On the Track of Alien Planets – The Transit Method (∼23% of All Exoplanet Primary Discoveries)

Abstract

Transits, eclipses and occultations are all essentially the same phenomenon. They are events when one astronomical object passes in front of another. During an eclipse the two objects are of comparable angular sizes – like the Moon eclipsing the Sun (Figure 6.1). In an occultation the distant object is angularly small compared with the nearer one – like the Moon occulting a star, whilst for a transit the situation is reversed – like one of Jupiter’s satellites being silhouetted against the disk of the planet.

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Transits, eclipses and occultations are all essentially the same ­phenomenon. They are events when one astronomical object passes in front of another. During an eclipse the two objects are of comparable angular sizes – like the Moon eclipsing the Sun ­(Figure 6.1). In an occultation the distant object is angularly small compared with the nearer one – like the Moon occulting a star, whilst for a transit the situation is reversed – like one of Jupiter’s satellites being silhouetted against the disk of the planet.

Figure 6.1

Eclipses, transits and occultations.

Transits have had a long history of being of interest to astronomers. To begin with, that interest lay in measuring the distance between the Earth and the Sun (the Astronomical Unit). When Mercury or Venus transits the Sun, observations of the transit from two well-separated spots on the Earth combined with simple trigonometry theoretically enables the Sun’s distance to be found.

Transits of Venus gave the best hope of measuring the ­astronomical unit since Venus is much closer to the Earth than Mercury when it transits the Sun, but they only occur four times every 243 years – at intervals of 8, 121.5, 8 and 105.5 years. The last transit occurred on 8th June 2004 (Figures 3.2 and 6.2), and the next will be on 6th June 2012. In the eighteenth century epic voyages were made to set up observing sites as far as possible from European observatories so that as long a base line as was practicable was obtained. Captain Cook’s first round-the-world voyage, for example, enabled observations of the 1769 transit to be made from Tahiti. Unfortunately, the values obtained for the astronomical unit from Cook’s and other expeditions were of low accuracy because the high contrast between the black silhouette of Venus and the bright photosphere of the Sun rendered their observations of poor quality.

Eighteenth and nineteenth century astronomers were interested in measuring the position of Venus with respect to the Sun in order to determine the distance between the Earth and the Sun. However as can be seen in Figure 6.2, during the transit, the planet obscures a small part of the radiation coming to us from the Sun – typically the brightness of the light we get from the Sun decreases by about 0.1% during a transit – so had they been interested, those earlier astronomers could also have tried to measure that change in luminosity. Success in that measurement would have produced a graph showing a slight dip in the Sun’s brightness as Venus moved across its disk (Figure 6.3).

Figure 6.2

The transit of Venus across the Sun on the 8th June 2004. Images obtained at several stages throughout the transit have been ­combined to show the motion of the planet across the face of the Sun. (Copyright © C. R. Kitchin 2004).

Figure 6.3

Schematic graph of the variations in the solar brightness during a transit of Venus.

Modern astronomers now undertake exactly the same type of observations, not of Venus and the Sun, but of distant stars as their exoplanets transit in front of those stars’ disks. The transit of Venus, however, as seen from the Earth, exaggerates the change in brightness because we are so close to the planet. A distant ET astronomer looking at a transit of Venus would see a brightness change in the Sun of only 0.008%. That alien astronomer though would see transits every 225 days – the long and irregular intervals between Venusian transits as seen from the Earth arises from the two planets’ orbital motions and the angle (3.4°) between their orbits.

With equipment similar to that which we have today, the alien astronomer would be pushed to detect a transit of Venus because the change in the Sun’s brightness is so small. He / she / it though would be much more likely to pick up a transit by Jupiter or Saturn. The change in the Sun’s brightness would then be by 1% and 0.8% respectively and even Uranian or Neptunian transits would cause solar brightness changes 16 times that of Venus.

Observing one transit is insufficient to count as a discovery of an exoplanet – many other processes can cause similar changes to a star’s brightness. A variation in a star’s brightness that looks as though it might have been due to an exoplanetary transit, but which is due to some other process is called a false positive. Predominating amongst the causes of false positives are eclipsing binary stars, especially where the eclipse is a grazing one or where the eclipsing binary is so closely aligned with a foreground star that the two cannot be seen separately, star spots and random variations in the stars’ brightnesses.

A single brief diminution in a star’s brightness that has the characteristics of a transit, such as a flat-bottomed minimum, results in the star being labeled as an exoplanetary candidate. If transits alone can be observed then confirmation that an exoplanet has been detected requires the detection of a minimum of three transits (four or five transits would be much better), separated by the same time intervals (i.e. the exoplanet’s orbital period). Thus an alien astronomer would need to observe the Sun for a minimum of 24 years (twice Jupiter’s orbital period) in order to detect the presence of Jupiter with some certainty. Since it was only in 1999 that the first exoplanet was detected by the transit method, we have over another decade of observations to make before we can hope to find exoplanets in Jupiter-like orbits this way.

