Observation methods

During the past nine years, astronomers have successfully used three methods to discover extrasolar planets.

They are:

In this section, we will look at each of these methods, discussing their strengths and weaknesses, as well as summarizing the results from each method.

It is a common misconception that planets simply orbit stars.  We often say that the Earth orbits the Sun, for example.  However, this turn out to be not quite true.  It is much more accurate to say that the Earth and Sun each orbit their common center-of-mass.  Consider the example in Figure 2, which shows a planet and its star connected by a solid rod. 

Figure 2.  Center of mass

The center of mass is the point along this hypothetical rod at where the two masses would balance.  As the two masses orbit the common center-of-mass, the planet travels in a relatively large circle, while the star travels in a very small circle.  It is this slight ìwobbleî that gives us two different tools to detect the orbiting planet.

Radial Velocities

If the orbital plane is aligned with an observerís line of sight, we should be able to detect the motion of the star around the center of mass.  As we can see in Figure 3, there are two observable components of this wobble.

Figure 3. Radial velocities

In order to measure the motion across our line of sight, astronomers attempt measure the starís astrometric displacement.  They can also measure changes in the starís Doppler shift to detect the motion along our line of sight.

Astrometric Displacement

If the star is moving back and forth across our line of sight as it orbits the center of mass, we should be able to measure this motion by carefully measuring the distances between that star and others near it in photographs.  As the star moves, the relative distances to the other field stars should also change.  This change is known as astrometric displacement.  An animation demonstrating this is found in Figure 4.

Figure 4.  Demonstration of Astrometric Displacement and Doppler Shift

Unfortunately, there is a major problem with this method.  The displacement caused by the starís wobble is very small, especially when seen from interstellar distances. It requires very high-resolution images over the period of any possible planetís orbit, and the ability to detect and measure slight changes in position over time.

While this method is perhaps the easiest to understand measurement of radial velocity, it turns out to be exceedingly difficult to accomplish.  So far, only two planets have been discovered using this method, both circling Lalande 21185 (Marcy, 2000) . 

Doppler Shift

A much more fruitful approach has be developed for measuring a stellar RV.  It is well known that the spectrum of any stellar object is altered if the object is moving toward or away from the observer, due to Doppler shifting.  If the object is approaching the observer, the spectrum will be shifted toward the blue end of the spectrum (shorter wavelengths).  If it is moving away, its spectrum will be shifted toward the red end (longer wavelengths) as shown in Figure 5.  The animation in Figure 4 illustrates the change in Doppler shift as the star moves toward and away from the observer.

Figure 5.  Doppler shifts

Unfortunately, the Doppler shift caused by the starís motion is very slight and is beyond the means of normal spectroscopy to detect.  In 1987, Marcy and Butler modified a technique developed by a Canadian team to increase the resolution of their spectroscope.  They placed a container of iodine gas into the light path of their spectrograph.  By doing so, they were able to superimpose the spectrum of iodine onto the stellar spectra they were collectingóin essence; they were adding a ruler of great precision directly onto their data.  Using this technique, they were able to detect stellar motions along their line of sight with a precision of 3 meters per second, which would be good enough to detect a Jupiter-sized mass around another planet (and almost good enough to detect a Saturn-sized mass) (Croswell, 1997) .    This method is best used to detect massive planets that orbit very close their stars.

Figure 6 illustrates the RV curve that was observed for 51 Pegasi (Korzennik & Contos, 1997) .

Figure 6.  RV curve of 51 Pegasi (Korzennik & Contos, 1997)

One of the major drawbacks to the RV detection methods is that they both require large telescopes and very high-resolution instruments.  The next method discussed requires neither of these.

Transits

As we discussed in the introduction, astronomers in the 17^th century looked for planets by watching for transits across the disk of the sun.  Over three centuries later, astronomers are again turning to transits in order to find new planets.  However, now they are looking for planets around distant suns. 

The most extreme example of a transit is a solar eclipse.  As the moon passes between the Earth and the Sun, a portion of the Sunís disk is blocked and the amount of light reaching the Earth is diminished.  But how does this apply to finding extrasolar planets?

Figure 7.  Transit Detection

If a planet is orbiting at star so that the orbital plane is exactly edge-on to our point of view, we should be able to detect a drop in luminosity as the planet transits the starís disk.  David Charbonneau, a graduate student at Harvard University, was analyzing the brightness of star HD 209458, when he detected a 1.8% drop in the starís brightness for an interval of approximately three hours (Doyle, Deeg, & Brown, 2000) . This star was believed to have a planet orbiting it, derived from RV studies, and Charbonneau was trying to establish that the star was photometrically stable, supporting the hypothesis that the RV variations observed were in fact due to an orbiting body and not an artifact of stellar variability (Charbonneau, Brown, Latham, & Mayor, 2000) .  It was realized that this dip in brightness occurred when the RV studies suggested that the planet would be ìin front ofî HD 209458.  They were seeing the starís brightness decrease as the planet transited its disk, blocking some of its light, as demonstrated in Figure 7.

Figure 8.  HST light curve of HD 209458 transit event (Brown, 2000)

The transit method has on serious disadvantage.  For a planet to transit the starís disk from our point of view, its orbital plane must be precisely aligned with our point of view. The probability that the Earth would transit across the Sun, as seen by a randomly placed observer, is approximately one-half of one percent.  Luckily, the RV results to date have shown that there are many large planets orbiting close to their stars.  These close-in orbits increase the odds of visible transit alignments ten-fold (Doyle et al., 2000) .

