Paul O. Hayne
Planets form through a process of accretion of gas and dust within circumstellar disks, which are made of raw materials condensed from the protostellar nebula. The nebula itself begins as a relatively dense fragment ("core") collapsing under self-gravity from within a larger molecular cloud, composed primarily of hydrogen gas (H$_2$). After H, the next most abundant element is He, followed by O, C, N, Ne, Mg, Si, Fe, S, Ar. These are the raw materials from which stars and planets form (Fig. 1).
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Figure 1: (Left) Hubble Space Telescope (HST) image of star-forming region NGC 2174 in the Orion nebula, showing several likely protplanetary disks and young stars. (Right) "The Astronomer's Periodic Table", showing the most cosmically abundant elements, from which stars and planets form.
Not just any combination of these elements comes together to make planets. Only certain compounds occur in nature with any appreciable abundance:
\begin{align} \mathrm{H,~He} &\rightarrow~\mathrm{\textbf{Gas}: H_2,~He~~~ (\textit{gas})} \\ \mathrm{H+(C,~N,~O)} &\rightarrow~\mathrm{\textbf{Ice}:~H_2O,~NH_3,~CH_4~~~ (\textit{solid, liquid, gas})} \\ \mathrm{O+(Mg,~Si,~Fe,~...)} &\rightarrow~\mathrm{\textbf{Rock}: SiO_2~(quartz),~Mg_2SiO_4 (forsterite),~Fe_2SiO_4 (fayalite),~...~~~ (\textit{solid, liquid})} \\ \mathrm{Fe,~Ni,~...} &\rightarrow~\mathrm{\textbf{Metal}: Fe,~Ni,~...~~~ (\textit{solid, liquid})} \end{align}In our Solar System, gas and ice make up the bulk of the jovian planets, whereas the terrestrial planets are dominated by rocks and metals. This difference is mostly due to their relative locations in the protoplanetary disk: very little ice condenses in the inner Solar System, and the planetary embryos do not grow large enough to accrete H and He gas before it is dissipated by the solar wind. Further away from the Sun, ice accretes along with the rock to form much more massive cores ($\sim10\times$ Earth mass, $M_\mathrm{E}$). These cores are large enough to accrete substantial H and He gas before it is cleared.
Once the nebula begins to collapse, planet formation is a relatively rapid process. Below are the essential stages and their approximate timescales. Note that planet formation is not well understood, and the information here is a sketch of the accepted model. Research in this area is active, using both models and new observations of protoplanetary disks around other stars.
During the contraction phase, the initially diffuse nebula collapses under its own gravity. In order to conserve angular momentum, particles increase their orbital speed as they move inward toward the center of mass (the protostar). Gas drag damps motion out of the mid-plane, especially for larger particles; the settling time is only $\sim100$ yr for a particle orbiting at 1 AU. The edge of the disk is not well defined, but beyond a certain distance ($\sim$200 AU in the Solar System), particles do not experience efficient damping to the midplane, and their dynamical interactions are too slow to accrete planets.
The minimum mass solar nebula (MMSM) is a disk whose mass and composition match the observed masses, compositions, and current orbital locations of the planets. It is composed of 98% H+He, 1% C+N+O, and $<$1% Mg+Fe+Si. Protoplanetary disks such as the MMSM are often described by an initial surface density:
\begin{equation} \Sigma = C\left(\frac{a}{\mathrm{1~AU}}\right)^{-3/2} \end{equation}where $C \sim 10^4$ kg m$^{-2}$ is a constant, and $a$ is the orbital distance from the star. The total mass of the MMSM is $\sim 0.01 - 0.1M_\mathrm{Sun}$, of which only $\sim$1% is composed of "dust" (ice, rock, metal); the rest is gas (H, He).
Once most of the dust and gas has settled to the midplane, particles begin to grow by: 1) direct condensation of gas, and 2) coagulation of smaller ($< 1~\mu$m = 10$^{-6}$ m) to larger particles. This period is characterized by slow, but regular growth as particles bump into one another on their orbits of the central star. In the inner disk, temperatures are higher due to heating of the gas by the star, and only rock and metal condense. Beyond an imaginary boundary called the frost line (or the snow line), the major ices can condense: H$_2$O (water), NH$_3$ (ammonia), CH$_4$ (methane). Hydrogen (H$_2$) and helium (He) gases do not condense anywhere in the disk.