Clearly, though, if a Jupiter-sized planet were in a close orbit to its star, the orbital period would be shorter and the discovery could be made that much more quickly. Thus the first exoplanet transit to be observed was that of HD 209458 b (discovered via the radial velocity method) in 1999 and it has an orbital period of just 3.5 days. HD 209458 b is also around 40% larger than Jupiter so that the star’s brightness decreases by 1.5% (a dimming by 0.016^m on the normal stellar magnitude scale) during a transit. The planet is just 0.047 AU away from its star giving it a cloud top temperature in excess of 1,000°C. The heating effect of the star has also inflated the planet’s atmosphere considerably so that despite being significantly larger than Jupiter its mass is smaller – just 69% that of Jupiter.

In practice the initial observations of transiting exoplanet candidates are often confirmed by separate radial velocity measurements. In any case radial velocity measurements are usually necessary in order to determine all the exoplanet’s parameters although the depth of the transit can be used to indicate the size of the exoplanet (Appendix IV) – something that is generally unknown for exoplanets discovered by other methods.

The radial velocity changes of the Sun arising from the Earth’s orbital motion are just 100 mm/s, while the current state-of-the-art accuracy in measuring Doppler shifts spectroscopically is still around ten times poorer than that. Until the precision of radial velocity determinations improves by considerably – which is likely to take a decade or more – confirming Earth-sized ­exoplanets in Earth-type orbits requires a different approach. The transit ­timing variation method is one such possible approach although it can only be applied to multi-exoplanet systems. In multi-planet ­systems the planets’ gravities pull on each other so that the ­planets are slightly speeded-up or slowed-down at times compared with their average orbital velocities. This results in the transits occurring very slightly sooner or later than expected. The transit ­timing variations can then be computer modeled to confirm both the reality of the exoplanets and to give accurate estimates of their masses, orbital periods and orbital sizes. (This is essentially the same method that Urbain Le Verrier and John Couch Adams used in 1846 to predict the position of Neptune in the sky from the changes its gravitational pull produced in the motion of Uranus). The transit timing method has so far been used to confirm the exoplanets in the Kepler-9 (three exoplanets) and Kepler-11 (six exoplanets) systems although the planets involved in both cases are considerably more massive than the Earth and a lot closer to their host stars than is the Earth to the Sun.

HD 209458 b, along with TrES-1, has been observed in eclipse (this should, more properly, be called an occultation but is generally labelled as an eclipse in the literature) as well as in transit. In 2004 NASA’s Spitzer infrared space telescope was able to detect the decrease in total radiation from the system by about 0.25% at 24 μm as the planet passed behind its star. At these long infrared wavelengths the planet itself is radiating and the star is relatively dim so that the contrast between them is less overwhelming than that at visual wavelengths.

Like the Doppler approach to exoplanet detection, the transit method is biased towards finding hot Jupiters. The first exoplanets discovered via transits – OGLE-TR-56-b and OGLE-TR-10-b in 2002 – illustrate this well with masses of 0.63 and 1.3 Jupiter masses and orbital periods of 3.1 and 1.2 days respectively. That bias in the case of transiting exoplanets is exacerbated because transits by planets close to their stars are visible over a greater range of angles than those of more distant planets (Figure 6.4). If we take a Jupiter-sized exoplanet and a solar-sized host star, then 4% of such systems will be correctly oriented for us to see transits if the planet and star’s separation is 0.1 AU, but only 0.08% if they are as far apart as Jupiter and the Sun (5.2 AU). We are thus more likely to be in the right position to see close exoplanetary transits than those with wider separations.

Figure 6.4

Transits for the exoplanet closer to its host star are visible from a wider range of angles than is the case for the more distant exoplanet.

Observing the transit of an exoplanet is much simpler than determining a Doppler shift and some surprisingly small telescopes – down to 0.1-m – are employed in the task. Measuring brightness also requires equipment that is simple when compared with a sophisticated spectrograph. Not surprisingly therefore, exoplanet transit observation is an area wherein amateur astronomers can and do make a real contribution to research. The problem with transit observation is that in order to pick up a transit in a reasonable amount of time, very large numbers of stars have to be monitored at frequent intervals. Taking the case discussed above of a planet in a 0.1 AU orbit, then 4% or so of such systems will be oriented so that we can see a transit. The transit, however, only lasts for a short while – around 3 h or 4 h every 10 days or so. Thus even if stars could be selected in some way so that they all had exoplanets in 0.1 AU orbits, 1,500 would need to be observed in order to catch one in transit. In reality 10,000 to a 100,000 or more stars need to have their brightnesses measured at intervals of an hour or two over a period of weeks or months in order to succeed in a transit search. Thus the equipment used for transit searches differs from that for simpler photometric tasks mainly by being able to observe many stars simultaneously.

Detection of an exoplanet via its transits gives the orbital period of the planet (from the interval between successive transits), the size of the planet (from the depth of the dip in the star’s brightness and the size of the star) and the size of the orbit (from Kepler’s third law of planetary motion – Appendix IV). The planet’s mass is not determined from the transit information though. Exoplanets discovered via transits are therefore also observed spectroscopically in order to measure their host stars’ Doppler shifts. This then fills in the missing information on the exoplanet’s mass.

Even with just a single transit, some estimate of the orbital period may be made, though with large uncertainties. It is necessary to assume that the exoplanet passes across the centre of the star’s disk during the transit, that the orbit is circular and that the star’s radius and mass can be estimated. The duration of the transit then suggests a value for the orbital period (Appendix IV).

