Light also consists of waves—electromagnetic waves—that are shorter than sound waves. So, light is subject to the same Doppler effect as sound, and we can measure the relative speeds of stars, galaxies, and more. This is of huge importance to astronomy, where we have no way to approach these distant objects and measure their motions.
To use the Doppler effect, scientists employ a telescope, a prism, and a camera to record the light spectrum of a star. Then they look for a marker in the spectrum. The marker will be shifted to longer wavelengths (toward the red light) if the star in question is moving away from you—the faster the star is moving, the more the marker is shifted. If the star is approaching you, the reverse is true. The majority of the visible light coming from a star is just like what we get from the hot filament of an incandescent lightbulb, and when dispersed into a spectrum it looks like a rainbow. But when a scientist looks at it with a prism, for example, she sees lots of markers. In the spectra of most stars these markers are narrow dark lines which indicate that light at specific wavelengths is missing. These lines—spectrum absorption lines—are caused by atoms and ions near the star’s surface. When light passes through a gas made of atoms, for example, some of it gets absorbed by the atoms; we see this every day with clouds. However, our eyes are not equipped to see that the light is also absorbed in numerous specific wavelengths, or colors, of that light. These absorption lines and their corresponding wavelengths are due to the electrons that orbit atoms (and ions and molecules). Electrons have numerous, strictly defined states of energy—different orbits, if you will—and that is where light gets lost. Because these energy states are strictly defined, so are the absorption lines and their wavelengths. Therefore each atom of every known element—from hydrogen to the heaviest known metals—has an unmistakable fingerprint consisting of thousands of absorption lines all over the spectrum.
These spectrum absorption lines are the markers we use to measure the Doppler effect in stars. In doing so, we can discern very small changes in the speeds of stars, including the wobble that an orbiting planet would cause. What is more, the Doppler effect measured this way will allow us to measure the actual speed of the star on its own orbit around the center of mass. That orbital speed, together with the orbital period—which is the same for star and planet as they revolve around their center of mass—will allow us to measure their masses. We know how to estimate the mass of a star by measuring its spectrum; these absorption lines carry a lot of information. Therefore, we can determine the mass of the planet. There is one small hitch: we can’t measure the angle at which the orbit is inclined toward us, as the Doppler effect gives us relative motion only. Consequently some uncertainty about the mass of the planet remains. To remove that uncertainty, we need to turn to other methods of planet discovery and study—for example, the transit method (more on that in the next chapter).
The third practical way to detect the wobble is by timing. If there is a strictly periodic signal we can measure and time with a precise clock, the wobble due to a planet will appear as a cyclic variation in the period of that signal. What could such a periodic signal be? Well, it could come from a pulsar—a neutron star spinning very quickly and emitting radio pulses—or from two stars orbiting very close to each other and eclipsing periodically (every few hours or days). That is how in 1992 the planets orbiting the pulsar PSR 1257+12 were discovered by the radio astronomers A. Wolszczan and D. Frail.6 This was a remarkable discovery, but it did not gather the attention lavished on the 1995 discovery of 51 Peg b for two reasons. First, the pulsar planets were exotic—both as planets and as a planetary system.7 Second, it turns out that pulsar planets are extremely rare. With only a couple of systems known, there is not much to study and little to help us understand their origin.
The timing technique can be used also when one planet is pushed and pulled around by a second planet. For example, if we have a system with a hot Jupiter and keep observing the hot Jupiter as it regularly orbits its star (e.g., by marking events like eclipses or transits; see the next chapter), we can catch variations in its regular orbit caused by an unseen second planet.8 In some cases, the second planet is easier to catch by such timing variations, than by seeing the corresponding wobble of the star. This technique has become one of the big early science successes of the Kepler planet search mission. For example, five transiting planets in the Kepler-11 system could be confirmed and their masses derived by using transit timing variations alone.9
There is another method of planet discovery that also exploits the favorable star-to-planet mass ratio—gravitational lensing, an effect predicted by, and famous for its help in confirming, Einstein’s general theory of relativity. The pioneering theoretical work of the late Princeton astrophysicist Bohdan Paczynski showed the practical uses of Einstein’s prediction and led to the creation of several international projects to monitor stars for gravitational lensing.10 For this, a source of light is needed, usually another star, behind the star being investigated. As we look at it, the light from the background star will be bent by the gravity of the intervening star. If the intervening star has an attendant planet, this will alter the lensing effect in a noticeable way.11 In 2005 J. P. Beaulieu and his team discovered a planet with about five to six times the mass of Earth, which we call a super-Earth.12 The planet bears the impossibly complex name OGLE-2005-BLG-390Lb, and it orbits a small star at a distance at least two to three times greater than the distance at which our planet orbits the Sun.13
That is probably as much as we will ever learn about planet OGLE-2005-BLG-390Lb, because the gravitational lensing method allows just a single glimpse, a sort of a snapshot. By its nature the observation cannot be repeated.14 However, the value of the gravitational lensing method to extrasolar planets is in the statistics. In essence, the method is a general scanning approach that allows the discovery of super-Jupiters and super-Earths on an equal footing. So, even though very few planets have been discovered with this method so far, it was possible to notice a statistical trend that smaller planets are at least as common as giant planets, and probably are even more numerous.15
The first decade of extrasolar planets saw the maturation of several methods of discovery. Some of them complement each other and also help us study the planets we discover. This is crucial in our quest to find out if the Solar System, planet Earth, and—ultimately—Earth life, are unique, rare, or common in the Universe. Once we have achieved that, we will have completed the Copernican revolution. The last of these, which exploits the size ratio of planets and stars, and is known as the transiting method, seems to be the easiest. After all, the inequality between star and planet is the least daunting, with a factor 10 to 100 difference in size. And indeed, in our quest, transiting plays a special role. But, as often happens, there is a catch.