Gravitational interactions cause smaller particles to be consumed by larger particles, which leads to steady growth called accretion. In the inner Solar System, only rock and metal are accreted. In contrast, beyond the frost line, ice is accreted by planetesimals that will eventually become the jovian planets.
The sizes of the protoplanets depends on their feeding zones, determined by their gravitational sphere of influence, or the Hill radius:
\begin{equation} r_H = a\left(\frac{m}{M_*}\right)^{1/3} \end{equation}where $m$ is the mass of the protoplanet, and $M_*$ is the mass of the star. (Where does this formula come from?) As the protoplanet revolves around the star, this Hill sphere sweeps out a well-defined region, which contains an amount of material known as the isolation mass. Once a protoplanet reaches the isolation mass, its growth is limited, because it has exhausted its feeding zone.
Accretion proceeds in three somewhat distinct phases:
Note: There is still considerable debate about the timescales and details of the accretion phase. For example, simulations have only recently succeeded in preventing meter-sized planetesimals from spiraling into the star (due to gas drag) before forming planets. The resolution seems to lie in turbulence and shear in the disk, which create vortices and knots of material, trapping particles long enough to grow.
During the final stages of planet formation, stellar wind and radiation from the newly formed star clears any remaining gas and dust, while the planets tug and pull one another. Remaining debris (material too small or dispersed to form planets) up to $\sim 100$ km becomes asteroids (rocky bodies) in the inner disk and comets (icy bodies) in the outer disk. Both asteroids and comets are sometimes perturbed by the giant planets, bringing their orbits on collision courses with the planets. Bombardment of both terrestrial and jovian planets is an important process in the final stages of accretion, which accounts for radial mixing of materials in the disk. Planetary migration is also possible: in the Solar System, orbital resonances among the giant planets probably caused Neptune to migrate outwards by $\sim10$ AU during this period. In the so-called Nice model (named for the location in France where the theory was developed), this reorganization of the planets led to a massive influx of small bodies (comets and asteroids) to the inner solar system - the "Late Heavy Bombardment" (LHB). There is still some debate about the timing and magnitude of the LHB, which may have occurred around 3.9 billion years ago, based on evidence from lunar rock samples collected by Apollo astronauts.
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Figure 2: Schematic of plantary formation, from the contraction of a diffuse molecular cloud to the accretion and dynamical evolution of planets. (Adapted from: The Cosmic Perspective, Pearson Publishing)
Temperature in the protoplanetary disk decreases with distance from the star. Inside of the frost line, only compounds with high melting points are stable: these are the refractory compounds, including most rocks and metals. Beyond the frost line, volatile compounds (often simply called "ices") remain in the solid phase. Each "ice" compound has its own frost line, depending on its condensation temperature: H$_2$O ($\sim$150 K), NH$_3$ ($\sim$100 K), CH$_4$ ($\sim$50 K). In our Solar System, the water frost line (often called the frost line) occurred around $\sim$3 AU, near the outer edge of the present-day Main Asteroid Belt. This is why the jovian planets are more massive and contain substantially more volatiles. It also explains their array of large icy moons.
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Figure 3: The frost line is the location in the protoplanetary disk where the temperature indicates the condensed phase of a given compound (e.g., H$_2$O) is stable. Beyond that imaginary line, the compound is solid, but closer to the star, and it must be gas. In the case of water, our Solar System's frost line occurred around 3.0 AU, near the present-day asteroid belt. (Right panel adapted from: Barshay and Lewis, 1976)
The inner part of the disk was relatively dry, yet the terrestrial planets clearly contain some water. A large fraction of this was probably delivered after these planets formed, during the clearing phase and Late Heavy Bombardment. After a planet forms, its atmosphere can change due to:
We will cover the details of these secondary processes in later sections.