Since the planetary radius is not measured for planets with only radial velocity data (only 19% of exoplanets have known radii), we have significantly more information regarding those exoplanets that have been observed both via transits and Doppler shifts (whichever method led to their discovery). Furthermore, not only is the planetary radius known, but the mass that is determined is an actual value, not a minimum. This is because, in order for us to see a transit at all, we know that the exoplanet’s orbit must be inclined at very close to 90° to the plane of the sky.

If the host star can be observed spectroscopically during a transit, then it may be possible to measure the angle between the rotation of the star (i.e. its equatorial plane) and the orbital plane of the planet’s orbit. With rotating stars, some parts of the star’s surface are approaching us. The spectrum lines from those parts of the star are Doppler shifted slightly to shorter wavelengths. Other parts of the star’s surface will be moving away from us and the spectrum lines from those parts of the star are shifted to slightly longer wavelengths. When we look at the star’s spectrum as a whole these ­individual Doppler shifts cause the spectrum lines to be slightly wider than they would be if the star were not rotating. At the start of a transit, the planet obscures a small portion of the approaching limb of the star, thus reducing the intensity on the short wavelength edges of the observed spectrum lines. The lines therefore appear to move slightly to longer wavelengths (i.e. a red-shift). At the end of the transit, the planet obscures a small part of the star’s receding limb, and the spectrum lines appear to move to shorter wavelengths (a blue-shift). This change in the wavelengths of the star’s spectrum lines during a transit of its exoplanet is called the Rossiter-McLaughlin effect and careful computer modeling of the changes gives the angle between the equator and orbital plane. For HD 189733 b, for example, the angle is just 0.85° – as might be expected if star and planet formed from a single rotating nebula (Chap. 13) – for comparison the angle between the Earth’s orbit and the Sun’s equator is 7.25°.

One highly successful exoplanetary transit hunter with 36 exoplanets on its score sheet (30% of all those discovered from exoplanet transits) is SuperWASP (Super Wide Angle Search for Planets). SuperWASP (a development from a similar but simpler instrument called WASP) comprises two separate instruments. One of these is sited with the Isaac Newton group of telescopes on La Palma in the Canary Islands to cover the northern half of the sky and the other at the South African Astrophysical Observatory in Sutherland to cover the southern half of the sky. Both instruments have eight cameras, each of which images about 61 square degrees. The total sky coverage in a single pointing is thus about 500 square degrees – about 15,000 times larger than the area of sky covered conventional telescopes. Up to a million stars can be imaged in each set of exposures (depending upon the star density in the area of the sky being covered) – and exposures are taken every minute throughout the night. Given clear weather therefore some 100 Gbytes of data are obtained every 24 h covering stars down to about 15th magnitude (a 15th magnitude star is about the faintest star that can be seen by eye from a good observing site using a 0.5-m telescope).

SuperWASP’s ‘telescopes’ have apertures of just 0.11 m. They are in fact more-or-less off the shelf telephoto lenses ­(Cannon™ 200 mm f1.8 lenses) that feed CCD detectors. The cameras are mounted together onto a single mount (Figure 6.5) and the whole instrument operates automatically. The data is also ­processed ­automatically, firstly to correct for known problems such as variations in the sensitivity of the pixels and to reduce background noise. The stars are then identified from catalogues and their brightnesses determined. After several months of data have been accumulated the light curves for each star are examined for dips in the brightness that could be due to an exoplanetary transit. Finally stars that have had probable transits detected are observed spectroscopically and the exoplanet discovery (if that is what it is) ­confirmed by the Doppler shifts of the host star.

Figure 6.5

The SuperWASP North instrument. (Reproduced by kind permission of the SuperWASP project).

The first two SuperWASP exoplanet discoveries, both hot Jupiters, were reported in September 2006 with the confirming spectroscopic observations being made by SOPHIE. WASP-1b in Andromeda is a 0.89 Jupiter mass planet that is 35% larger than Jupiter and which orbits its slightly-larger-than-the-Sun host star at a distance of 0.038 AU every 2.5 days. WASP-2b orbits a star in Delphinus that is slightly cooler, less massive and smaller than the Sun. The exoplanet has a mass of 0.91 Jupiter masses, a radius almost identical to that of Jupiter and an orbital period of 2.15 days.

The 17th SuperWASP exoplanet – WASP-17b, discovered in August 2009 – was a surprise in several respects. It was the first exoplanet to be found whose orbital motion was in the opposite sense to the rotation of its host star. Such retrograde motion is quite unusual but not unknown – within the solar system for example, the well-known Halley’s comet has a retrograde orbit. The second surprise came when the exoplanet’s size and mass were determined. Its diameter is about 1.7 times that of Jupiter – making it the largest known exoplanet at the time of its ­discovery – and its mass about 0.5 Jupiter masses. The resulting average density is thus around tenth of that of Jupiter (or about 2% of the Earth’s density and about the same density as that ubiquitous lightweight packaging, expanded polystyrene foam). WASP-17b orbits a star somewhat hotter than the Sun every 3.7 days at a distance of 0.05 AU on average. However its orbit is quite elliptical so that the planet’s actual distance from the star varies from around 6.5 to 8.5 million kilometres. The changing distance for the planet from its star results in huge tidal stresses inside the planet which heat up its interior. This internal heating combined with the energy coming from the star is sufficient to have led to the enormous bloating of the planet so leading to its extraordinarily low density.

