Most hot Jupiters have values less than 0.1

a At 13 January 2007: 205 planets in 177 exoplanetary systems, 20 systems with 2 or more planets; planets around pulsars are excluded. b These are minimum masses for those discovered by the radial velocity technique, in terms of Jupiter's mass mJ. c Above about 13mJ the object is a brown dwarf, a 'failed star' not massive enough to attain central temperatures sufficiently high for hydrogen (1H) fusion, but only a brief phase of fusion of the rare isotope 2H (deuterium).

a At 13 January 2007: 205 planets in 177 exoplanetary systems, 20 systems with 2 or more planets; planets around pulsars are excluded. b These are minimum masses for those discovered by the radial velocity technique, in terms of Jupiter's mass mJ. c Above about 13mJ the object is a brown dwarf, a 'failed star' not massive enough to attain central temperatures sufficiently high for hydrogen (1H) fusion, but only a brief phase of fusion of the rare isotope 2H (deuterium).

alien astronomer would have to observe the Sun for at least this time to discern the motion that Jupiter induces in it. Also, the probability of an edge-on view to give a transit decreases with the size of the orbit. It is therefore quite possible that planetary systems like ours are more common than in the presently known population of exoplanetary systems. Rather more than 10% of the stars investigated have planetary systems, so there is plenty of scope for this proportion to rise as the precision of observations increases, and as data are accumulated for longer times.

But already we reach the important conclusion that planetary systems are fairly common, at least around solar-type stars. Before 1995 this was believed to be the case. Now there is growing observational evidence that it is so.

Migration of planets in exoplanetary systems

Another important conclusion emerges from the exoplanetary systems, in particular from the presence of hot Jupiters. You will see in the remainder of this chapter that though it is beyond reasonable doubt that the giant planets formed within their systems, it is extremely unlikely that they could have formed so close in.

□ In this case, what is the only logical alternative to formation where there are today? The hot Jupiters must have formed further out, and then moved inwards.

Mathematical models show that the most common cause of inward movement is the gravitational effect of the (growing) giant planet on the circumstellar disc of gas and dust in which it is embedded and from which it has formed (Section 2.2). At first, this disc is symmetrical about an axis perpendicular to it and running through the growing star (protostar) at its centre. But as the mass of the embryonic giant grows, its gravity produces spiral density enhancements in the disc that destroy its symmetry. These spiral density waves have a net gravitational effect on the growing giant planet that causes it to migrate inwards. Figure 2.2 shows an advanced stage of migration.

Migration has to stop if a giant planet is to become a hot Jupiter rather that meet a fiery death. There are several plausible stopping mechanisms, such as tidal forces between the protostar and giant. Details are beyond our scope, but can be found in Further Reading. Ultimately, the disc is dispersed by the protostar as it becomes a main sequence star, as outlined in Section 2.1.3.

The question arises, why do some exoplanetary systems, including the Solar System, not have hot Jupiters? The answer is two-fold. First, the extent of migration depends on various properties of the circumstellar disc (density, thickness, temperature, and so on). Certain values give very low migration rates, with not a lot of inward movement before the disc is dispersed. Second, there will usually be more than one giant planet. Interaction between the gravitational effects they have on the disc can slow migration and even reverse it for some of the giants.

We thus reach the important conclusion: the giant planets in the Solar System might not have formed where we find them now. They could have formed elsewhere and migrated, with effects on the smaller bodies in the Solar System,

Question 2.1

Discuss why, in the astrometric technique,

(a) planets with large mass will be easier to detect than planets with small mass;

(b) it will be easier to detect planets around nearby stars than around distant ones.

Figure 2.2 A computer simulation of an advanced stage of migration of a growing giant planet through the circumstellar disc of gas and dust from which it has formed. (Reproduced by permission from F Masset, CEA/CNRS/Universite Paris, 2004)

Question 2.2

Discuss whether you would expect hot Jupiters to have orbits with eccentricities far larger than those of Jupiter and Saturn.

