Lecture 13: The Nebular Theory of the origin of the Solar System

Any model of Solar System formation must explain the following facts:

1. All the orbits of the planets are prograde (i.e. if seen from above the North pole of the Sun they all revolve in a counter-clockwise direction).

2. All the planets (except Pluto) have orbital planes that are inclined by less than 6 degrees with respect to each other (i.e. all in the same plane).

3. Terrestrial planets are dense, rocky and small, while jovian planets are gaseous and large.

I. Contraction of insterstellar cloud

Solar system formed about 4.6 billion year ago, when gravity pulled together low-density cloud of interstellar gas and dust (called a nebula)(movie).
The Orion Nebula, an interstellar cloud in which star systems and possibly planets are forming.

Initially the cloud was about several light years across. A small overdensity in the cloud caused the contraction to begin and the overdensity to grow, thus producing a faster contraction --> run away or collapse process

Initially, most of the motions of the cloud particles were random, yet the nebula had a net rotation. As collapse proceeded, the rotation speed of the cloud was gradually increasing due to conservation of angular momentum.
Going, going, gone

Gravitational collapse was much more efficient along the spin axis, so the rotating ball collapsed into thin disk with a diameter of 200 AU (0.003 light years) (twice Pluto's orbit), aka solar nebula (movie), with most of the mass concentrated near the center.

As the cloud contracted, its gravitational potential energy was converted into kinetic energy of the individual gas particles. Collisions between particles converted this energy into heat (random motions). The solar nebula became hottest near the center where much of the mass was collected to form the protosun(the cloud of gas that became Sun).

At some point the central temperature rose to 10 million K. The collisions among the atoms were so violent that nuclear reactions began, at which point the Sun was born as a star, containing 99.8% of the total mass.

What prevented further collapse? As the temperature and density increased toward the center, so did the pressure causing a net force pointing outward. The Sun reached a a balance between the gravitational force and the internal pressure, aka as hydrostatic equilibrium, after 50 million years.

Around the Sun a thin disk gives birth to the planets, moons, asteroids and comets. Over recent years we have gathered evidence in support of this theory.
Close-up of the Orion Nebula obtained with HST, revealing what seem to be disks of dust and gas surrounding newly formed stars. These protoplanetary disks span about 0.14 light years and are probably similar to the Solar Nebula.

II. The structure of the disk

The disk contained only 0.2% of the mass of the solar nebula with particles moving in circular orbits. The rotation of the disk prevented further collapse of the disk.

Uniform composition: 75% of the mass in the form of hydrogen, 25% as helium, and all other elements comprising only 2% of the total.

The material reached several thousand degrees near the center due to the release of gravitational energy --> it was vaporized. Farther out the material was primarily gaseous because H and He remain gaseous even at very low T. The disk was so spread that gravity was not strong enough to pull material and form planets.

Where did solid seeds for planet formation come from? As the disk radiated away its internal heat in the form of infrared radiation (Wien's law) the temperature dropped and the heaviest molecules began to form tiny solid or liquid droplets, a process called condensation.

There is a clear relation between the temperature and the weight of the particles that become solid (Why?). Near the Sun, where the T was higher, only the heaviest compounds condensed forming heavy solid grains. In the outskirts of the disk the T was low enough that hydrogen compounds lighter ice particles.

The ingredients of the solar system fell into four categories:

Metals: iron, nickel, aluminum. They condense at T~1,600 K and comprise only 0.2% of the disk.

Rocks: silicon-based minerals that condense at T=500-1,300 K (0.4% of the nebula).

Ices: hydrogen compounds like methane (CH₄), ammonia (NH₃), water (H₂O) that condense at T~150 K and make up 1.4% of the mass.

Light gases: hydrogen and helium that never condensed in the disk (98% of the disk).

The great temperature differences between the hot inner regions and the cool outer regions of the disk determined what of condensates were available for planet formation at each location from the center. The inner nebula was rich in heavy solid grains and deficient in ices and gases. The outskirts are rich in ice, H, and He.

Meteorites provide evidence for this theory.
A piece of Allende meteorite showing white inclusions. The inclusions are aluminum-rich minerals that formed first in the solar nebula. The inclusions are surrounded by material with lower condensation temperatures which aggregated later.

III. Formation of the planets

The first solid particles were microscopic in size. They orbited the Sun in nearly circular orbits right next to each other, as the gas from which they condensed. Gently collisions allowed the flakes to stick together and make larger particles which, in turn, attracted more solid particles. This process is called accretion.

The objects formed by accretion are called planetesimals (small planets): they act as seeds for planet formation. At first, planetesimals were closely packed. They coalesced into larger objects, forming clumps of up to a few kilometers across in a few million years, a small time compared to the age of the solar system (movie).

Once planetesimals had grown to these sizes, collisions became destructive, making further growth more difficult (movie). Only the biggest planetesimals survived this fragmentation process and continued to slowly grow into protoplanets by accretion of planetesimals of similar composition.

