Exoplanets

Beginning

The first exoplanet discovered orbiting a normal star was announced by Swiss astronomers Didier Queloz and Michel Mayer in December, 1995. They had actually detected the planet weeks earlier, but waited for confirmation by other astronomers before telling the world. Radial velocity data indicated that the star 51 Pegasi, a Sun-like star in the constellation Pegasus, was partnered by an unseen planetary companion.

The evidence for this planet consisted of a slight motion of the star toward and then away from Earth in a cyclical pattern. The motion was similar to that seen in spectroscopic binary stars, except that in this case there was only one set of stellar lines present. What’s more, the small motions suggested that the companion was much smaller than the star. Smaller, in fact, than the planet Jupiter. As has become typical for naming extrasolar planets, this discovery was designated 51 Peg b.

We should note that there had been extra-solar planets confirmed earlier, in 1992, but these were orbiting the pulsar PSR1257+12, not a normal star. Their detection was possible because the orbital motion of the system caused slight shifts in the period of the pulsar, a method that is roughly analogous to, but distinct from, the method used to detect the planet orbiting 51 Peg. Several other pulsars with planets are known, but because the nature of these systems is distinct from those around normal stars, we will leave off discussing them further.

After the discovery of 51 Peg b was announced, additional detections followed rapidly. This was possible because the planets had been hiding in plane sight in datasets already in possession of astronomers. The first to announce were Geoff Marcy and Paul Butler, two astronomers from San Francisco State University in California. In looking over their own radial velocity measurements of numerous stars, they found evidence for several planets that had gone unnoticed earlier.

They, like other astronomers, had not been expecting to see very massive planets orbiting very close to their stars. As a result, earlier searches had not been optimized for detection of such systems. But their data, like that of Queloz and Mayer, belied this expectation. Over the years that followed, Marcy and Butler went on to discover many more extrasolar planets, as did other astronomers. The kinds of planets they discovered were more varied than the first few.

Fast-forward two decades and there are thousands of planets known around many different kinds of stars. These include Sun-like stars, but also stars both larger and smaller. And unlike the first planets found, some of the more recent discoveries are comparable in size to Earth. But before we get into all that, let’s have a closer look at how planets around other stars are found in the first place.

Radial Velocity

We generally think of planets orbiting stars, and in our minds we likely think of the planet moving while the star remains stationary. This is not an accurate picture of what is happening. Instead, both planet and star orbit their common center of mass. This center of mass is a weighted average of their positions.

In trying to grasp this idea, it is probably easier, at least at first, to imagine that the two objects have the same mass. In addition, it simplifies understanding if both move in circular orbits. Neither of these simplifications will make our conclusions less general, they only server to make the understanding come more easily.

So imagine a binary star system. The center of mass (COM for short) for the system is at a point halfway between the two stars. That is probably easy enough to picture. As the stars orbit the COM, they follow identical circular paths, each directly opposite the other. Each of them takes the same amount of time to orbit (what would happen if they didn’t?), so each moves at the same speed around its orbit. That is about a simple as a system can be.

Now imagine that the two stars have different masses. They will still orbit their common COM, but now it will not be halfway between them. If one star is two times more massive than the other star, the COM will be closer to the more massive star. In fact, the COM will be one third the distance from the center of the massive star to the center of the less massive star. If the more massive star is nine times the mass of its companion, then the COM will lie ten percent of the distance from the massive star to the lower mass star, and so on.

Since both stars orbit around the COM, the star that is closer to it will have a smaller orbit to cover than the more distant star. Both still require the same amount of time, one orbital period, to complete their orbit. As a result, the more massive star will move more slowly than the less massive star because it is traveling a smaller distance.

The situation is illustrated in the diagram below. The stars are taken to have unequal masses, and for simplicity we will assume they move on circular orbits. This assumption, while not necessary, avoids some complications but still conveys the essential points of the method.

The observer is taken to be off the screen to the left at a great distance. The two stars orbit around each other in the plane of the screen. Their orbits are shown as dashed lines. At the moment shown, the massive star is moving toward the observer and the less massive one is moving away. Their speeds are represented by the blue and orange arrows, respectively, and the length of each arrow indicates speed.

Half a period after the moment depicted above, the two stars will have reversed their orientation. The blue star will be above the orange one in the diagram, and it will be moving toward the observer instead of away, but with the same speed. This situation is shown in the figure below. This cycle will repeat indefinitely.

The observer can use the Doppler effect on stellar absorption lines to determine the motion of the stars toward and away from her. If velocities toward her a taken to be negative, and velocities away from her are positive, then the velocities can be plotted vs. time. The stars’ velocities follow a sine wave. Both have the same period, but they will be shifted by exactly half a period from one another. When one star has a positive velocity (it is moving away) the other star will have a negative velocity, indicating motion toward the observer. Furthermore, the amplitude of the velocity curve of one star (the more massive one) will be smaller than the amplitude of the other star’s velocity curve. Possible examples of the curves the observer might plot are shown below.