WASP-12 b, discovered in 2008, is in a 0.023 AU orbit around its solar-type host star. This is sufficiently close that material is lost from the planet to the star at a rate of about one Jupiter mass every ten million years. Since the planet’s mass is only 1.4 Jupiter masses it seems likely that it will be reduced to its metallic/rocky core in a relatively short time. Spitzer observations have recently shown that WASP-12 b’s atmosphere is dominated by ­carbon ­compounds, but whether or not this is related to the mass loss is still unclear.

Four searches that are similar to SuperWASP and with ­successful exoplanet discoveries to their credit are HATNet ­(Hungarian Automated Telecope Network), TrES (Trans-atlantic Exoplanet Survey), the XO project and the Alsubai project. HATNet uses six 0.11-m wide-angle robotic telescopes mainly based on Mauna Kea, Hawaii and at the Smithsonian Astrophysical Observatory in Arizona. Collaboration with a similar instrument based at the Wise observatory in the Negev desert in Israel enhances the sky coverage. Since its first discovery in 2006, HATNet has found 26 exoplanets, mostly hot Jupiters, although HAT-P-11b, discovered in 2009 and with a mass of 0.081 Jupiter masses is only about twice the size of Uranus or Neptune. TrES uses three 0.1-m Schmidt telescopes based at Mount Palomar, the Lowell Observatory in Arizona and the Canary islands. Its four exoplanet discoveries to date are again all hot Jupiters. The XO Project uses two commercial f1.8, 200 mm telephoto lenses on a single mounting and is sited at the summit of Haleakala on Maui, Hawaii. Amateur astronomers as well as professionals are involved in its search. Since 2006, the project has discovered five hot Jupiter exoplanets. The Alsubai project uses a 0.1 m and four 0.035 m cameras and is based in New Mexico. It has recently discovered its first exoplanet, Qatar-1 b, a hot Jupiter orbiting 3.5 million kilometres out from a cool star in Draco.

MEarth (pronounced ‘mirth’) is a similar system to SuperWASP but using larger telescopes. It comprises eight 0.4-m independently-mounted robotic telescopes housed at the Whipple observatory on Mount Hopkins, Arizona. The project monitors 2,000 small cool stars (red dwarfs) individually for transits. In 2009 a super-Earth was found by the project orbiting a star 40 light years away in Ophiuchus. The discovery was confirmed through radial velocity measurements by HARPS. The star, GJ 1214, is only 0.3% as bright as the Sun and its exoplanet, GJ 1214 b, is about two-and-a-half times the size of the Earth with a mass of six Earth masses (0.018 Jupiter masses). It is the second smallest exoplanet currently known (after CoRoT-7 b – amongst those that have their radii measured). Although the planet is only two million kilometres out from its star, that star is so cool and dim, that the planet is amongst the coolest found so far with a surface temperature of about 200°C. In late 2010 Jacob Bean et al. were able to analyze the atmosphere of GJ 1214 b using VLT observations of the planet obtained during a transit. The near infrared spectrum of the atmosphere turned out to be featureless, ruling out hydrogen as a primary constituent of the atmosphere. The researchers suggest that the atmosphere either has a thick high level cloud layer that masks any hydrogen that may be present or that it contains a high proportion of water vapour (steam).

Yet another robotic planet hunter has recently achieved first light. This is the 0.6-m telescope at La Silla of the TRAPPIST (Transiting Planets and Planetesimals small telescope) project, but it has yet to make any discoveries.

The OGLE (Optical Gravitational Lensing Experiment) project has been operating since 1992 and is led by Prof. Andrzej Udalski of Warsaw University and by the late Prof. Bohdan Paczyński of Princeton University. The details of gravitational lensing are discussed in Chap. 8. Here it is sufficient to note that OGLE can also detect exoplanets via the transit method.

OGLE is now in its fourth phase of development (OGLE IV). OGLE initially used the 1-m Swope telescope at the Las Campanas observatory in Chile. Later, the 1.3-m Warsaw telescope (also at Las Campanas) was purpose built for the project. In the current phase (OGLE IV), the telescope feeds a mosaic of 32 2,048  ×  4,096 pixel CCDs giving it a total field of view of 1.4 square degrees. Because the programme’s main objective is detecting dark matter, its primary observational targets are the Milky Way’s galactic bulge and the Magellanic clouds. For this reason many of OGLE’s discoveries are among the most distant known exoplanets. OGLE-TR-56 b, for example, the first exoplanet discovered by OGLE in 2002, is around 5,000 light years away from us. It has a mass of 1.3 Jupiter masses and is in a 29-h orbit just three and third million kilometres away from its solar-type host star. At the time of its discovery OGLE-TR-56 b had the smallest known separation from its host star of any exoplanet – its temperature at the top of its atmosphere is likely to be 1,600–1,700°C, which, since iron melts at 1,538°C, gives rise to the intriguing speculation that there may be clouds of molten iron droplets in the planet’s atmosphere and even iron raindrops! OGLE-TR-56 b was amongst a list of over 40 possible exoplanetary transit stars compiled from earlier OGLE observations. Radial velocity measurements by the 10-m Keck telescopes and others showed that most of these transiting objects were too ­massive to be planets, but OGLE-TR-56 b (and later, in 2004, OGLE-TR-10 b) turned out to be planet-sized. OGLE has now ­discovered a total of eight exoplanets via the transit approach.

