Planet Building

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In this section we will look at the Solar Nebula Theory in more detail with the objective of creating a robust theory of planetary formation that can explain not only the formation of our own solar system but of planetary systems around other stars.

What was the Composition of the Solar Nebula?

How "Big" was the Solar Nebula?

We know the mass of the Sun - 1.99 X 10³⁰ kg. Can we estimate the mass of the Solar Nebula? A crude way to set a minimum mass for the Solar Nebula is to add up the masses of the known planets, sub-planets and asteroids in the solar system. This suggests that the minimum mass for the Solar Nebula would be about 0.002Mo. More detailed computer models of planet building put this number much higher - somewhere between 0.01Mo and 1 Mo. The key point is that the planetary system represents only a tiny fraction of the mass that must have been present in the earliest stages formation for the sun and planets.

Problems With the "Simple" SNT

There are a number of problems with a naive application of the Solar Nebula Theory. Three of the more significant problems are:

1. Computer models of rings formed in accretion disks do not tend to break up into smaller bodies but instead disperse. There must be something more subtle occurring that leads to the formation of planetary bodies.
2. The Sun does not have enough angular momentum. Another way of saying this is that we would expect the Sun to be spinning much faster than it is.
3. Not all bodies in the solar system move in a way that can be explained by the SNT. An example of this is Neptune's moon Triton. Triton orbits around Neptune in a retrograde fashion. This means that it is traveling "backwards" when compared to the rotational motion of other planets and moons in the solar system. This suggests that there must be more happening (perhaps collisions between bodies) than the simple SNT implies.

The Condensation Theory

An important extension of the SNT is to recognize the critical role that condensation of materials played in the formation of the solar system. Indeed, the condensation theory helps to naturally explain why we have two very distinct class of planets - the Terrestrial planets and the Jovian planets. Table 16.4 illustrates an important property of the Terrestrial planets - average density. Tabulated are two different ways of expressing density. The observed density and the uncompressed density.

Condensation is driven by one critical property - temperature of the solar nebula and temperature of the planets at the time of formation. Figure 16.8 shows the condensation sequence as a function of temperature for the Terrestrial planets. The first materials to condense from a vapour to a solid state are the metal oxides, iron and nickel. This occurs at temperatures between 1500 K and 1000 K and helps explain why Mercury has the highest density of the Terrestrial planets. Eventually, at the location of Earth's orbit lighter materials (minerals found in terrestrial rocks) begin to condense.

Figure 16.8 Condensation sequence for the Terrestrial planets.

The SNT and Condensation Theory together provide a plausible explanation for the two distinct classes of planets. As you progress farther out in the Solar nebula the condensation sequence reaches a critical point called the ice-line. At a point between the orbits of Mars and Jupiter the temperature of the Solar Nebula had dropped to the point at which water vapour would condense and freeze. This marks the demarcation between the Terrestrial and Jovian planets. Beyond this point gases such as methane and ammonia would condense and freeze. Figure 16.9 shows the condensation sequence for the outer part of the solar nebula.

Figure 16.9 Condensation sequence for the outer part of the Solar Nebula - the realm of the Jovian planets.

The ice-line is particularly important. Once water ice began to form it did so as small, sticky grains or flakes that acted as sites on which other materials, including traces of silicate and metal grains from deeper in the nebula could begin to accumulate. Water ice and the other kinds of ices (methane, ammonia etc) are of much lower density than the dust grains that formed closer to the sun. This provides a natural explanation for the marked difference between the Terrestrial and Jovian planets.

Example 16.5 A planet forms at a location in a protostellar nebula where the temperature is 100 K. What kind of planet would you expect this to be?

Solution: SInce this is outside the ice-line you should expect that this will be a gas giant planet similar to Uranus or Neptune.

Planetesimals, Protoplanets and Planets

The formation of planets involves three important processes: condensation, accretion and differentiation.

Condensation

The speed of atoms and molecules in a gas depends on temperature. As you lower the temperature of a gas the average velocity of the particles in the gas drops. At low enough temperatures the atoms or molecules in the gas are able to stick together when they collide and this marks the beginning of condensation. You have already seen this in the previous discussion of the condensation sequence in the solar nebula and how this accounts for the change in density and composition of material as you move outward in the solar nebula. Condensation begins particle by particle and over time leads to the formation of microscopic dust grains.

Example 16.6 Explain why the change in size of a dust grain formed by condensation increases rapidly at first but then slows as the grain grows.

Solution: Grains will grow particle-at-a-time. At first, if the grain consists of only a few atoms or molecules adding one more particle represents an appreciable increase in mass and size of the grain. However, if the grain consists of 1 million particles then adding one more has a very small effect on mass and size.

