### NEBULAR CONTRACTION

One of the earliest heliocentric models of solar system formation is termed the nebular theory, which may be traced back to the seventeenth-century French philosopher René Descartes. In this model, a large cloud of interstellar gas began to collapse under the influence of its own gravity. As it contracted, it became denser and hotter, eventually forming a star—the Sun—at its center. While all this was going on the outer, cooler, parts of the cloud formed a giant swirling region of matter, creating the planets and their moons essentially as by-products of the star-formation process. This swirling mass destined to become our solar system is usually referred to as the solar nebula.

In 1796 the French mathematician-astronomer Pierre Simon de Laplace tried to develop the nebular model in a quantitative way. He was able to show mathematically that the conservation of angular momentum (see More Precisely 15-1) demands that an interstellar cloud like the hypothetical solar nebula must spin faster as it contracts. A decrease in the size of a rotating mass must be balanced by an increase in its rotational speed.

The increase in rotation speed, in turn, must have caused the nebula's shape to change as it collapsed. In Chapter 11 we saw how a spinning body tends to develop a bulge around its middle. (Sec. 11.1) The rapidly spinning nebula behaved in exactly this way. As shown in Figure 15.1, the fragment eventually flattened into a pancake-shaped primitive solar system. If we now suppose that planets formed out of this spinning material, we can already begin to understand the origin of some of the large-scale architecture observed in our planetary system today, such as the circularity of the planets' orbits and the fact that they move in nearly the same plane.

Figure 15.1 (a) Conservation of angular momentum demands that a contracting, rotating cloud (a) must spin faster as its size decreases. (b) Eventually, the primitive solar system came to resemble a giant pancake. The large blob at the center would ultimately become the Sun.

Astronomers are fairly confident that the solar nebula formed such a disk because similar disks have been observed (or inferred) around other stars. Figure 15.2(a) shows a visible-light image of the region around a star called Beta Pictoris, lying about 50 light years from the Sun. When the light from Beta Pictoris itself is suppressed and the resulting image enhanced by a computer, a faint disk of warm matter (viewed almost edge-on here) can be seen. This particular disk is roughly 500 A.U. across—about 10 times the diameter of Pluto's orbit. Astronomers believe that Beta Pictoris is a very young star, perhaps only 100 million years old, and that we are witnessing it pass through an evolutionary stage similar to the one our own Sun experienced some 4.6 billion years ago.

Figure 15.2 (a) A computer-enhanced view of a disk of warm matter surrounding the star Beta Pictoris. The top image is the actual data taken at visible wavelengths; the bottom image is a false-color rendition that accentuates the details and makes the structure clearer. In both images the overwhelmingly bright central star has been removed in order to let us see the much fainter disk surrounding it. The disk is nearly edge-on to our line of sight. It is made mostly of microscopic dust grains of ices and silicate particles (see Section 15.3) and is illuminated by the reflected light of the central star. For scale, the dimension of Pluto's orbit (78 A.U.) has been drawn adjacent to the images. (b) An artist's conception of the disk of clumped matter, showing the warm disk with a young star at the center and several comet-sized or larger bodies already forming at large radii. The colors are thought to be accurate—generally speaking, if you know the temperature and the density of the nebula, then you can derive its color. At the outer edges of the disk the temperature is low, and the color is a dull red. Progressing inward, the colors brighten and shift to a more yellowish tint as the temperature increases. Mottled dust is seen throughout—such protoplanetary regions are probably very dirty.

Formation of Warp in Beta Pictoris Disk

The nebular theory is an example of an evolutionary theory, which describes the development of the solar system as a series of gradual and natural steps, understandable in terms of well-established physical principles. Evolutionary theories may be contrasted with catastrophic theories—theories that invoke accidental or unlikely celestial events in order to interpret observations. (A good example of such a theory is the collision hypothesis, which imagines that the planets were torn from the Sun by a close encounter with a passing star. This hypothesis enjoyed some measure of popularity during the nineteenth century, in large part due to the inability of other theories to account for the observed properties of the solar system, but no scientist takes it seriously today. Aside from its extreme improbability, it is completely unable to explain the orbits, the rotations, or the composition of the planets and their moons.) Scientists usually do not like to invoke catastrophes to explain the universe. However, as we will see, there are instances where pure chance has played a critical role in determining the present state of the solar system.

