Level 4: Structure — \(2\text{M}\) years
Elements
Size: \(300 \text{pm}\)
Initial state: Light atoms and molecules (first period)
Production process: Stellar nucleosynthesis
Meta-stable equilibrium: Heavy atoms
Stable future: Iron-56 nucleus
Cosmic foam
Size: \(100 \text{MPc}\)
Initial state: Matter-dominated, transparent universe
Production process: Gravitational collapse
Meta-stable equilibrium: Large-scale structures
Stable future: Distorted structural ruins
We have left the universe in the darkness that characterized its early times in the matter-dominated era. But we know that is not how the universe looks today. What we see when we raise our heads are countless stars! As observations have improved, humans could distinguish that those stars make up distinct galaxies, which in turn assemble into groups, clusters, superclusters, and lastly filaments. All of this fractal organization amounts to what we may call a cosmic foam: at each scale, denser and more complex areas form a thin lineament around enormous voids.
In terms of our levels of organization, (4\(\Omega\)) is indeed zooming from the whole matter-dominated universe (which, remember, is not a snapshot, but a spatiotemporal extension) to that "foam", i.e. to the multiple large-scale structures that appear within that object.
It’s important to note that, even though we’ll evoke smaller objects, like the first stars or quasars in this section, the reference scale is still larger, since those structures are more temporary, and the ones we want to "zoom" on later, such as our Sun and it planetary system, are a different breed of astral objects, born in galaxies, which will be the object of our next section.
The dark epoch : \(2 \text{M}\) to \(100 \text{M}\) years
The main storyline of structure formation might seem quite intuitive: with gravitation now the dominant force, matter gathers into dense clumps, to a point where it can collapse into a ball that’s hot enough to trigger nuclear fusion... aka, a star.
But the details are far from obvious: some matter clouds can be stelliferous, while others will never be. Galaxies only seem to exist within a narrow size range. Protostars can only evolve under specific conditions...
To gain some fascinating insights into this topic, we need to delve in basic thermodynamics. It is quite remarkable that equations and analytical methods that were developed to study steam engines in the nineteenth century can be almost directly ported to to the study of primordial gas clouds in the early universe! Although some of the inputs (like the gas cooling rate) incorporate results from quantum mechanics, the general concepts are the same as in classical studies of thermal systems.
Where did we stand right after recombination, when the world went dark? The contents of the universe were as follows:
Radiation was mostly made up of the products from neutrino and photon decoupling. The latter, the Cosmic Microwave Background had already been redshfited deep into infrared territory by that point.
Matter had settled into a ratio of about 3/4 dark matter to 1/4 ordinary matter.
Since dark matter is not subject to electromagnetic interaction and cannot find itself in a thermal equilibrium with radiation, as hadrons and leptons had, its behavior had been dominated by gravity for a long time. As we’ve seen, the tiny quantum fluctuations that had been blown up by inflation could then act as gravity wells for dark matter, in what would later become the filaments that make up the cosmic foam.
After decoupling, ordinary matter found itself dominated by gravity for the first time, and started to concentrate in these filaments. As we’ve seen, it had settled into a cold, gaseous molecular cloud of mostly dihydrogen, plus some helium.
Dark energy, a cosmological constant term representing the energy from a constant curvature term, cannot be neglected at the cosmic level (it is the reason the universe is near-flat), but doesn’t have any local impact on structure formation.
The dark epoch has elapsed in that monotonous way, a story of cooling and accretion. Right after recombination, the amplitude of overdensities was still very small for regular matter (around \(10^{-6}\)), but much larger already for dark matter, since accretion was already well on its way (on the order of \(1000\)).
Now that we’re looking at longer timescales, it is crucial to take into account that the universe is expanding. It can be summed up with one figure, the scaling factor \(a\), which effectively dilutes distances. Another metric is often used: the redshift \(z\), whose decrease follows the decrease in frequency of a free photon in the expanding universe. For high values, it moves in inverse proportion to the scaling factor: \(a= (1+z)^{-1}\).
The scaling factor itself, in a matter-dominated universe, increases with time following a power law: \[a \propto t^{2/3}\]
\(a\) being a scaling factor, it is expected that the average density evolves as: \(\overline{\rho} \propto a^{-3}\), since it can be seen as the ratio of a constant mass over and increasing volume.
Interestingly, we can also demonstrate that small over-densities (roughly, below \(1\)) evolve linearly with \(a\): \[\frac{\delta\rho}{\overline{\rho}} \propto a\]
At the start of the dark epoch, dark matter is already way beyond that point. But although we’ll focus on ordinary matter structures in this section, it is interesting to rewind and observe what happened to dark matter. Indeed it’s a simpler version of what occurs for ordinary matter, which crucially has the extra ability to react electromagnetically and from a nuclear perspective.