CHAPTER FOUR
CHASING TRANSITS
It is about 5:30 in the morning and I am racing down an empty avenue by the Charles River in Cambridge, Massachusetts. Crossing the bridge into Harvard Square, I keep an anxious eye on the eastern horizon, where the rising sun is competing with clouds for a piece of the sky. My destination—the Harvard University Science Center, just north of Harvard Yard—is a bizarre scene. By the entrance, the Harvard marching band plays an obscure piece over and over again, as hundreds of people try to get to the roof. Everyone is here to see a sight not seen by humankind for 122 years. It is June 8, 2004, and a transit of Venus is under way.1
The transit—during which the little black disk of Venus passes in front of the big glowing disk of the Sun—is one of those spectacles in the sky that lets you “see” the inner Solar System as if it were a mobile. Transits of Venus are spectacular but rare: only every other generation can witness them. This generation is lucky: the transits of Venus now happen in pairs and the next one will occur on June 6, 2012.2 Mark your calendar!
Today the transit of Venus is of little value to the research astronomer, but two transit cycles ago, back in the year 1769, the scientific rewards of witne
ssing such a transit were great, and international efforts to observe it were remarkable. According to William Sheehan and John Westfall, these efforts represented an eighteenth-century equivalent of the twentieth-century race to the Moon.3 At stake was a unique opportunity to use the passage of Venus in front of the Sun to measure precisely the distance between Earth and the Sun, and thus distances across the Solar System. This was important for more than pure science, as the British Transit Committee duly noted in a memo to King George III in 1767; it was also crucial for navigation. That was enough to convince the king to support a mission. On May 25, 1768, Captain James Cook was appointed to do the job, and his famous trip to the South Pacific ensued.
A transit is in essence an eclipse of the Sun by either Mercury or Venus, although the event is not nearly as dramatic as when the Moon eclipses the Sun. Planetary transits do little to diminish the amount of sunlight we see—just a small fraction of a percent, too tiny for us to notice—but they do form a black dot against the Sun as they pass between us and the star. Historically, the term “transit” was reserved for Mercury and Venus, but these days it finds a much wider application in the hunt for planets around other stars. As with Mercury or Venus, the planet will obscure only 1 percent or less of its surface (see Figure 4.1).
FIGURE 4.1. schematic illustration of a transiting planetary system. The transiting planet is shown in three different positions on its orbit. When in transit, the dark night side of the planet is facing us, but we can glimpse its atmosphere in the stellar light that passes through it. When the planet is on the side (left side), it shows phases to us, just as our Moon does. Half an orbit after a transit, the planet will pass behind its star—known as occultation or eclipse.
As it passes across the disk of its parent star, a planet will dim the star’s light by a fraction equal to its projected area compared to the star’s shining projected area. The area of a circle depends on its radius, r, squared. Therefore the star’s light will dim by a fraction (rp/rs)2, where rp and rs are the respective radii of the planet and star. For a planet the size of Jupiter and a star the size of the Sun, this dimming effect would be roughly 1 percent, which is easily detectable even with amateur equipment.4 Earth, however, some 109 times smaller than the Sun, will dim just 1/(109)2 = 0.008 percent of the Sun’s light when transiting. That is challenging to see, but not impossible.
The transiting method for planet discovery works because the dimming due to a planet transit can be measured by using the brightness of the star, known as photometry (measuring photons). Photometry is different from spectroscopy, the measurement of the color of light; for one thing, you need a camera to do photometry, and most often that camera is attached to a smaller telescope. The main difficulty is that a transit requires the planet’s orbit to be almost exactly edge-on as we look at the star, which is very unlikely, as planetary systems in our Galaxy are inclined randomly in all possible directions (Figure 4.2).5 Therefore, from our own vantage point, the probability that we’ll see a transiting planet among the ones that are out there will be equal to the ratio of the stellar radius to the size of the planet’s orbit.6 This is generally less than 1 percent.
FIGURE 4.2. Planetary systems are inclined at random angles. When we observe them from Earth, few of them will be aligned so that we can see a planet transit. The closer the orbit of the planet to its star, the higher the probability that we can see a transit.