In December 2006 the French CNES (Centre National d’Etudes Spatiales) together with ESA launched the CoRoT (Convection, Rotation and planetary Transits – Figure 6.6) spacecraft with a twofold mission –

Figure 6.6

Artist’s concept of the CoRoT spacecraft in orbit. (© CNES/DUCROS David, 2006. Reproduced by kind permission of CNES and David Ducros).

• 1. To study the interiors of stars by observing their vibrations (‘stellar seismology’ or ‘asteroseismology’) and

• 2. To discover Earth-like exoplanets.

The spacecraft carries a 0.27-m off-axis telescope feeding four 2,048  ×  4,096 pixel CCDs that cover a 2.8°  ×  2.8° area of the sky. Two of the CCDs are devoted to asteroseismology and two to transits, though at the time of writing only one of each is functioning. CoRoT is in 900-kilometre high polar orbit and observes two parts of the sky for 6 months at a time each. The two fields of view are in Aquila and Monoceros and the spacecraft switches between them when the Sun threatens to interfere with the observations in one of the areas. Recently the mission has been extended to continue at least until March 2013. CoRoT’s observations are supported by a small ground-based telescope. The Berlin Exoplanet Search Telescope II (BEST II) is a 0.25-m diameter robotic instrument sited near Cerro Armazones in Chile.

CoRoT has discovered and had confirmed 17 exoplanets to date. The first, CoRoT-1 b (Figure 6.7), announced in 2007, is an enormous hot Jupiter orbiting a solar-type star 1,560 light years away from us in Monoceros. The exoplanet has a radius 50% larger than that of Jupiter and a mass equal to that of Jupiter so that its mean density is only a third of that of water.

Figure 6.7

The transit of CoRoT-1 b. (Reproduced by kind permission of ESA and the CoRoT exo-team).

Most of the CoRoT exoplanet discoveries are hot Jupiters with the exceptions of CoRoT-7 b (2009) and CoRoT-9 b (2010). In CoRoT-7 b (Figure 6.8), the spacecraft’s mission to find Earth-sized planets was almost fulfilled. This exoplanet has a radius just 70% larger than that of the Earth (15% of Jupiter’s radius) making it the smallest known exoplanet at the time of writing. Its mass is 4.8 times that of the Earth (0.015 Jupiter masses) ­giving it an average density 5.6 times the density of water (5,600 kg/m³ compared with 5,500 kg/m³ for the Earth). It is thus almost ­certainly of a rocky composition, perhaps with an iron core like the Earth. In other respects though, CoRoT-7 b is not a twin for the Earth. It orbits only 0.017 AU out from its slightly-cooler-than-the-Sun host star so that its surface temperature is variously estimated to be at least 1,000°C and perhaps as much as 2,500°C. The surface is thus likely to be covered by oceans of molten rock and it may have a very thin atmosphere comprised of sodium, oxygen and ­silicon monoxide. CoRoT-7 b’s ‘year’ is just 20.5 h long – the shortest known for any exoplanet. It is quite likely that the ­planet’s ­rotation is tidally locked onto its host star so that it always keeps the same face towards the star. The temperature on the side away from the star could then fall as low as −220°C. If the planet’s orbit is even slightly elliptical tides could heat up its interior and lead to continuous and intense volcanic activity at the surface. If there is volcanic activity occurring, then the James Webb Space telescope may in due course be able to detect the gases that have been emitted. It is possible that the planet was at one time as large as Neptune and has been evaporated down to its present size (a chthonian planet).

Figure 6.8

An artist’s impression of CoRoT-7 b and its host star. (Reproduced by kind permission of ESA, ESO and L. Calcada).

CoRoT-9 b is unusual in that its orbit is relatively large. It is in an orbit larger than that of Mercury (0.41 AU) with an orbital period of 95 days. It is very close to Jupiter in size and has a mass of 0.84 Jupiter masses. Although not a Jupiter-twin, the temperature of its outer layers probably lies between −20°C and 150°C – far cooler than that of the other exoplanets found via the transit approach.

NASA’s Kepler mission is based upon a $600 million, 1,000 kg spacecraft that was specifically designed and built with the aim of discovering Earth-sized planets within the habitability zones of Sun-like stars (Figure 6.9). The spacecraft was launched in March 2009 into a Sun-centred orbit (i.e. it does NOT orbit the Earth). The spacecraft’s orbital period is 6 days longer than the Earth’s year so that it gradually drops further and further behind the Earth at a rate of a million kilometres every 3½ weeks. The orbit was chosen so that the Earth did not block the spacecraft’s field of view and so that gravitational disturbances, etc. would be minimized. Sixty-one years after its launch the spacecraft will return to the vicinity of the Earth. There is no possibility of it colliding with the Earth, but what a magnificent opportunity for the salvage experts of 2070!

Figure 6.9

The Kepler spacecraft. (Reproduced by kind permission of NASA Ames and Ball Aerospace).