2.1.3 Star Formation

Observations of star formation provide further insight into the origin of the Solar System. Star formation is a relatively rapid process by astronomical standards, but it still takes many millions of years, and therefore the process has been pieced together by observing it at different stages in different locations, linking the observations together by physical theory. This is rather like observing a large number of people at a particular moment - they are seen at all stages of their lives, and it is therefore possible to use general biological principles to construct a theory of the complete human life cycle from an observation that occupied only a small fraction of the human lifespan.

From dense clouds to cloud fragments

Stars form from the interstellar medium (ISM) - the thin gas with a trace of dust that pervades interstellar space. Its chemical composition everywhere is dominated by hydrogen and helium.

In the region from which the Solar System formed, hydrogen typically accounts for about 71% of the mass, helium for about 27%, and all the other chemical elements (the 'heavy' elements) for only about 2%. Elsewhere in the ISM the proportion of helium is not very different, whereas the proportion of heavy elements can be as low as about 1% and as high as 5%, sometimes more. Almost all of the hydrogen and helium is in the form of gases, but a significant fraction of most of the heavy elements is condensed in the dust in a variety of compounds. Dust accounts for roughly 1% of the mass of the ISM.

The density and temperature of the ISM vary considerably from place to place. Star formation occurs in the cooler, denser parts of the ISM, because low temperatures and high densities each favour the gravitational contraction that must occur to produce a star from diffuse material. Low temperatures favour contraction because the random thermal motions of the gas that promotes spreading are then comparatively weak. High densities favour contraction because the gravitational attraction between the particles is then relatively strong. The cooler, denser parts of the ISM are called, unsurprisingly, dense clouds. They are often components of giant molecular clouds, 'molecular' because the predominant form of hydrogen throughout them is the molecular form, H2.

Dense cloud temperatures are of order 10 K. They must not, however, be thought of as chunky things - a typical density at the high end of a wide range is only of order 10-14kgm-3, rather less than the density in a typical laboratory vacuum! A typical size is, however, a few light years across, and therefore most dense clouds are massive enough to form many hundreds of stars. They are also large enough for the dust content to make them opaque at visible wavelengths.

Though the conditions for gravitational contraction are best met in dense clouds, it is likely that in most cases they will contract only if they are subject to some external compression, particularly because magnetic fields and gas flows within the cloud hinder contraction. Compression can occur in one or more of a variety of ways, such as in a collision between two clouds, or by the impact of a shock wave from an exploding star, or by the action of a so-called spiral density wave that sweeps through the whole Galaxy (thereby sustaining its spiral arms). One way or another, a dense cloud, or a good part of it, becomes dense enough to become gravitationally unstable, and it starts to contract. As it contracts it becomes denser, to the point where the denser parts of the cloud, called dense cores, each contract independently, and are destined to become stars. This leads us to expect stars to form in clusters, and indeed the great majority of young stars are found in clusters (though a few form in isolation, from small dense clouds). Typically, a cluster contains a few hundred stars, and Plate 23 shows an example. Star clusters gradually disperse, and therefore older stars, like the Sun, are no longer in clusters.

From a cloud fragment to a star

Let us now follow the fate of a typical cloud fragment as it contracts. The gas molecules and dust particles gain speed as they fall inwards, and when they collide there is an increase in the random element of their motion. Temperature is a measure of the random motion of an assemblage of microscopic particles, and therefore the temperature rises. However, the rise is initially small because when the gas molecules collide they are raised into higher energy states of vibration or rotation. When the molecules return to lower energy states they get rid of their excess energy by emitting photons, usually at infrared (IR) wavelengths. Initially the density of the cloud fragment is so low that most of these photons escape. This loss of energy by the fragment retards the temperature rise.

The fragment continues to contract, and its density rises further. Detailed calculations show that the central regions of the fragment contract the most rapidly. It is therefore these central regions that become opaque to the photons emitted by the molecules. The temperature rise is then rapid and the central object is regarded as a protostar. Contraction continues, now more slowly, and a few million years after the fragment separated from the dense cloud the temperature in the core of the protostar has become high enough for nuclear fusion to occur - about 107 K. This fusion releases energy and creates a pressure gradient that halts the contraction of the protostar. At this point the protostar has become a star - a compact body sustained by nuclear fusion.