For any volume in the universe (a "cloud" of dark matter), we start with a certain average density and temperature, as well as local perturbations. Then what? The key point, which is the bedrock of structure formation and of all astrophysics really, is as follows: what determines the evolution of any cloud is the balance of power between two opposite actions:
Gravity pulls stuff in: it acts as an attractive force, and over-densities naturally tend to draw everything around them.
Pressure pushes stuff out. In the case of dark matter, the dynamics are collisionless: there are no shocks between particles; however there is gravitational scattering.
We can prove rigorously, but also understand intuitively that, all else being equal:
When the temperature \(T\), the measure of thermal agitation, increases, pressure wins out.
When the density \(\rho\) increases, the cloud’s mass increases and gravity wins out (that is because the cloud’s gravitational energy is about a mass interacting with itself, a \(\rho^2\) term, whilst thermal energy is a linear function of density).
When the length of the cloud \(L\) increases, the volume, and thus the mass of the cloud also increases, and gravity wins out.
For a spherical cloud of diameter \(L\), density \(\rho\) and temperature \(T\), we can define a Jeans parameter, with \(m\) the mass a single gas molecule or atom: \[J = L \sqrt{\frac{G\rho m}{ k T}}\]
When \(J<1\), pressure wins, and the cloud settles in an oscillating state, with pressure waves similar to the ones from acoustic phenomena. When \(J>1\), gravity wins and the cloud experiences collapse: it starts getting continuously smaller and denser.
Equivalently, we can consider the characteristic times for each process. Considering gravity (and ignoring pressure), the free-fall time \(t_{ff}\)(the time it would take for particles on the edge of the cloud to reach its center) defines the scale of the collapse’s timeframe.
\[t_{ff} \approx \frac{1}{\sqrt{G\rho}}\]
Considering pressure (and ignoring gravity), the "speed of sound" \(c_s\) represents the speed of pressure waves in the gaseous medium:
\[c_s \approx \sqrt{\frac{P}{\rho}} = \sqrt{\frac{kT}{m}}\]
The "sound-crossing time" for a cloud of length \(L\) is:
\[t_{sc} = \frac{L}{c_s} = L \sqrt{\frac{m}{KT}}\]
We can see that
\[J=\frac{t_{sc}}{t_{ff}}\]
If the free-fall time is shorter than the sound-crossing time: \(t_{ff}<t_{sc}\), then the cloud collapses faster than the medium is able to redistribute the pressure via "sound waves"; indeed, \(J>1\).
What happens concretely? It’s probably best to work with a simple numerical example to understand the various forces at play.
The first time that structures can form is when dark matter decouples from all forms of radiation and is only influenced by gravitational forces. Of course, we don’t know what dark matter is. For illustration, let’s make one hypothesis that is at least plausible, and assume dark matter is made of supersymmetric neutralinos of mass: \[m_{\tilde{N}^0_1}=1000 \text{GeV/c}^2= 1.7\times 10^{-24} \text{kg}\]
For ordinary particles, decoupling happens when they stop absorbing and emitting photons, so much so that there can be no thermal equilibrium with photons. Of course, dark matter never interacted with photons in the first place. Decoupling simply means that it stops transforming into other particles and becomes inert from the point of view of all interactions except gravitation.
This happens very shortly after the end of cosmic inflation. For the sake of argument, let’s start from there. So early after the Big Bang, it is clear that basic calculations straight out of Newtonian physics are a shamefully rough approximation. Yet remarkably, this approach provides a perfectly valid picture of the structure formation process, at least as a "toy model".
In cosmology, we can extrapolate long-past values of the main thermodynamic parameters using the relations we’ve already mentioned between \(t\), \(a\), and \(\rho\). We can add the temperature \(T\), a length \(L\) and a volume \(V\) to that group.
\[\begin{aligned} a \propto & \quad t^{q} \\ L \propto & \quad a \\ V \propto & \quad a^3\\ T \propto & \quad a^{-1}\\ \rho_{\text{m}} \propto & \quad a^{-3} \end{aligned}\]
For the radiation-dominated era, \(q=1/2\), but when matter dominates, \(q=2/3\). What I’ve called \(\rho_\text{m}\) is the density of matter (either ordinary or dark).