We have shown that these three techniques can be used successfully to detect extrasolar planets.  The rest of this section will discuss what these results tell us about the planets that they have found.

What do they tell us?

While perhaps the most important result of the planet searches is the detection of the planets themselves, the detection methods also provide valuable data about them.  Each methodology allows for certain physical parameters to be measured for each planet.  In order to derive the maximum amount of information about each planetary system, they should ideally be observed by all three methods.  Unfortunately, this is not always possibleófor example, Doppler measurement of RV can detect planets that are beneath the detection threshold of the astrometric displacement method.  Letís take a look at the parameters have been measured, as well as which methods were used.

Size of Orbit

Radial velocity measurements can be used to determine three important parameters about each extrasolar planet.  The first of these is the size of the planets orbit.  As we know from Keplerís Laws, as the orbital diameter increases, so does the period.  In this relationship, the square of the period is proportional to the cube of the orbital diameter. 

Since the RV measurements yields accurate information about a planetís orbital period, it is quite easy to then calculate the orbital diameter.  For example the observed period of the planet around 51 Pegasi is 4.2 days.  This equates to a orbit with a diameter of 0.05 astronomical units (AU) (Croswell, 1997) .

Minimum Mass of Planet

The second parameter that can be determined via RV measurements is the minimum mass of the planet.  The range of motion observed (how far the star wobbles) can be used to determine how massive the planet is, compared to the star.  The more massive a planet is, the more it will displace the starís orbit, since their common center of mass will be farther away from the starís center.

It is important to realize that the range of motion can only be used to determine the planetís minimum possible mass.  Since the RV measurements only indicate the velocity along one axis of the starís true motion in three spatial dimensions, this measurement only indicates the minimum mass required to displace the star the observed amount (Brown, 2000) .  In particular, the planetís orbital inclination to our line of sight is critical to this parameter.  If we observe a planet whose orbit is edge-on to our line of sight, it will result in a stronger Doppler signal than one whose orbit is face-on to us, as illustrated in Figure 9.  Ideally, we would correct for these inclination effects, by multiplying the observed mass by the sine of the orbital inclination (Brown, 2000) .

Figure 9.  Inclination effect on Doppler signature

Since the actual inclination of a planetís orbit cannot be determined via RV measurements, a standard correction factor is applied in order to derive a representative mass for each planet.  Most catalogs list the planet mass as 1.27 times the minimum mass.  Using the planet orbiting 51 Pegasi as an example once again, itís minimum mass is ~0.47 Jupiter masses (the common measurement unit for extrasolar planet mass).  Multiplying this by 1.27, we arrive at 0.6 Jupiter masses, which is the mass listed in most catalogs (Croswell, 1997) .

Shape of Planetís Orbit

The final planetary parameter that can be derived by the RV measurements is the shape of the planetís orbit, i.e., its orbital eccentricity.  An orbit that is perfectly circular has an eccentricity of 0.  The most elliptical orbit possible has an eccentricity of just less than 1.0, and a parabolic orbit has an eccentricity of 1.0.  But how do we determine the eccentricity of an extrasolar planetís orbit?

It turns out that the shape of the RV curve can be used to determine the orbital eccentricity.  If the RV curve follows a smooth sinusoidal curve, the planet is in a circular orbit, with an eccentricity near 0.  Take a look at the RV curve for 51 Pegasi, shown in Figure 6 above.  As you can see, the curve is smooth and sinusoidal.  The derived eccentricity for this planet is 0.0 (Croswell, 1997) .  On the other hand, take a look a the RV curve for the planet orbiting 16 Cygni B in Figure 10.

Figure 10.  RV curve for 16 Cygni B (Schneider, 2000)

The planet orbiting 16 Cygni B has an eccentricity of 0.67, giving it one of the most eccentric extrasolar planet orbits known (Croswell, 1997) .  As you can see, the curve is not sinusoidal in nature, but rather demonstrates a rapid velocity change of 104 meters per second over a relatively short time.  This radical change is caused by the planetís changing velocity as it travels through its elongated orbit.  When the planet is far from 16 Cygni B, it is traveling much more slowly than when it is nearóin accordance with Keplerís Laws.  The planet rapidly changing direction as it makes its closest approach to the star causes the radical velocity change.

Although these three parameters are all that can be derived from the RV measurements, perhaps we can learn something else from observing a planetís transit of its star.

Size of Planet Relative to Star

By measuring the decrease in brightness of a star as a planet transits its disk, astronomers can determine the planetís size relative to the starís. The amount of starlight blocked by the planet is proportional to the cross-sectional area of that planet.  Therefore, the photometric signal varies with the ratio of the square of the planetís radius to the square of the starís radius (Doyle et al., 2000) .  The 1.8% drop in brightness observed in HD 209458 equates to diameter of 1.3 times that of Jupiter, which marks the first time an extrasolar planetís diameter has been directly measured (Doyle et al., 2000) .

Radius of Orbit

The second parameter that can be calculated from transit measurements is the radius of the planetís orbit.  Once you have measured the period of the planetís orbit, as well as timed how long each transit event lasts, you can determine the diameter of its orbit.  In the case of the planet around HD 209458, the semimajor axis of its orbit has been determined to be 0.045 AU (Doyle et al., 2000) .

So far, we have discussed the methods by which extrasolar planets have been discovered, as well as what type of information can be obtained by these observations.  The next section will summarize the results so far in our search for extrasolar planets, as well as discussing what these results have meant to our understanding of planetary formation and evolution.