thus, if we need to increase Earth's orbital speed by a factor of 100 we would have to decrease the semi-major axis by 1002= 10,000.  This would require the Earth to be 10,000 times closer to the center of the Sun, at 0.0001 AU.  Where would this place the Earth?

Since 1 AU = 150 x 106 km,  one ten-thousandth of 1 AU would be 1 AU  / 10,000 = 150 x 106 km / 104 = 15,000 km.

Note that the radius of the Sun is 700,000 km.  Thus, this would place Earth far beneath the surface of the Sun, actually in the Sun's core!  Unless the Sun turned into a neutron star, this situation would not be possible.  And if the Sun were a neutron star, the situation would be mighty uncomfortable.  Therefore, with today's technology, we could never detect an Earthlike planet with the Doppler Wobble technique.

You could easily calculate the velocity the Earth would have if it were located very close to the Sun, say at 0.05 AU. From that, you could calculate the velocity of the Sun.  Your answer would tell you just how much improvement you will need in measurement accuracy in order to detect Earths.

3. Could we detect a Jupiter at 1 AU? At 1 AU, the planet's velocity is 29,800 m/sec (remember, the orbital velocity does not depend on the mass of the planet) and for a Jupiter, the mass ratio is 0.001; thus, Vstar = 0.001 x 29,800 m/sec = 29.8 m/sec.  This is a non-trivial measurement and likely would require several years of data to establish the veracity of the measurement, but it is quite doable.  And this is why in recent years, Jupiter and slightly sub-Jupiter sized planets have been detected at 1-4 AU.

We clearly can see from this that it is easier to detect more massive  than less massive planets, that it is easier to detect planets in small orbits than in large orbits, and it is impossible to detect an Earthlike planet at all.
 

A Brief History of the Detection of Extrasolar Planets: A lesson in humility
On 25 October, 1995, the Swiss team of Michael Mayor and Didier Queloz announced the discovery of the first extrasolar planet around a normal star.  The star, known as 51 Pegasus, or Peg 51, is very similar to the Sun and is at a distance from Earth of 13.7 parsecs (42 light years).  The planet orbits Peg 51 in only 4.23 days!  The mass is about one-half that of Jupiter.  The temperature at this distance from Peg 51 is 1300 K (1900 F).  This announcement absolutely shocked the professional astronomy community.  Why?

A Jupiter-like planet in a 4.23 day orbit? Insane.  Impossible.  We know how planets form (or so we think or thought) and we know that Jupiters form out beyond the snow line.  Consequently, despite the fact that several research groups has been monitoring the light from Peg 51 for several years, those groups has been expecting to find an object in a 10 or 20 year orbit at a very low velocity.  They had emphasized collecting data, to be examined more fully when many years of data had been collected, and improving the accuracy of their detectors.  If they had known that they should have been looking for planets in 4 day orbits, they would have found it years before!  But since theory says "close in giant planets don't exist," astronomers were not looking for such objects in their data.

The American group of planet hunters, led by Geoff Marcy and Paul Butler, was and remains the premier such group in the world. They had the most sensitive equipment, having improved their accuracy from 10 m/sec in 1988 to 3 m/sec in 1994.  No other groups could do better than 15-20 m/sec. Marcy and Butler had been in the business the longest (since 1987) and had been systematically studying a group of 107 stars - including Peg 51! This group has discovered far more planets than any other group, yet they did not discover the first known extrasolar planet, despite having the data in hand.  Mayor and Queloz had begun their work much later, monitoring 140 stars with lower sensitivity than Marcy and Butler.  So why didn't Marcy and Butler discover the first planet?  Their vision was clouded by the theory that motivated their search.  And the theory, apparently, was wrong.

By January of 1996, Marcy and Butler, having worked night and day for two months, announced a second planet, around 70 Virginis,  and a third, around 47 Ursa Majoris.  By April, they had another, around 55 Rho Cancri.  Suddenly, planet hunting had become easy; anybody can play, and now their are dozens of research groups around the world hunting for planets.

So why were our expectations so completely wrong?  Do we throw out the theory? Or is the theory incomplete and ultimately fixable?

Theorists have convinced themselves that the formation process to make giant planets can't operate inside the snow line - large masses of solids are needed to create an accretionary core and this can't happen close to the star.  Therefore, they conclude that the planets like that around Peg 51 must have formed out at 5 AU and beyond.

So how did they end up at 0.05 AU?  They spiraled in.  The basic theory we outlined assumes that accretion takes place in a frictionless environment. But if the gas disk still exists, as it must if the planetary core is to sweep up the H and He gas once the growing planet reaches critical size, then the growing planet must continually push its way through the disk.  Bit by bit, the planet loses orbital energy to friction and spirals ever closer to the star.

When does the inward spiral stop?  When the retarding force, friction with the gas in the disk, goes to zero, i.e., when there is no more disk.  This occurs naturally for a young star because newborn stars have very strong winds, analogous to the solar wind that helps create the ion tails of comets, and these winds act like vacuum cleaners in reverse: they blow all the gas in the disk away.  Thus, the planets stop spiralling in when the central stars blow away all the residual gas in the disk and truncate the planet building process. For some planets, this occurred when they were at 2 AU, for others at 1 AU and 0.5 and 0.05 AU.  Others may have spiralled all the way in and been absorbed into the atmosphere of their stars.
[note the high metallicities of the stars with planets].

What are the implications of these results?  About 6% of the stars studied thus far have Jovian planets close in.  Perhaps many of the others have giant planets at "normal" distances.  If so, we will know in 20 years.  And if so, we can feel comfortable knowing that our planetary system is normal, that in this instance the Copernican Principle holds.  On the other hand, perhaps these 6% of the stars are the only ones around which the planets stopped their inward spirals before being swallowed.  Perhaps none of these stars have any planets.  On these 94% or so stars, we have to withhold comment for now.

But what of the 6% with planets?  One of the most dramatic discoveries in astronomy in the 20th century is this one of finding planets around other stars.  But these planets are a serious problem for us.  Assuming they did form at 5-10 AU and spiralled inwards.  What happened to the small rocky planets, the Earths, that were forming at 0.5 and 1 and 2 AU?  They were swallowed up by the giant planets.  These stars have no Earths.

Thus, one very real possibility that comes from our discovery of extrasolar giant planets is that our theory is correct for the formation of giant planets and that it is now, post 1995,  a much improved version.  Furthermore, it is possible that our planetary system is quite normal.  However, it is also quite possible to imagine, based on our current knowledge of extrasolar planets, that our solar system is quite unusual.

Stay tuned ...