Through observation, we know what these values are for the observable universe today, \(13.8\) billion years after the Big Bang. In the below, we call \(L_\Omega\) the diameter of the observable universe (we don’t know the size of the whole universe and it might very well be infinite). \(\rho_{DM}\) is the density of dark matter specifically (3/4 that of all matter).
\[\begin{aligned} t =& \quad 13.8 \text{Gy}\\ a =& \quad 1\\ L_{\Omega} =& \quad 31 \text{Gpc}\\ T =& \quad 2.7 \text{K}\\ \rho_{\text{DM}}=& \quad 2.2 \times 10^{-27} \text{kg/m}^3 \end{aligned}\]
Now, we can use the formulas above to "rewind" to any point in time and get the approximate value of those parameters. We’ve assumed that dark matter decoupled right after cosmic inflation ends. We know that happened roughly \(10^{-32}\text{s}\) after the Big Bang and can deduce the other parameters.
\[\begin{aligned} t =& \quad 10^{-32}\text{s}\\ a =& \quad 2 \times 10^{-26}\\ L_{\Omega} =& \quad 19 \text{m}\\ T =& \quad 1.4 \times 10^{26} \text{K}\\ \rho_{\text{DM}}=& \quad 2.7 \times 10^{50} \text{kg/m}^3 \end{aligned}\]
The observable universe was just a volume nineteen meters wide at the time, of course incredibly dense, since all the matter now in large-scale structure was tightly packed in that volume.
For now, let’s assume the distribution of matter and temperature to be entirely homogeneous. Since \(\rho\) and \(T\) are then given, we can compute the Jean length, the minimum cloud size \(L_J\) for which \(J>1\).
\[\begin{aligned} L_J =& \quad 0.48 \mu\text{ m}\\ M_J =& \quad 62 M_\odot\\ t_{ff} =& \quad 1.5 \times 10^{-20} \text{s} \end{aligned}\]
The outcome is that \(L_J\) is less than a micron. Despite the small size of the observable universe at the time, the possibility of cloud collapse is there. Good news for us: complexity could never emerge if the universe’s matter just settled in an eternal oscillating state; it would be the end of our story. The corresponding cloud mass is \(62\) solar masses.
Cloud of size roughly \(L_J\), called proto-haloes then start to separate and attract the matter around them, all the while collapsing. We have computed above the characteristic free-fall time of \(1.5 \times 10^{-20} \text{s}\): it is huge as compared to the age of the Universe at that point, but of course infinitesimal compared to what we know of actual structure formation. What gives?
In a gravitational collapse, the cloud’s radius diminishes in \(\cos (t/t_ff)\). This means that originally \(L_{halo}\) decreases very slowly. But all the while, the universe expands, which mechanically makes \(L_{halo}\) bigger. The halo’s enlargement from cosmic expansion massively outweighs the halo’s diminution from gravitational collapse. This means that the halo’s density diminishes (in \(1/L^3\)) and that \(t_{ff}\) recedes in the future (it increases in \(L^{3/2}\)).
Gravitational collapse is playing catch up with cosmic expansion for a long, long time!
A quick numerical simulation shows that, taking only graviational energy into account, the halo’s size peaks at \(0.8\) parsec, then complete collapse happens around \(t=2.8\text{Myr}\), almost three million years after its start. Of course, in a physical situation, complete collapse (such that could give rise to a black hole) does not necessarily happen, and the halo usually virializes (reach thermal equilibrium again due to pressure forces).
That does not sound right either. From actual over-densities in ordinary matter, we know that dark matter must have formed structures already before photon decoupling, creating the gravity wells that would later welcome ordinary gas.
The big assumption we’ve made is that dark matter distribution was quasi-homogeneous. What we observe today shows it cannot have been: quantum fluctuations from the quantum gravity era have likely been frozen in the inflation process, generating energy clumps that immediately translated into over-densities after dark matter decoupling.
These over-densities are generally represented as a gaussian random field: local over-densities of all scales exist (\(10^{-6}\), \(1\), \(10^{6}\)...), but the higher the over-density, the rarer and smaller the corresponding volumes are.
We can see that there is an interplay with the Jeans length. Consider an extreme over-density of one million. There are a large number of such over-dense areas (\(\rho>10^{6} \overline{\rho}\)), but their median volume is tiny. The Jeans length for a dense area is much shorter than for an average area, but whatever its value it still acts as a cut-off: most over-dense volumes as too short and will just dissipate via thermal equilibrium; some of them, however, are large enough to undergo gravitational collapse.
Naturally, the free-fall time is shorter, the larger the over-density is. Before, we’ve simulated an effective free-fall time of two million years, starting with no over-density at all. For a Jeans volume with over-density \(1\) starting in the same era, the effective free-fall time is \(166,000\) years. For an over-density of \(100\), it is only \(8,000\) years.