Accretion

When dust grains collide with each other (and again if the temperature is low enough) they can stick together to form larger clumps. A good example of this is the formation of snowflakes which occurs through collision and sticking together of many ice crystals. This process is called accretion. In the solar nebula dust grains that formed by condensation would begin to accrete. Eventually, the dust grains accrete to become larger objects known as planetesimals. Figure 16.10 shows a simulation of accretion of 300 spherical dust grains at low temperature undergoing "sticky" collisions. (The grains are contained within a bounding box and are able to bounce off the sides of the box which is not shown in this simulation.)

Figure 16.10 Accretion of small "sticky" dust grains into larger bodies

Gravitational forces between atoms and molecules are completely negligible and play no role in either condensation or accretion. For both processes the dominant forces are molecular bonding forces. The evolution of tiny dust grains into, eventually, kilometer sized planetesimals is still a puzzling and poorly understood phenomenon.

Differentiation

By the time planetesimals grew to tens to hundreds of kilometers across, gravitational forces became important and larger planetesimals were able to gravitationally attract and collide with smaller planetesimals. The solar nebula would have contained "swarms" of planetesimals orbiting the centre of the nebula at speeds measured in tens of km/s. In many cases the collisions between planetesimals would have been head-on and violent enough to shatter the planetesimals into smaller pieces. More gentle collisions could occur however if planetesimals orbited in roughly the same direction with one gently "rear-ending" the other. Eventually a few large planetesimals would emerge and their gravitational fields would become large enough to hold them together, even in the more violent collisions.

As large planetesimals formed a new process appears. The heat released during collisions would melted the more volatile materials (water ice, CO2 ice etc) and the heavier metals would begin to sink into the centre of the planetesimals. This process is called differentiation and leads to a stratification very much like the structure we observe for the Terrestrial planets today.

Figure 16.11 Flash animation of planetary differentiation in the early solar system

Wrinkles - The Jovian Problem

Astronomers now realize that the growth of very large - "Jovian" planets cannot proceed by accretion alone. According to recent calculations using the most sophisticated supercomputers, once the central star begins to form the accretion disk and nebula will clear out far too quickly. There simply is not enough time for Jupiter-sized planets to form by accretion. In our own solar system this problem is made worse by the fact that the Jovian planets are the outermost ones in the solar system and hence travel with a much lower velocity around the the Sun that do the inner planets. If these planets grew by accretion then the formation of Uranus and Neptune becomes very hard to explain. As you will see in the next section, however, Jovian planets abound in other "extra-solar" planetary systems. Astronomers call this puzzle the Jovian Problem and it suggests that there may be another way in which planets can form.

It is possible that instabilities in the accretion disk around the newly forming star can develop that themselves will collapse to form Jupiter-like planets. This would by-pass the accretion phase. It is quite likely that both processes can occur in the same system.

Example 16.7 What is the "essence" of the Jovian Problem?

Solution: Time! Large, gas-giant planets like Jupiter would take too long to form if accretion was the only planet building mechanism. It is probable that these planets from by direct collapse during the formation of the proto-star and planetary system.

Putting the Pieces Together

You can now understand the basic principles and ideas behind the formation of planetary systems. In the following we will explore a number of the most important properties of our own planetary system and make the tacit assumption that these same principles will apply elsewhere in the universe. We will also make use of two important ideas - gradualism and catastrophism:

Consider the following properties of our own solar system listed in Table 16.5

Cleaning House - Clearing of the Solar Nebula

The Solar Nebula was soon swept away from the newly forming Sun and planets. The two most important reasons for this were: The pressure exerted by the light pouring out of the new star at the centre of the nebula The gusting solar wind produced by the new star This created an outward force that caused the most of the material to drift into interstellar space. Secondary affects to clear the nebula were: The entrainment of solar nebula material by newly forming planets Close encounters between the newly forming planets leading to ejection of material from the nebula

Figure 16.12 The Solar Nebula being cleared from the early solar system

Figure 16.12 depicts this with the outer Jovian planets beginning to form and to "shepherd" material into their orbits.

Practice

1. Define the terms "Terrestrial" and "Jovian" planet.
2. Why would the discovery of Jovian planets close to a hot star challenge the standard Solar Nebula Theory?
3. What are Kuiper belt objects?
4. What composition would you expect for a planet that formed in a region in the solar nebula where the temperature was 500 K? Explain your answer.
5. What is the ice-line and why is it an important idea in understanding planetary formation?
6. Explain the difference between accretion and condensation.