The spacecraft is built around a large Schmidt camera. The camera has an aperture of 0.95 m and a primary mirror with a diameter of 1.4 m (for comparison the largest ground-based Schmidt camera, at the Karl Schwarzschild observatory, has an aperture of 1.34 m and a primary mirror with a diameter of 2 m). The instrument’s field of view encompasses over a 100 square degrees (roughly the area covered by the spread hand held at arm’s length) and its detector is a mosaic of 42 1,024  ×  2,048 pixel CCDs (Figure 6.10). The camera points permanently towards an area of the sky mid-way between Deneb and Vega in the constellations of Cygnus, Lyra and Draco. The area was selected to provide a large number of observable stars, to minimize the number of asteroids and Kuiper belt objects that might be encountered and so that the Sun never interferes with the observations. The volume of space observed by The Kepler spacecraft lies along the Orion spiral arm of the Milky Way, and Earth-sized planets should be detectable out to a distance of 3,000 light years.

Figure 6.10

The Kepler spacecraft’s detectors – the CCD mosaic. (Reproduced by kind permission of NASA Ames and Ball Aerospace).

A hundred and fifty-five thousand solar-type stars are ­monitored by The Kepler spacecraft with the CCDs being read out every 6 s in order to avoid over-exposure. For magnitude 12 stars (a ­quarter of a million times fainter than Sirius), the stars’ brightnesses are measured to a precision of ±0.002%. In every-day terms this level of precision is the equivalent of being able to distinguish the difference in brightnesses between two otherwise identical street lamps, one of which is 100 km (100,000 m) away from the observer and the other which is 1 m closer to the observer (99,999 m). To aid reaching this level of accuracy and perhaps counter-intuitively, the camera is NOT sharply focused. The stellar images are thus a bit fuzzy (about 10 s of arc across) and so are shared amongst 20–30 pixels. An anomalously high or low sensitivity pixel therefore has little effect upon the total measured brightness of the star.

The transit of an Earth-sized planet should produce a drop in the star’s brightness by around 0.008–0.009% – about four times larger than the minimum change measureable for a 12^m star. ­During the mission’s scheduled 3.5 year life (which may be extended – the planned life of the spacecraft is 6 years) it is hoped that some 50 Earth-sized planets might be found along with 100 or 200 twice the size of the Earth and up to a 1,000 Jupiter-sized exoplanets. The first exo-Earth discoveries though (Earth-sized and with orbital periods in the region of a year) should not be expected before around 2012–2013 because of the necessity of observing three or more transits. Cold Jupiters (giant planets in long-period orbits) are only likely to have a single ­transit observed – ­insufficient to count as a discovery. However the transit for such planets should be readily recognizable as being a transit and will be deep enough to be observed from the ground. Follow-up observations from Earth-based instruments may therefore be used to detect subsequent transits in such cases although the area of sky observed by the Kepler spacecraft is only accessible to such instruments from around about May to October. In this way, Kepler is expected to pin point up to 30 stars that are likely to host cold Jupiter exoplanets. It is also likely that confirming radial velocity observations could be made of these candidate stars without waiting for a second or third occultation and the exoplanets confirmed via that approach.

In the case of Jupiter-sized planets, Kepler should also be able to detect them directly from their reflected light. The exoplanet will change its phase (as Kepler ‘sees’ it) from zero when it is transiting its host star through a crescent shape, half ‘moon’, gibbous and finally to full just before it passes behind the star. The phase sequence will repeat in reverse as the planet comes out from behind the star and moves round towards its next transit. This will lead to a small but regular change in the star’s brightness that has the same period as that of the exoplanet (Figure 6.11). Since the planet’s orbital period will be known very precisely from the transit timings, several of these stellar modulation patterns can be added together to improve their detectability. It is expected that the Kepler spacecraft will be able to observe giant exoplanets in this way when their orbital periods are less than about 7 days. The spacecraft has indeed already observed the effect for the previously-known exoplanet HAT-P-7 b whose orbital period is 2.2 days.

Figure 6.11

The modulation of a star and giant exoplanet system’s total brightness as the phase of the exoplanet changes.

The Kepler spacecraft commenced observations of its target area of the sky on May 12th 2009. By August of the same year it had confirmed its ability to detect exoplanets by picking up the transit of an already known exoplanet. TrES-2, now also ­designated Kepler-1 b, was discovered in 2006 by the Trans-atlantic Exoplanet Survey and is a 1.2 Jupiter mass hot Jupiter in an orbit with a radius of 0.036 AU around a solar-type star 700 light years away from us on the Cygnus/Draco boundary. A minor problem with the spacecraft developed in November 2009 when 3 of the 84 data channels were found to be noisier than expected. Nonetheless with the January 2010 data release five exoplanet discoveries were announced together with the detections two more previously known planets. All five of the new exoplanets (Figure 6.12b) are hot Jupiters with the exception of Kepler-4 b which is small enough to be classed as a hot Neptune.

Figure 6.12

(a) An artist’s impression of the recently discovered pair of hot Jupiters forming the Kepler-9 exoplanetary system. (Reproduced by kind permission of NASA/Ames/JPL-Caltech). (b) Transits of Kepler’s first five discoveries. (Reproduced by kind permission of NASA Ames).