We don’t know exactly the nature of the initial over-density distribution, and if it is indeed Gaussian, we don’t know its characteristic parameters. But we can see qualitatively that a bottom-up scheme is promoted here:
Tiny, hyper-dense regions undergo a quick collapse, and virialize into an even tinier halo.
Larger, denser regions undergo a slower collapse, resulting in larger halos.
On a very large scale, there’s almost no over-density and the parameters of the collapse correspond to our homogeneous scenario.
It’s important to understand that haloes of different sizes are not distinct regions of the universe. It’s a Russian doll system where the tiny haloes are born within larger ones. What we’ve been describing as the thermodynamics of a gas cloud can perhaps be more usefully represented in terms of gravitational mechanics: smaller haloes (dense clumps bathing in a less dense gas) start attracting each other and slowly coalescing, thus creating an over-density over a larger area, boosting the accretion of the surrounding gas, and accelerating the collapse.
When the dark ages start, at the two million-year mark, we can then expect that dark matter as a whole is virialized and that structure formation is more of less stabilized: the cosmic web structure is then already extremely mature. We’re facing the following structures then:
Over-dense regions where dark matter has accrued appear as large surfaces called walls (thus called because today they appear like a wall of galaxies. The largest wall in our observable universe is about 3 billion parsecs wide).
Regions where walls intersect are called filaments.
Regions where filaments intersect are the future loci for galaxy clusters.
Volumes inside the space delineated by the walls are simply called voids.
We have seen that ordinary matter fully decoupled at the start of the golden epoch. Whatever the original over-density distribution, it would be impossible to reach current over-density levels for ordinary matter if dark matter didn’t exist. The gravitational inhomogeneity from the cosmic web leads ton an incommensurable acceleration of that process: hydrogen and helium just slide into pre-existing gravity wells.
Ordinary matter follows the same type of evolution as was just described, , grounded in the gravity/pressure balance, with a major difference: ordinary matter can cool through the dissipation of energy. All that dark matter can do is to swap its thermal agitation for gravitational energy. But an ordinary gas, when dense enough, can also dissipate energy via radiation, thanks to its interactions with the electromagnetic field. Simply put, the kinetic energy of ions, atoms or molecules can be carried away by a photon!
For effective cooling to take place, pressure and temperature need to be high enough, so ordinary matter doesn’t radiate at all when it first starts accreting into the dark matter structures. And when it does, the resulting photons are not in the visible spectrum, so "cosmic dawn" is not on yet!
The cosmic dawn epoch : \(100\) to \(250 \text{M}\) years
At first, cooling then has little impact, and ordinary matter doesn’t behave very differently from dark matter. As density increases, however, the cooling rate becomes more and more significant, and more energetic photons are emitted, resulting in a warm ambient light around the dark matter filaments: that is cosmic dawn.
Just like the free-fall time is a characteristic yardstick for gravitational collapse, we can now define a cooling time \(t_{cool}\). It is inversely proportional to the cooling rate (which only depends on temperature), but also to the gas density. In addition, the cooling rate and cooling time depend on the chemical composition of the gas.
If we consider a Jeans cloud of ordinary matter, its collapse will then largely depend on the cooling time:
If \(t_{cool}>>t_{ff}\): cooling is not important and can be ignored: the cloud evolves like a similar cloud of dark matter.
If \(t_{cool}>t_{ff}\): cooling cannot be ignored. As pressure increases, temperature is not as high as in a dark matter scenario, due to dissipation. This accelerates the collapse (\(t_{ff}\) does not depend on the temperature because it’s a theoretical metric that ignores pressure; thhe actual collapse time depends on it). However cooling is slow enough that the system always finds itself in thermic equilibrium.
If \(t_{cool}<t_{ff}\): cooling is catastrophic. Temperature drops fast on a time scale shorter than the collapse time. The Jeans length then decrases too, and the gas quickly clumps into smaller and smaller, denser and denser volumes.
Thus, the composition and characteristics of an ordinary matter cloud strongly determine its history. Dissipation-less dark matter is much more amorphous: the density distribution can determine the pace and order of structure formation, but the landing zone is known. For any given pressure/density couple, there is a certain volume which will collapse, and then on the long run, aggregates with others, etc. For a molecular cloud, the pressure and density similarly determine a Jeans length, but also a cooling time which influences everything that follows.
At the start of the dark epoch, the gas cloud is too cold for cooling to be efficient, at around \(1000\text{K}\). As it gravitates to the dark matter structures over dozens of millions of years, temperature, pressure and density increase, up to a point when the cooling time of some volumes becomes shorter than their free-fall time.