With such a low probability, tens of thousands of stars must be monitored patiently to detect periodic dimming due to planet transits in a handful. In this only the gravitational lensing method rivals the transiting method. Perfecting the transiting method and making it work in practice took a lot of work, but the effort was worthwhile because of the method’s added benefits: when we can measure both transits and Doppler wobble, we can deduce the planet’s radius and mass, and hence mean density. But that was just the bonus! The transiting method turned out to be the best path to discover really small planets, whether super-Earths or Earth analogs.
By 1999, more than twenty-five extrasolar planets had been discovered by the Doppler shift method, most of them hot Jupiters. Because hot Jupiters orbit so close to their stars, the probability that they will transit increases. Figure 4.2 shows how for the same planetary system an inner planet might transit, while another planet on a larger orbit would not. For such close-in planets there is a 5 to 10 percent chance that they will be seen in transit. In other words, for the more than twenty hot Jupiters discovered by the Doppler shift method, we should expect at least one of them to transit. The relatively high probability of finding a transiting planet makes the hunt for them a little more competitive. As planet-hunting teams discover new planets, they may keep their existence a secret until they check to see if the planet is transiting.
The lucky hot Jupiter turned out to be HD 209458b, an otherwise ordinary system of a planet orbiting a Sun-like star every 3.5 days, about 150 light-years from Earth. The planet was discovered by the Doppler shift method in the summer of 1999 by a collaboration of the Geneva Observatory and planet hunters from the Harvard-Smithsonian Center for Astrophysics. By September 1999 they handed their data to a Harvard graduate student, David Charbonneau, who was spending time in Boulder, Colorado, with the small photometric telescope setup built by Tim Brown of the National Center for Atmospheric Research. David and Tim detected a transit, and so did the team of Geoff Marcy and Paul Butler, who had been racing to do the same. They had handed their own Doppler shift data to Gregory Henry of Tennessee State University, who did the photometric measurements with an automated telescope in Arizona.7
This success was a watershed for two reasons: it confirmed beyond doubt the planetary nature of the extrasolar planets that had been found with the indirect Doppler shift method since 1995, and it boosted the effort to use transits as a method of discovery.
In the early 2000s the transiting method seemed to have a clear recipe for planet discovery: (1) do photometry of tens of thousands of stars simultaneously and (2) wait until you find a star that “blinks” in a regular fashion. If the star’s light dims for a couple of hours by about 1 percent once every few days, then you have discovered a transiting hot Jupiter similar to HD 209458b. Two things seemed crucial: being able to measure a very large number of stars simultaneously and being able to do it with better than 1 percent precision. The former meant using either a small telescope that can see a lot of sky or a regular large telescope but measuring only faint stars. The latter meant mostly improving the software and the details of the photometric measurements.
Many astronomers rushed to discover the first planet with the transiting method. The expectations were high and the predictions were very optimistic.8 Measuring the light dimming due to the transit was thought to be sufficient to confirm the planet. Consequently even teams with very limited resources could compete with Michel Mayor’s team in Geneva and Geoff Marcy’s team in California in discovering new extrasolar planets. The recipe was easy; reality turned out to be much more difficult. Three years passed after the discovery of HD 209458b with no new transiting planets.
As it turns out, the problem is that a few stars do “blink” regularly, but for the wrong reasons. For example, sometimes two stars in a close orbit would eclipse each other and a third star nearby would dilute the effect of that deep eclipse and cause it to appear shallow—say a 1–2 percent deep, as if due to a much smaller planet-size body. All three stars would appear as a single dot of light even in our best telescopes. Or a very small star would orbit a star slightly larger than our Sun and the eclipses would also be about 2 percent deep and difficult to distinguish from a planet transit. The list of different scenarios continues. The realization gradually dawned that these false positives were quite pervasive. David Latham, the pioneer planet hunter at the Harvard-Smithsonian Center for Astrophysics, was helping a couple of teams confirm possible transiting candidates with quick-look small telescope spectroscopy. Instead of planets, he kept uncovering false positives among th
e photometric transit candidates.
The problem came to a head in 2002. The OGLE team that we met earlier had equipped its telescope in Chile with a new large camera the year before. Before continuing with their primary experiment of detecting stellar gravitational lensing in our Galaxy, team members turned their telescope toward several patches of southern sky rich in stars and observed them nonstop every night for about four weeks, hoping to catch planetary transits. After a few months of dealing with the gigabytes of data that they gathered, the OGLE team found about sixty “blinking” stars. The “blinks” looked like planet transits, as the stars dimmed by just 1 to 3 percent; the trick was to make sure which, if any, were not false positives.
The photometric data obtained by the OGLE telescope alone was not sufficient to identify the kind of stars that showed the regular dimming. More information, such as stellar spectroscopy data or even distances from Earth, was not available because these stars were all faint and distant and previously unknown. The OGLE team had published its entire list of transiting candidates on the Internet (before publication in a journal) and invited the world community of astronomers and planet hunters to sort it out.9 A true race began.
The Life of Super-Earths Page 3