### THE ROLE OF DUST

Laplace imagined that as the spinning solar nebula contracted, it left behind a series of concentric rings, each of which would eventually become a planet orbiting a central protosun—a hot ball of gas well on its way to becoming the Sun. Each ring then clumped into a protoplanet—a forerunner of a genuine planet. The description of the collapse and flattening of the solar nebula is essentially correct, but when modern astronomers used computers to study the more subtle aspects of the problem, some fatal flaws were found in Laplace's nebular picture. Calculations show that a ring of the sort envisaged in his theory would probably not form and, even if it did, would not condense to form a planet in any case. In fact, computer calculations predict just the opposite: the rings would tend to disperse. The protoplanetary matter would be too warm, and no one ring would have enough mass to bind its own matter into a ball.

The model currently favored by most astronomers is a more sophisticated version of the nebular theory. Known as the condensation theory, it combines the good features of the old nebular theory with new information about interstellar chemistry to avoid most of the old theory's problems. The key new ingredient in the modern picture is the presence of interstellar dust in the solar nebula. Astronomers now recognize that the space between the stars is strewn with microscopic dust grains, an accumulation of the ejected matter of many long-dead stars (see Chapter 22). These dust particles probably formed in the cool atmospheres of old stars, then grew by accumulating more atoms and molecules from the interstellar gas within the Milky Way Galaxy. The end result is that our entire galaxy is littered with miniature chunks of icy and rocky matter having typical sizes of about 10-5 m. Figure 15.3 shows one of many such dusty regions found in the vicinity of the Sun.

Figure 15.3 Interstellar gas and dark dust lanes mark this region of star formation. The dark cloud known as Barnard 86 (left) flanks a cluster of young blue stars called NGC 6520 (right). Barnard 86 may be part of a larger interstellar cloud that gave rise to these stars.

Dust grains play an important role in the evolution of any gas. Dust helps to cool warm matter by efficiently radiating its heat away in the form of infrared radiation, reducing the pressure (which is just proportional to the gas temperature) and allowing the gas to collapse more easily under the influence of gravity. Furthermore, the dust grains greatly speed up the process of collecting enough atoms to form a planet. They act as condensation nuclei—microscopic platforms to which other atoms can attach, forming larger and larger balls of matter. This is similar to the way that raindrops form in Earth's atmosphere; dust and soot in the air act as condensation nuclei around which water molecules cluster.

### PLANET FORMATION

Modern models trace the formative stages of our solar system along the following broad lines. Imagine a dusty interstellar cloud fragment measuring about a light year across. Intermingled with the preponderance of hydrogen and helium atoms in the cloud is some heavy-element gas and dust. Some external influence, such as the passage of another interstellar cloud or perhaps the explosion of a nearby star, starts the fragment contracting, down to a size of about 100 A.U. As the cloud collapses, it rotates faster and begins to flatten (just as described in the old nebular theory). By the time it has shrunk to 100 A.U., the solar nebula has already formed an extended, rotating disk (Figure 15.4a, b; see also Figure 15.1b and 15.2b).

Figure 15.4 The condensation theory of planet formation (not drawn to scale; Pluto not shown). (a), (b) The solar nebula contracts and flattens into a spinning disk. The large blob in the center will become the Sun. Smaller blobs in the outer regions may become jovian planets. (c) Dust grains act as condensation nuclei, forming clumps of matter that collide, stick together, and grow into moon-sized planetesimals. (d) Strong winds from the still-forming Sun expel the nebular gas. (e) Planetesimals continue to collide and grow. (f) Over the course of a hundred million years or so, planetesimals form a few large planets that travel in roughly circular orbits.