High-density cores then start appearing, accreting more and more matter, some of them becoming the first proto-stars. As I had mentioned, dark matter only interacts gravitationally, whilst ordinary gases are subject to all four interactions: electromagnetism (e.g. through dissipation), the weak nuclear force (but we know that one is short-range only), and the strong nuclear force.
The strong interaction is now ready to make a comeback! Some protostars never fullfil their destiny and just become brown dwarves (hot astral bodies in a long thermal equilibrium). But some become stars: very hot, very luminous astral bodies that are characterized by nuclear fusion.
As the protostar’s gravity is "pushing in", temperature is rising dramatically, even as cooling is preventing it from becoming too high (which would disperse the matter back into a volatile hot cloud). The star is now a "time machine" that brings us back to previous states of matter in the universe: first, \(\text{H\_2}\) molecules dissociate; then, electrons break free, turning the gas into a plasma of protons and helium nuclei. Finally, the temperature gets high enough that fusion starts. With a similar process to that of the primordial nucleosynthesis, hydrogen nuclei start to turn into helium.
These primordial stars are called (confusingly) "Population III" stars. Although their initial mass is a strong determining factor of their lifecycle, stars’ formation involve more complex factors than the simple cloud dynamics we’ve evoked in this section, such as magnetic fields, angular momentum, etc.
Although that is still a very speculative area of research, those primordial stars are believed to have been super-massive, at least one thousand solar masses, and thus short-lived, going through their lifecycle in a matter of a few million years.
Unlike today’s massive stars, which morph into giants and produce heavier elements like carbon or oxygen in a stable fusion reaction, it is thought that primordial stars undergo complete core collapse before they’ve moved to that phase.
The specific collapse that’s suspected to happen is called "pair instability" and happens when electron-positron pair productions temporarily reduce the radiation pressure, resulting in a sudden and irreversible "win" for gravity. The star implodes, and the sudden burst of energy results into accelerated nuclear fusion that produces heavier elements (for primordial stars: up to iron, but not heavier). Those then get ejected into a diffuse nebula following an explosion, called supernova, leaving behind a neutron star or a spacetime singularity called black hole.
Coming back to our specific case: a few million years into the cosmic dawn epoch, a first generation of primordial start must have come and gone. Even though neutron stars and black holes do take away some density from the molecular cloud the process still continues. The ambient chemical composition is changing enough, though, that a new type of stars may emerge.
In astronomy, metallicity designates the relative density of elements heavier than helium. Primordial stars had quasi-zero metallicity, but the fusion process that stems from their explosion peppers heavier elements in the molecular clouds, resulting in new stars with higher and higher metallicity in some areas.
When that metallicity reaches \(10^{-5}\) (for comparison the metallicity of our Sun is around \(1\%\)), the resulting star is deemed to be part of Population II. Because chemical composition affects the cooling function and multiple nuclear processes, these stars are smaller and longer-lived than primordial stars. Both populations have kept developing in a positive feedback loop.
The reionization epoch : \(250\) to \(400\text{M}\) years
Hower, that equilibrium was to be broken in a key, if still poorly understood, event: re-ionization.
You remember that ordinary matter had become neutral when the universe’s baryonic content turned from an ionized plasma (an electron, nuclei and photons "soup") to a gas of neutral atoms or molecules.
During cosmic dawn, the inside of stars has reverted to a plasma, but the giant surrounding cloud is still molecular. About a quarter billion years after the Big Bang, that is changing however, as the high-energy photons from the billions of hyper-luminescent Population II and III stars are re-ionizing the molecular gas.
A key difference with earlier events is that the original "de-ionization" made the universe transparent, but this re-ionization is not making it opaque all over again: in the meanwhile it has expanded enormously. Ordinary matter can then be back to a plasma state, but it is not dense enough to meaningfully interact with photons, which thereby stay free.
A direct consequence, however, is the end of the first stelliferous era. Re-ionization makes cooling very inefficient, both by virtue of the higher temperature (remember, cooling is efficient within a "sweet spot", and neither at very high nor very low temperatures), and of the medium’s composition (molecules cool much better).
The former molecular cloud then settles into a hot plasma state that doesn’t cool, whose Jeans length is very large, and whose free-fall time is very long (billions of years). This is enough to hinder star production for the time being.
The stable future
The small-scale structures at Level 4 are heavy nuclei and atoms. We had already discussed the fact that no nucleus is truly stable in the very long run, save for Iron, which then constitutes the sole stable state.