For the example curves, the mass ratios are 1:1, 2:1, 10:1 and 100:1. These ratios are shown in the upper right of each plot. When the stars have the same mass, their velocities are the same. But if they have unequal masses, then their velocities are also unequal.

Since the more massive star moves more slowly than the lower mass star, the ratio of the amplitude of their radial velocity curves is the inverse of the ratio of their masses. The velocity plots clearly show this inverse relationship. Star 1, the more massive of the two, is plotted in red. As its mass increases in relation to the mass of Star 2, its maximum velocity decreases in proportion to the mass ratio. Of course, this is all due to the fact that its orbital radius (its distance from the COM) is smaller, and so its orbital path is smaller, too.

When we are discussing planets orbiting stars, the mass ratios are much greater than the ratios in these examples. The Sun is about 300,000 times more massive than Earth. So the COM of the Earth-Sun system is deep inside the Sun. The amplitude of the speed of the Sun around that point is very small, only a few centimeters per second. For comparison, the orbital speed of two stars in a binary system can often be tens of kilometers per second, or more. For comparison, the orbital speed of Earth around the Sun is 30 km / sec. Clearly, trying to detect a planet like Earth orbiting a star like the Sun is quite difficult under this method, because the speed of the star is so small.

The radial velocity method is much more sensitive to detecting large planets, like Jupiter, for example. It is for this reason that the first exoplanets found were large planets, bigger than Jupiter, in fact. But unlike Jupiter, these bodies orbited very close to their stars, with orbital radii much smaller than Earth’s. Their large masses meant that their host stars had orbital speeds large enough to be seen, and their small orbital radii – and more important, small orbital periods – meant that the velocity curves could easily be seen on relatively short time periods; many, many orbits can be seen in only a few years of data.

The figure below (from Marcy and Butler, Astrophysical Journal, 464, L147-L151, 1996) shows the velocity curve for the planetary companion to the star 47 Virginis. Many orbital periods (P~117 days) fit within the 8 year series of observations plotted here. The planet has a mass 6.6 times that of Jupiter.

The proximity of giant planets like Jupiter orbiting very close to their host stars was a huge surprise to astronomers at the time. It caused them to rethink their ideas about planet formation and the evolution of planetary systems. In retrospect, we might have expected this to happen. Previous to the discovery of exoplanets, we had just a single example of what a planetary system might look like – the one containing us! As is often the case, it is difficult to derive universal truths about the world from a single example. Thus, as soon as we started to detect planets in other systems we were made dramatically aware of how parochial our thinking had been.

Transits

Radial velocities are not the only technique that can reveal the presence of planets orbiting distant stars. A different method had been suggested years before any planets were actually found. But because it seemed unlikely to yield positive results, it was never put into practice. That all changed once planets began to – it seemed – fall from the heavens almost like rain.

It had been known since late in the nineteenth century that some stars orbit in such a way that one periodically passes in front of the other. These eclipsing binary systems are quite rare because they require precise alignment of the stellar orbits with the direction to Earth.

reveal themselves most obviously by periodic dips in brightness of what appears as a single star from Earth. The most well-known of these eclipsing systems is the star Algol in the constellation Perseus. It has been known to vary in brightness for thousands of years, though its true nature has been known for only just over a century.

When a planet passes in front of its star we refer to the passage as a transit, not an eclipse. Transits of Mercury and Venus occur occasionally when they cross in front of the Sun. A series of images of Mercury transiting the Sun in 2019 are shown in the image at right: the apparent curve in its path is caused by the rotation of the Sun in the image plane due to the type of telescope mount used. The path of Mercury is actually a straight line across the Sun.

These transits are quite rare – the next one for Venus, for example, will not happen for almost two hundred years. However, when they do happen, the planetary disc blocks a small amount of light from the Sun, and this decrease in solar brightness can be measured.

William Borucki, an astronomer at the NASA Ames Research Center in Mountain View, California, had proposed to search for planets around other stars. The method he proposed relied upon the transit phenomenon. Borucki reasoned that transits for planets around other stars could be detected by a minute dimming of the starlight. This dimming would give away the presence of a planet that was itself too faint to see directly.

After many failed attempts, William Borucki’s proposal to build a dedicated planetary transit mission was finally accepted by NASA. It became the Kepler mission, launched on March 7, 2009. Kepler spent the next decade staring at a small patch of sky in the constellation Cygnus. Kepler was trying to catch tiny telltale dips in brightness in more than 150,000 stars. These dips would reveal the presence of unseen planets around those stars. During its lifetime Kepler saw more than 2600 of them.