In mid-2010 the discovery of three exoplanets transiting the same star in Lyra was announced. Kepler-9 b and Kepler-9 c are Saturn-mass exoplanets in 19 and 38 day orbits 0.09–0.14 AU out from their solar-type host star (Figure 6.12a). While Kepler-9 d is a super-Earth with a mass seven times larger than the Earth. Kepler-9 c is about four million kilometres out from its host star giving it a probable surface temperature around 1,200°C. For the first time the transit timing variation method (Chap. 9) was used, as well as the radial velocity method, to confirm these exoplanets. The discovery of Kepler-10 b was announced in January of 2011 as the first small, rocky planet found by Kepler. It is a super-Earth of 4.6 Earth masses and 40% larger than the Earth. The resulting density of nine times that of water (nearly twice the Earth’s average density) is higher than that of iron and suggests that the planet must not only be rocky but have a high proportion of metals such as iron and nickel and a large, highly compressed and dense core.

The February 2011 Kepler data release based upon observations up to mid September 2009 saw the announcement of the discovery of the six-exoplanet system, Kepler-11 (Figure 1.1), with its confirmation being based entirely upon the transit timing variation method. The inner five planets of the system are super-Earths or Hot Neptunes and all are closer to their solar-type host stars than Mercury is to the Sun. Even the outermost member of the system, which possibly has a mass near to that of Jupiter, is closer to the star than Venus is to the Sun.

The 2011 data release also increased the number of exoplanetary candidates to over 1,600 – and the Kepler team expect that some 80% of these will eventually be confirmed to be genuine planets. Of these, 54 were in or near their host stars’ habitable zones. While most of the latter were likely to be super-Earths or larger exoplanets, one candidate, KOI 326.01, has a possible size less than that of the Earth and so might be a potential exo-Earth. Statistical analysis of the properties of the exoplanet candidates (which is likely to contain significant uncertainties at the moment) suggests that amongst the solar-type stars selected for study by Kepler we may expect to find that:-

• 6% of the exoplanets are similar to the Earth in size (less than 1.25 Earth radii)

• 24% of the exoplanets are super-Earths (1.25–2 Earth radii)

• 55% of the exoplanets are Neptune-sized (2–6 Earth radii)

• 14% of the exoplanets are Jupiter-sized (6–15 Earth radii)

• 1.5% of the exoplanets are larger than Jupiter (15–22 Earth radii) and

• 17% of the stars with exoplanets have multiple planet systems.

As already noted though, it will take some time, possibly several years, before discoveries of exo-Earth planets can be hoped-for, so this initial detection of a preponderance of large exoplanets close to their host stars is as expected.

A striking aspect of the data on exoplanetary candidates is that the number of candidates peaks at an orbital period of around 2–4 days (an orbital radius of about 0.1 AU). If this is a real effect for genuine exoplanets then it could arise either from the exoplanets’ inward migrations coming to a halt close to the star as tides transfer some of the star’s rotational energy (angular momentum) to the planets or from the planets breaking-up and crashing into the star – or both effects could be in operation.

Details of the exoplanets discovered by Kepler to February 2011 plus the exoplanet candidate KOI 326.01 (From http://kepler.nasa.gov/) are listed in the following table

Name	Mass (Jupiter masses)	Radius (Jupiter radii)	Orbit radius (AU)	Orbit period (days)	Temperature (top layer of planet’s atmosphere or the solid surface) (°C)	Host star mass (solar masses)
Kepler-4 b	0.077	0.357	0.046	3.2	1,400	1.22
Kepler-5 b	2.114	1.431	0.051	3.5	1,600	1.37
Kepler-6 b	0.669	1.323	0.046	3.2	1,200	1.21
Kepler-7 b	0.433	1.478	0.062	4.9	1,250	1.35
Kepler-8 b	0.603	1.419	0.048	3.5	1,500	1.21
Kepler-9 b	0.252	0.842	0.14	19.2	400	1.07
Kepler-9 c	0.171	0.823	0.225	38.9	250	1.07
Kepler-9 d	0.022	0.147	0.0273	1.59	1,200	1.07
Kepler-10 b	0.014	0.127	0.0168	0.837	1,600	0.89
Kepler-11 b	0.0135	0.176	0.091	10.3	600	0.95
Kepler-11 c	0.0425	0.282	0.106	13.0	500	0.95
Kepler-11 d	0.0192	0.307	0.159	22.7	350	0.95
Kepler-11 e	0.0264	0.404	0.194	32.0	300	0.95
Kepler-11 f	0.0072	0.234	0.25	46.7	200	0.95
Kepler-11 g	<0.95	0.327	0.462	118	90	0.95
KOI 326.01	0.002?	0.08?	0.005?	9?	60?	0.21

As mentioned in connection with the XO project, observing the deeper transits of exoplanets is well within the capabilities of amateur astronomers. There is even a book – Exoplanet Observing for Amateurs by Bruce Gary devoted to the topic (Reductionist Publications – first edition available to down-load free of charge from http://brucegary.net/book_EOA/x.htm). Gary was among the first ‘amateur’ astronomers (though now retired, he spent many years working professionally in the field of planetary radio astronomy) to observe an exoplanet transit – that of HD 209458 b (discovered via the Doppler method in 1999) in 2002 using a 0.25-m telescope. The transit of HD 209458 b had first been observed by non-­professional astronomers using a 0.4-m ­telescope 2 years earlier by a group led by Arto Oksanen working at the Nyrölä Observatory in Finland. Gary’s book is full of useful advice on such essentials as flat ­fielding, obtaining dark frames for the CCD images, limiting the exposures to avoid saturation etc. There is also a useful introductory article – Imaging Exoplanets by David Shiga (Sky and Telescope magazine page 44, April 2004) that any prospective transit observer is advised to read. Since the main requirement for observing an exoplanet transit is accurate photometry, the tips given in Shiga’s article for achieving this are worth summarising (together with a few additions):

• 1. If you have a choice of observing sites use the photometrically best one – i.e. the one with the least light pollution, the highest altitude (usually), the least likelihood of haze or cloud and the steadiest atmosphere (least scintillation or twinkling of the stars).