Heavier elements are either radioactive (and become lighter through beta decay), or can still undergo \(\alpha\) decay, double-beta decay or spontaneous fission, all extremely infrequent nuclear processes. Elements lighter than Iron can undergo cold fusion to grow heavier. The point of convergence of either process is Iron-56, which cannot undergo a fusion nor a fission.
The large-scale structures from Level 4, which make up the cosmic foam, also have a clear end state, which is simply their demise. Continued expansion of the universe combined with the inevitable increase in entropy entails that the gravitational liens that keep matter tightly knit will stretch to a point where any hint of a structure becomes undetectable. Technically, over-densities will still exist, since expansion will prevent entropy from fully re-homogeneizing the universe’s matter content. But such structures will be loose, decaying, distorted ruins of what they used to be.
Level 5: Systems — \(400\text{M}\) years
Molecules
Size: \(0.6\text{nm}\)
Initial state: Heavy atoms
Production process: Cosmic chemistry
Meta-stable equilibrium: Heavy molecules
Stable future: Noble gases and most stable molecules.
Galaxies
Size: \(50 \text{kPc}\)
Initial state: Large-scale structures
Production process: Galactogenesis
Meta-stable equilibrium: Galaxies
Stable future: Sterile gas haloes
Level 5 is set under the sign of systems. That surely seems very generic and deserves some explanation. As we’ve moved up on this ladder of levels, more and more complexity has developed. Granted, an Iron atom is certainly a complex systems of quarks and electrons. But here we focus on the macroscopic \(\Omega\) level: the mesosphere, where the production of the higher levels is brewing. Up to Level 3, the theater of operations was still universal, with the cutoff still spatiotemporal in the broadest sense: the matter-dominated 4D universe is formally included in the most general post-Big-Bang higher-dimensional universe, yes. But for denizens of the epochs described in Level 3, the higher dimensions and past epochs were inaccessible. The mesosphere was then not a specific identifiable object that entities may be in or out of, but the whole world at that point. Level 4 is somewhat intermediary: it was significantly labelled as the level of structure, and not of structures. As much as we can try to divide the cosmic foam into clusters, walls and filament, we’re still talking about one ur-object, not easily dividable into a coalition of smaller ones.
At Level 5 there is marked change, since the new focus will be on clearly identifiable ordinary objects: galaxies. What makes each of them singular is not just their composition or physical characteristics, in which case two galaxies near enough to each other could be deemed to form the same "stuff"; instead it is the distinction between inside and outside, and the feedback processes governing their relationship that make a galaxy a individual complex system. There is a clear distinction, beyond sheer scale, between a galaxy (assemblage of stars and gases) and a cluster (assemblage of galaxies). The latter is a mere set of objects that are mechanically and thermodynamically connected to each other, without the self-perpetuation feedback loops obeserved in galaxies.
Systems, which are familiar to us from our experience of many other levels, as we’ve seen, can then be deemed an emerging quality. Systems will make the production of more and more complex entities in successive mesospheres possible. Galaxies, solar systems, biosopheres, etc. will form more and more hospitable havens where the march of entropy is temporarily halted, even reversed. Galaxies are a perfect example. Although the universe as a whole is very cold (less than \(3\text{K}\)), galaxies are not hot spots in a uniformly cold environment. They are a cold spot in the high-energy furnace that is cosmic gas after re-ionization. Voids within the cosmic foam are cold, too cold and empty to see anything interesting emerge. But the reionized foam itself is scorching, its particles to energetic to allow even molecules to form. Galaxies provide us with the best of both worlds: dense enough but cold enough that stars can form in a consistent way over many generations, without hindering their own birthrates, like the first populations did.
The galactic epoch : from \(400\text{M}\) years
Our definition of epochs is also changed compared to how we’ve proceeded so far. Cosmic dawn, or reionization, were definite spans of time with a beginning and an end, both in our past. The galactic epoch has not ended. And even though we will attempt to predict their demise, there is no set date we can assign.
When we last discussed the state of the universe, it was being fully ionized by the radiative activity of its stars, quasars and black holes, while frequent super- or hypernovae kept exciting even further this already hot brew. Star formation found itself completely hindered, and the story of complexity in our universe could well have ended right there, with a hot plasma soup, slowly cooling down for eternity.
Luckily, this didn’t come to pass. How, then, did we get out of this ionized trap? At temperatures between \(10^6\) and \(10^7\text{K}\), cooling is highly inefficient, and Jeans volumes the size of our current clusters collapse at free-fall time scales, over hundred of billions of years. In fact, this is the collapse process that clusters are still going through right now! It will never come to fruition though, since we’ve seen that universal expansion will bring about structural ruin much earlier...