Unlike the radial velocity planet search method, the transit method is not especially sensitive to planets that are particularly close to their host star. However, it does have greater sensitivity to large planets. This is because large planets have larger areas, and thus they cover more of the star during the transit. That means the decrease in brightness will be greater, making the transit easier to detect.

Some numbers will make this effect more concrete. We can imagine ourselves in a nearby planetary system, looking at the solar system and trying to detect planets around the Sun. We will take Earth and Jupiter as representative examples of a “small” and “large” planet, respectively. The relevant numbers are shown in the table.

From the table, we see that Jupiter would be much easier to detect as it transited the Sun. It would cause a 1% decrease in brightness as seen from some distant viewer. Small, but not compared to Earth. Earth would diminish the light of the Sun by a meager 0.008%, a tiny amount. The ability to detect these changes depends on the quality of the data, of course. This in turn depends on a number of different things, but primarily upon the amount of light from the star that can be collected by the telescope. In any event, it is clear that large planets are easier to find using transits than small planets.

To date, the number of exoplanets found orbiting normal stars exceeds 4000 (as of the date of this article, February 2020), and these are found in more than 3000 different stellar systems. Kepler, which is no longer operating, was responsible for the majority of these systems.

However, other ground and space-based telescopes have also contributed. One interesting example is a project called MEarth. It uses a collection of small robotic telescopes in Arizona to conduct a transit survey of red dwarf (spectral type M) stars, looking for Earth-like companions. Hence the name… M-Earth, or MEarth. So far, MEarth has not found another Earth orbiting a nearby M-dwarf star, but it has found a number of rocky planets as well as some gas giant planets, and it is still searching.

From space, the search for new exoplanets is being carried out by the Transiting Exoplanet Survey Satellite, or TESS. Like Kepler, and as one can infer from its name, TESS employs the transit method to detect planets. However, unlike Kepler, TESS is looking over 85% of the entire sky, and it is directing its attention primarily to stars that are much closer to Earth than the stars Kepler viewed. In this respect it is somewhat similar to the MEarth project, but it has a much larger scope, monitoring more than 200,000 stars for transits.

Launched in July, 2018, TESS is expected to discover many thousands of new planets over its two year primary mission. And because TESS’s program stars are much closer than Kepler’s stars, following up TESS detections with ground-based observations will be much easier. As a result, astronomers will be able to characterize the properties of the new-found planets more precisely than was the case with many Kepler exoplanets.

The figures below show TESS light curves for two planets orbiting the star HD 21749. At left is a confirmed exoplanet with properties that lie between a super Earth and gas dwarf. On the right is a candidate Earth-analogue slightly smaller than Venus. If confirmed, this object would be the first Earth-sized exoplanet discovered by TESS.

The census of planets is ongoing. The information obtained to date has given scientists a rudimentary understanding of the various kinds of stellar systems that exist in the space relatively near to the Sun. Based on our current crude understanding, we know that there are basically three categories of bodies detected: the super earths, the gas dwarfs and the gas giants. Super earths are rocky planets that are a few times more massive than Earth, the gas dwarf planets are similar to Neptune and Uranus. They are bigger than the rocky worlds, but smaller than the gas giants, which span upward in mass to objects that start to become more like stars, the brown dwarfs. Further divisions are also possible, but these categories give the general trend; basically, there are planets found at size scales that range from near-terrestrial to sub-stellar.

At the low-mass end we know there should be planets like our own terrestrial planets, with masses like Earth and Venus, and lower down to minor planets and asteroids. Our current detection methods do not allow us to find these sorts of bodies, though TESS should be able to find Earth/Venus analogues if they are present in its survey data.

Coronagraph

One of the primary goals astronomers have set for the coming decades is to capture direct images of planets around nearby stars. Because these planets are much fainter than their host stars, imaging missions generally employ a sort of mask that blocks the starlight. These socalled coronagraphs use a combination of disks and optics to occlude the direct starlight, allowing the telescope to see the faint reflected light from nearby orbiting planets that lie outside the masked area. The method is similar to the one used by space-based solar telescopes, which use a disk to block the bright photosphere of the Sun, allowing them to see the much fainter solar corona. The accompanying image illustrates the method, though in this instance the detection turned out to be a false positive.

The star Fomalhaut was known to have a disk of material orbiting it, and the sharp inner edge of the disk suggested the presence of a planet. Images taken using the Hubble Space Telescope and ground-based telescopes between 2004 and 2008 seemed to confirm the presence of the planet. The HST image below, taken using the coronagraph method in 2012, shows clear evidence of the planet; the inset gives its position for several epochs between 2004 and 2010, and its position at the time of this image is marked by the arrow.