• 2. Try to choose a star and a time of the year so that the star will be at least 45° above the horizon throughout the observing period. Details of known exoplanet transits, predictions of the times of future transits and images for locating the star may be found at the Exoplanet Transit Database (http://var2.astro.cz/ETD/). Predictions of transits are also available at the NStED (http://nsted.ipac.caltech.edu/index.html).

• 3. Use a comparison star (or several comparison stars) within the same field of view as the transit candidate star which has (have) as similar a colour (spectral type – see Appendix IV for a brief summary of stellar spectral and luminosity classification) and brightness (magnitude) as possible to that of the candidate star. The widest possible field of view (i.e. the biggest CCD chip that you can ­afford) will assist in providing suitable comparison stars.

• 4. Keep the two (or more) stars’ images on the same pixels of the CCD camera throughout the observing period.

• 5. Slightly de-focus the telescope so that the stars’ images are spread over several (20–30) pixels. However in crowded star fields be careful that the star images do not start to over-lap.

• 6. Choose an exposure that is sufficiently short that none of the pixels recording the images of the stars of interest are anywhere near to being saturated. At the same time the exposure should be long enough to even-out variations in brightness due to ­atmospheric scintillation. In practice this probably means ­exposures of around 10 s duration. The use of a broad-band filter and/or increasing or decreasing the level of de-focussing of the telescope may help to optimise the exposure. In some CCDs the response starts to become non-linear well before the pixels are saturated. In these cases make sure that the exposures remain within the linear part of the response.

• 7. Obtain as many images as you can, starting well before the predicted time of transit and continuing until well after its predicted end – you will be unlikely to see the change in brightness whilst still at the telescope.

• 8. Obtain calibration images (flat field, dark frame, etc.) regularly throughout the observing period – but note point (3) and if you have to move the telescope to obtain the calibrations make sure that the stars images are returned to exactly the same places on the CCD (not easy!!).

• 9. Keep an accurate record of the times and durations of each exposure together with the usual observing notes regarding weather conditions, instrument problems, observing procedures, etc.

When you have obtained your data, you may be satisfied just with the achievement of detecting the transit. However the sense of achievement will undoubtedly be greater if you can contribute to improving our knowledge of the host star and its exoplanet. To this end there are several programmes that you can join or contribute towards. The American Association of Variable Star Observers (AAVSO – http://www.aavso.org/observing/programs/ccd/transitsearch.shtml), for example, collaborates with Transitsearch (http://www.transitsearch.org/) in observing selected ­target stars systematically and welcomes contributions from ­amateur ­astronomers. AAVSO provides advice and tutorials on how to obtain useful measurements and how to analyse them. A similar scheme, project TRESCA (TRansiting ExoplanetS and CAndidates), is run by the Czech Astronomical Society’s Variable Star and Exoplanet section (see Exoplanet Transit Database – http://var2.astro.cz/ETD/).

Amateur astronomers and any other readers with an interest in finding exoplanets can contribute to the analysis of Kepler’s data through PlanetHunters.org (http://kepler.nasa.gov/education/planethunters/) – a part of the Citizen Science project (http://citizensciencealliance.org/projects.html). This scheme has over 16,000 contributors at the time of writing, but more are always welcome.

The discovery of a new exoplanet completely through amateur astronomer contributions has yet to occur, although it seems likely to do so fairly soon. Amateur astronomers though have contributed to exoplanet discoveries, working in collaboration with professionally-operated searches. The five XO project planet discoveries have already been mentioned as one such example. Another is for the exoplanet HD 17156 b that orbits a solar-type star 250 light years away from us in Cassiopeia. HD 17156 b was discovered in April 2007 through the radial velocity method by a team led by Debra Fischer using observations from the 10-m Keck and 8.2-m Subaru telescopes. The possibility of the orbit being suitably aligned with the Earth for transits to occur seemed likely and in October 2007 a transit was indeed observed by several groups including members of Transitsearch. HD 17156 b turns out to be in a highly elliptical orbit, at one point being 0.27 AU from its host star but then approaching to within 0.05 AU of the star at the opposite point of its orbit. Similarly the transit of HD 80606 b (discovered through radial velocity variations by Mayor and Queloz et al. in 2001) was detected by Transitsearch participants amongst others in 2009. Somewhat remarkably, HD 80606 b is in an even more elliptical orbit than HD 17156 b, ranging from 0.03 to 0.88 AU away from its slightly-cooler-than-the-Sun host star. The orbital eccentricity of 0.93 for HD 80606 b is the second largest of any known exoplanet and comparable with that of the orbit of Halley’s comet. Amateur astronomers have also made confirming and follow-up observations for many other transiting exoplanets.