How did smaller structures emerge, then. The key reason is chemical enrichment. Before the first stars, the universe was only hydrogen and helium. Towards the end of reionization, metallicity rates are still low (below \(10^{-4})\)), but every little helps, as far as cooling is concerned. Not only is cooling efficiency positively correlated with metallicity, heavier elements tend to coalesce into dust particles, and "dusty clouds" cool even more efficiently than clouds that are chemically similar on average but made of a homogeneous gas.
Of course the metallicity and dust distribution is far from homegeneous: novae, winds, and general thermal agitation have spread heavier elements randomly. We find ourselves with a similar gaussian distribution as previously when we considered dark matter haloes, except that this time, we’re interested in both mass density and chemical composition.
For a given density, metallicity and temperature, there is a Jeans volume within which a cooling-supported collapse could happen. Such volumes start cooling rapidly, becoming proto-galaxies.
At the time these objects formed, star formation rates were severely depressed, but there were still lots of Population II stars around. Early galaxies were then made of hot, but quickly cooling, ionized gas, as well as population II stars and other objects (most current galaxies seem to be endowed with an active galactic nucleus (AGN), in practice a giant quasar or a supermassive black hole).
The formation process of galaxies is complex, as it involves thermic, mechanical (angular momentum in particular) and chemical effects vastly beyond the reach of this quick overview, and is still an active topic for research. These effects’ interplay leads to the familiar shape of galaxies, spiral (like our Milky Way), elliptical or lenticular.
As the gas inside a galaxy cools, the collapse of small, dense clumps accelerates, and star formation rates pick up again! Galaxies act as cosmic nurseries!
A galaxy is not like a biological cell and doesn’t have a clear membrane separating it from the outside. The change of medium is observable in terms of phases. We can recapitulate the different mediums in the cosmic foam after the first generation of galaxies has formed:
The Intergalactic Medium (IGM) is the same reionized gas that was pervasive in the cosmic foam before galaxies first appeared. It still represents 90% of the universe’s ordinary matter. It is then a hot ionized gas (\(10^5\) to \(10^7\text{K}\)) of mostly hydrogen and helium, with small amounts of dust. Its density is low at less than 1 atom per \(\text{m}^3\).
A subset of the IGM, the Intracluster Medium (ICM) is even hotter, at \(10^8\text{K}\). It is a byproduct of galaxy formation since the ejection of gas following supernovae, and of radiation from stars and other bodies, can heat up the IGM, and make it denser (about \(1000\) times more). The more galaxies, the more gas and radiation coming out, so the ICM, as the name suggests, is primarily present within galaxy clusters.
The Interstellar Medium (ISM) is the gas that is present between stars, within a galaxy. It is far from uniform and we can arbitrarily distinguish three phases:
The coronal gas, or Hot Ionized medium is \(10^5\) to \(10^7\text{K}\), with a density between \(1000\) and \(10^4\) atoms per cubic meter. Its characteristic scale height is about \(3000\) parsecs (in the Milky Way). We can see that despite its presence within the locus of the galaxy, not much separates it from the ICM. Its mass is about \(50\%\) of the total ISM mass.
The Warm Ionized medium has a temperature around \(8000\text{K}\), with a density between \(0.2\) and \(0.5\) atoms per cubic centimeter. Its characteristic scale height is about \(1000\) parsecs and its mass is about \(30\%\) of the total ISM mass. It is a much denser, much cooler medium than the HIM. Unlike the coronal gas, it is present in the galactic disk (for disk galaxies, the most frequent type), within which it then consistutes the most massive component of the ISM.
The Warm Neutral medium has a temperature around \(6000\text{K}\) and a similar density to the WIM. Its characteristic scale height is about \(400\) parsecs and its mass is about \(15\%\) of the total ISM mass. As the name suggests, this phase has cooled enough that the gas is not ionized anymore: it is a neutral, atomic gas.
The Cold Neutral medium has a temperature around \(100\text{K}\), with a density between \(20\) and \(50\) atoms per cubic centimeter. Its characteristic scale height is about \(200\) parsecs and its mass less than \(5\%\) of the total ISM mass. It is a hundred time denser and colder than the WMN, but shares the same chemical composition.
Lastly, the Molecular clouds (MCs) show temperatures that don’t exceed \(20\text{K}\), with a density up to one million atoms per cubic centimeter. Their characteristic scale height is about \(80\) parsecs and their aggregate mass less than \(1\%\) of the total ISM mass. These clouds are cold enough to contain molecular.We’ve seen examples of that pre-reionization, when dihydrogen molecules helped bring up cooling efficiency dramatically. This time, as we’ve seen, the chemical enrichment undergone in past eras allows the emergence of much more diverse molecules: the very first chemical compounds.