Unfortunately, even apparently solid evidence can sometimes evaporate into empty space. Subsequent imaging of the system over the next two years showed that the planet had disappeared. The figure below, at left, shows HST images from 2014. On the right is a model simulation. What has been taken for a planet was apparently a dust cloud, the result of a violent collision between two proto-planetary bodies. Over time the cloud expanded, becoming brighter for a while, and then simply dissipating. The event offers a cautionary tale common when working at the frontiers of knowledge: sometimes early data can be misleading, and new findings require repeated verification before they can be fully confirmed.

Despite the mistaken case of Fomalhaut-b, the direct imaging method has advantages over the transit and radial velocity methods. First, it is not affected by the orientation of the system. Both the wobble and transit methods require a particular alignment that allows their planets and stars to line up with Earth. Only with this alignment will transits occur, and only with nearalignment will the radial velocity shifts be large enough to detect. Direct imaging can detect planets no matter what the inclination of the system is. However, it is not without its own set of limitations.

First, it is difficult to survey many systems at once. The need to block the light from the star makes multi-star monitoring effectively impossible. Second, the method is more sensitive to larger planets that are farther from their star. Planets that are too small are more difficult to see because they are faint. Those that are too close to the star will be blocked by the obscuring coronagraph. But these limitations are complementary to those of the other methods. Furthermore, larger telescopes in space and on the ground will be able to detect fainter planets than current telescopes can. By harnessing the capabilities of larger telescopes, like the James Image Credit: NASA, ESA, and A. Gáspár and G. Rieke (University of Arizona) Webb Space Telescope, direct imaging promises to greatly expand our understanding of exoplanets.

Microlensing

An additional detection technique utilizes the gravitational effect of planets on background stars. Whenever a planet passes in front of a distant star (not the star it orbits) it will cause a At left is an image of the solar corona taken using a disk to block the bright solar surface, allowing the faint corona to be observed. A similar technique has been proposed to block the light of stars, allowing the faint planets orbiting them to be seen. Courtesy HAO/SMM C/P project team & The planet Fomalhaut b is revealed in an image taken using the Hubble Space Telescope. To obtain this image an occulting disk (coronagraph) was used to block the starlight. Credit: NASA, ESA, and P. Kalas (University of California, Berkeley and SETI Institute) temporary increase in that star’s brightness. This gravitational lensing effect has already been used to good effect to search for dark stellar-mass objects in our galaxy. It can also be used to search for planet-sized bodies, and it can reveal many of them at a time. All that is required is that many stars be monitored and checked for the tell-tale brightening that would indicate a passing planet. The image below shows an example light curve from a gravitational micro-lens that is part of a survey from the 1990s called MACHOs (for MAssive Compact Halo Objects). These objects were typically much larger than planets, but the method could be used to reveal the presence of planetary bodies, too.

Astrometry

The tug of a planet causes its star to move slightly, and this can be detected through radial velocity measurements. This is a method we have already discussed. However, if we have very precise measurements of the positions of stars, then we can see their position on the sky change slightly as they engage in the gravitational dance with their family of planets. This method of detection is called the astrometry method. In principle it can reveal the presence of planets that are too faint to see. It can also reveal the presence of planets around many stars at once. That is a big advantage. We only have to be able to see the tiny shifts in the position of the stars being surveyed, and that is the crux of the matter.

A star like the Sun would not be detectable with this method because the point it orbits around (the solar system center of mass) is actually inside the star. The method is more sensitive to stars with large orbital motion, and that means stars with large planets that are orbiting at great distances. For systems like that, the center of mass can be outside the star (see discussion above about the radial velocity detection method), and that means the star will undergo larger motions.

However, even given its advantages, the method is quite difficult in practice. The truth of this statement is underlined by the fact that, though this is the exoplanet method that has been in use the longest – since the 1940s – it has yet to find any confirmed exoplanets. Several false alarms have been reported, but none has stood up to additional study and analysis.

This could change with the current and oncoming observational instruments. For example, the European survey satellite Gaia has the required positional sensitivity. It was designed to measure parallaxes and proper motions of stars. Astronomers expect that as it continues to collect data it will reveal the minuscule stellar motions caused by orbiting planets as well.

Summary

The past 25 years has seen our knowledge of planets orbiting other stars increase enormously. At first we had no knowledge of extra-solar planets, but once the first planets were discovered, new ones came in a near avalanche. To date we have found myriad systems, and not a one of them looks anything much like our own. In particular, we have not found an Earth twin, though we have discovered some close relatives, second cousins, perhaps. Nor have we yet found any planets on which we think life is present. Finding a close analogue to Earth is one of the primary goals for the future of exoplanet research. But we have only scratched the surface. The 4000 or so exoplanets cataloged so far are almost certainly the merest sliver of all the planets that exist. Our explorations are promising, and the coming years will certainly bring us new discoveries and exciting insights into ourselves and our place in the vastness of the cosmos.