According to the condensation theory, the planets formed in three stages (Figure 15.4c—e). Early on, dust grains in the solar nebula formed condensation nuclei around which matter began to accumulate. This vital step greatly hastened the critical process of forming the first small clumps of matter. Once these clumps formed, they grew rapidly by sticking to other clumps. (Imagine a snowball thrown through a fierce snowstorm, growing bigger as it encounters more snowflakes.) As the clumps grew larger, their surface areas increased and consequently the rate at which they swept up new material accelerated. They gradually grew into objects of pebble size, baseball size, basketball size, and larger.

Eventually, this process of accretion—the gradual growth of small objects by collision and sticking—created objects a few hundred kilometers across. By that time, their gravity was strong enough to sweep up material that would otherwise not have collided with them, and their rate of growth became faster still. At the end of this first stage, the solar system was made up of hydrogen and helium gas and millions of planetesimals—objects the size of small moons, having gravitational fields just strong enough to affect their neighbors.

In the second phase of the accretion process, gravitational forces between the planetesimals caused them to collide and merge, forming larger and larger objects. Because larger objects have stronger gravity, the rich became richer in the early solar system, and eventually almost all the planestesimal material was swept up into a few large protoplanets—the accumulations of matter that would eventually evolve into the planets we know today. Figure 15.5 shows a computer simulation of accretion in the inner solar system. Notice how, as the number of bodies decreases, the orbits of the remainder become more widely spaced and more nearly circular.

Figure 15.5 Accretion in the inner solar system: initially, many moon-sized planetesimals orbited the Sun. Over the course of a hundred million years or so, they gradually collided and coalesced, forming a few large planets in roughly circular orbits.

Gravitational Coalescence

As the protoplanets grew, another process became important. The strong gravitational fields produced many high-speed collisions between planetesimals and protoplanets. These collisions led to fragmentation, as small objects broke into still smaller chunks, which were then swept up by the protoplanets. Not only did the rich get richer, but the poor were mostly driven to destruction! Some of these fragments produced the intense meteoritic bombardment we know occurred during the early evolution of the planets and moons, as we have seen repeatedly in the last few chapters. A relatively small number of 10—100-km fragments escaped capture by a planet or a moon to become the asteroids and comets.

Mathematical modeling, like the calculation shown in Figure 15.5, indicates that after about 100 million years, the primitive solar system had evolved into nine protoplanets, dozens of protomoons, and the big protosolar mass at the center. Computer simulations generally reproduce the increasing spacing between the planets ("Bode's law"), although the reasons for the regularity seen in the actual planetary spacing remain unclear. (Interlude 6-1) Roughly a billion years more were required to sweep the system reasonably clear of interplanetary trash. This was the billion-year period that saw the heaviest meteoritic bombardment, tapering off as the number of planetesimals decreased. (Sec. 8.4)

The four largest protoplanets became large enough to enter a third phase of planetary development: sweeping up large amounts of gas from the solar nebula to form what would ultimately become the jovian planets. The smaller, inner protoplanets never reached that point, and as a result their masses remained relatively low. Alternatively, the jovian planets might have formed through instabilities in the cool outer regions of the solar nebula, mimicking on small scales the collapse of the initial interstellar cloud. In this scenario, the jovian protoplanets formed directly, skipping the initial accretion stage. In either case, these first protoplanets had gravitational fields strong enough to scoop up more of the remaining gas and dust in the solar nebula, allowing them to grow into the gas giants we see today. Their large size reflects their head start in the accretion process.

Many of the moons of the planets (but not our own—see Chapter 8) presumably also formed through accretion but on a smaller scale, in the gravitational field of their parent planets. (Sec. 8.8) Once the nebular gas began to accrete onto the large jovian protoplanets, conditions probably resembled a miniature solar nebula, with condensation and accretion continuing to occur. The large moons of the outer planets almost certainly formed in this way. Some of the smaller moons may have been "chipped off" their parent planets during collisions with asteroids; others may be captured asteroids themselves.