After protoplanet formed, accumulation of heat from radioactive decay of short-lived elements melted planet, allowing materials to differentiate (to separate according to their density).
Inner structure of the Earth

Formation of terrestrial planets:

In the warmer inner solar system, planetesimals formed from rock and metal, materials cooked billions of years ago in cores of massive stars.

These elements made up only 0.6% of the material in the solar nebula, so the planets could not grow very large and could not exert large pull on hydrogen and helium gas.

Even if terrestrial planets had hydrogen and helium, proximity to Sun would heat gases and cause them to escape.

Hence, terrestrial planets (Mercury, Venus, Earth, and Mars) are dense small worlds composed mostly from 2% of heavier elements contained in solar nebula.

Formation of jovian planets:

In the outer solar nebula, planetesimals formed from ice flakes in addition to rocky and metal flakes.

Since ices were more abundant the planetesimals could grow to much larger sizes, becoming the cores of the four jovian (Jupiter, Saturn, Uranus, and Neptune) planets.

The cores were sufficiently large (at least 15 times Earth's mass) that they were able to capture hydrogen and helium gas from the surroundings (nebular capture) and form a thick atmosphere.

They became the large, gaseous, low-density worlds rich in hydrogen and helium, with dense solid cores.

Far from Sun (beyond Neptune), in coldest regions of the nebula, icy planetesimals survived (movie). However, the density of the disk was so low that the icy/dusty planetesimals could only grow to the size of a few kilometers. They could not accrete the surrounding gas so they remained like small dirty snowballs. They constitute the family of Kuiper belt comets, a prediction of the theory of the formation of the solar system which was confirmed in 1990.

Pluto does not fit the category of terrestrial or jovian planet -- it is small, like terrestrial planets, but lies far away from Sun and has low density just like jovian planets. In fact, some astronomers believe that Pluto belongs to the family of comets (probably the largest member).

Asteroid belt -- located between Mars and Jupiter -- is made of thousand of rocky planetesimals from 1,000 km to a few meters across. These are thought to be debris of the formation of the solar system that could not form a planet due to Jupiter's gravity. When asteroids collide they produce small fragments that occasionally fall on Earth. These rocks are called meteorites and provide valuable information about the primordial solar nebula. Most of these fragments have the size of sand grains. They burn up in the Earth's atmosphere, causing them to glow like meteors (or shooting stars).

IV. Formation of moon systems

As the early jovian planets captured large amounts of gas, the same process that formed the solar nebula -- contraction, spinning, flattening and heating -- formed similar but smaller disks of material around these planets. Condensation and accretion took place within the jovian nebulae, creating a miniature solar system around each jovian planet (Jupiter has well over a dozen moons!).

``Double planet hypothesis'': the planet and its moon assembled independently at same time from the same rocks and dust. Explains why Earth and Moon rocks are so similar, BUT then iron core content should be the same as for Earth!

The moons formed elsewhere and then captured (``capture hypothesis''). Mars, for example. Other examples of likely captures -- Pluto and Charon, perhaps some of the jovian moons and moonlets (movie).
Mars' moons: Phobos and Deimos
Pluto and Charon

Giant impact of large body with young Earth explains Moon's composition (movie).

V. Evolution of Solar System

The Sun, planets, moons, comets, asteroids are believed to form within 50-100 million years.

Once nuclear burning began in the Sun, it became a luminous object and cleared nebula as pressure from its light and solar wind pushed material out of Solar System.

Planets helped to clean up by absorbing some planetesimals and ejecting others.

Some of the planetesimals collided with the planets, causing craters or major effects. Neptune's axis tilt may have been caused by a large impact. The Earth was probably hit by a Mars-size object, ejecting debris that coalesced to form the Moon. The vast majority of the impacts occurred in the first few hundred million years.

Gravitational encounters with the planets ejected other planetesimals to remote parts of Solar System.

Once Solar System was mostly clear of debris, planet building ended. Today, all solid surfaces scarred by craters from meteorite impacts (movie). The scars can be seen on the Moon, but erosion and geological processes on Earth have been erasing the craters.

Impacts still occur at a lower rate (65 million years ago, an asteroid or comet impact is thought to have caused the extinction of 90% of the species on Earth).

Venus, Earth and Mars acquired their atmospheres at later stages in formation of Solar System:

The early bombardment brought some of the materials from which atmospheres and oceans formed in the terrestrial planets. These compounds arrived in the inner planets after their initial formation, most likely brought by impacts of planetesimals formed in the outskirts of the solar system (Q: What was Jupiter's role in bringing water to Earth?).

Outgassing (from gas blown out of volcanos) is another likely source for atmosphere's formation.

On Earth, oxygen, essential to animals, was produced by plants breaking down CO₂.

Rings around giant planets, such as Saturn's, are probably result of stray planetesimals being torn apart by gravity when they ventured too close to planet (movie).