The fusion that dominates the nuclear reactions in the core of the star depends on its composition.

□ What element accounts for most of the mass of the star?

As in the dense cloud, typically about 71% of the mass is hydrogen. It is also the case that nuclear fusion involving hydrogen occurs at a lower temperature than fusion involving helium and the other elements. Therefore it is the fusion of hydrogen nuclei that is by far the dominant source of energy. This fusion results in the creation of nuclei of helium, by the pp chains (Section 1.1.3).

You saw in Section 1.1.3 that the onset of core hydrogen fusion marks the start of the main sequence phase of a star's lifetime. It lasts longer the less massive the star, and for a star of solar mass it lasts about 1011 years. The Sun itself is 4600 Ma through its main sequence phase. In all stars it is a period of relative stability, but it is immediately preceded by a well-observed period of instability that is of considerable importance to the formation of any planetary system. This is the T Tauri phase, named after the protostar that was the first to be observed in this phase. For a protostar of solar mass it is thought to last for a few million years. It is marked by a considerable outflow of gas, called a T Tauri wind, a protostar of solar mass losing the order of 10% of its mass in this way, and by a high level of ultraviolet (UV) radiation from the protostar. The root causes of T Tauri activity are the final stages of infall of matter to the protostar, plus its strong interior convection and rapid rotation.

After the onset of hydrogen fusion the T Tauri activity quickly subsides. The UV radiation falls to a much lower level, and the wind declines to a much smaller rate of mass loss, called a stellar wind in general, and the solar wind in the case of the Sun (Section 1.1.2).

2.1.4 Circumstellar Discs

Meanwhile, that part of the fragment that has remained outside the protostar has also been evolving. As it contracts, a dense core starts to form, with more tenuous material outside it. But the fragment is rotating, and so it is to be expected that only the material on or near the rotation axis falls fairly freely towards the core - the infall of the remainder is moderated by its rotation around the core. A circumstellar disc should thus form in the plane perpendicular to the axis of rotation. Planetary systems are thought to form from such discs.

In recent decades circumstellar discs have been detected around many protostars. The discs have masses ranging from a few times the mass of Jupiter to hundreds of times Jupiter's mass, and diameters typically a few hundred AU. The gas component in the discs is readily imaged through its emission at radio and millimetre wavelengths. This gas component is largely removed during the T Tauri phase of the star (Section 2.1.3), in the case of solar mass stars in the 10Ma or so that leads up to the main sequence phase.

Discs have also been detected around several hundred young main sequence stars through the IR emission from the dust in the discs. By this stage, the disc masses are considerably less than those around protostars. Dusty discs are observed around stars up to ages of about 10 Ma. There is a growing number of images of these dust discs, some utilising the dust emission at

IR and submillimetre wavelengths, others utilising IR and visible wavelengths with the disc in silhouette against a bright background. In Plate 24 the dust component in the disc around the young main sequence star Beta Pictoris is imaged through the light from the star that the dust scatters. There is good evidence that the dust in this disc is replenished by collisions of cometary bodies. This was one of the first discs to be imaged. A disc of dust around the star Rho1 55 Cancri, that has at least four planets, is thought to be sustained in the same way. The Beta Pictoris disc does not extend inwards of about 20 AU from the star - could the hole have been hollowed out by the formation of planets? This possibility is supported by a warping of the inner disc that could be caused by a giant planet just within the hole, in an orbit inclined at about 3° to the plane of the disc. Other discs have similar holes.

Thus, around protostars we have discs of material that could form a planetary system, and around young main sequence stars we have discs that seem to indicate that planetary formation has actually occurred. These observations lend strong support to solar nebular theories, to which we now turn.

Question 2.3

Identify the feature of the Solar System in Table 2.1 that is already present in circumstellar discs around protostars.

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