90% of ordinary matter mass is in the IGM, while 10% is today in galaxies. At first, these 10% were just capsules of gas inside proto-galaxies, that progressively evolved into the phases we’ve described. But star formation is still strong enough, even today, that 90% of galaxies’ mass is contained in astral bodies (mostly stars, but also, quasars, black holes...) and the remaining 10% in the ISM.
What characterizes the workings of galaxies, and partly explains their longevity as stellar nurseries, is a feedback loop that is only partially understood but involves these elements:
thermic feedback from stars and black holes: radiation from these astral bodies is bound to heat the surrounding medium. Star formation takes cold gas and turn it into very hot and luminescent objects, which are bound to re-ionize their birthplace. That is why molecular clouds are now thought to be only transient. In a given galaxy, they disappear and pop back up somewhere else at a rapid clip.
That picture is also complicated by magnetic fields and other effects which can direct the bulk of the radiative energy out into the IGM, thus playing a regulating role.chemical feedback from star formation takes the form of metallic enrichment. That’s an evolution that is not reversible. The more generations of stars, the higher the metallicity of the universe, no matter what happens after that. Not only is the ISM naturally enriched as the locus of star formation, supernovae winds ensure that the IGM’s chemical composition tracks that of galaxies, creating a chemically homoegenous environment. We’ve already talked of the enhancing effect of metallicity on cooling efficiency. This goes a long way into prolonging the life of galaxies.
The previous generations of stars were short-lived and, starting out with very low metallicity, they could only have a modest impact on chemical enrichment. This was not enough to prevent their super-luminescent radiation from re-ionizing the stellar nuseries. Now, stellar lifespan and metallicity are high enough that a virtuous cycle can set off where the heat from each new generation of stars is absorbed in a cooling process by the newly formed dust from their parents’ supernovae.mechanical feedback is also crucial: the interior of a galaxy is a turbulent domain. In other words, a given volume undergoes different phases of compressions and relaxation, which is exactly the kind of thermodynamic process that enhances stellogenesis.
Supernovae and AGN activity generate supersonic winds that can rage within the ISM or eject large amounts of matter into the IGM via galactic fountains (matter from the IGM also continually gravitates towards the galaxy, so the cycle goes on and on).
The intrinsic geometrical and mechanical properties of a galaxy also play a role. For instance, elliptical galaxies, which tend to be older, seem to have formed most of their stars early on, and those are also bigger (and then will be shorter-lived: their stars tend to be close contemporaries to each other, and by now are all older and redder). Spiral galaxies like our Milky Way however, appear to have formed fewer star in their early years. However their star formation is still going strong.
It may be that none of this is a concidence: the mechanical and magnetic properties that are believed to enable the gestation of proto-galaxies into spirals might well be only possible in second-generation galaxies; for instance, ones that are borne out of a merger between two earlier ellipticals.
A spiral galaxy’s arms are not rotating group of stars. Stars can move through them unaffected. They are waves of compression that move around the galaxy, "temporarily" changing the pressure in the local gas volume (the spiral pattern from the Milky Way takes more than 200 million years to complete a lap). These compression/relaxation patterns may keep star formation alive, but could also play a role in keeping it subdued enough that the galaxy’s fuel won’t burn as fast as in an elliptical. Blue, bright, short-lived stars are born and die within the time that the spiral arm is passing by. Since these stars are the most visible, that is why these density waves appear as shiny arms around the galaxy center. Smaller, longer-lived stars like our Sun are alternately in and out of spiral arms (they also rotate around the galactic nucleus, but with a different angular speed).
Ultimately, this equilibrium can cease, and a galaxy can "go red", suffering the fate of the universe after re-ionization. The ISM can get heated to a point where no new stars are forming. When all existing stars have reached the end of their life, the galaxy progressively dissolves and goes back to the IGM. Others suffer a more violent death, colliding or merging with one of their brethren, or with a supermassive black hole.
Be that as it may, galaxies are extremely successful systems at creating a stable environment for star formation. It is estimated there are \(10^{11}\) galaxies in the observable universe, each containing betwen \(10^7\) and \(10^{11}\) stars.
The stellar epoch : from \(1\text{bn}\) years
Within galaxies, star formation then hits its strides in earnest around one billion years after the Big Bang, reaches a peak around two, after which point it started a slow decrease. The first generations of stars, with near-zero metallicity, were very massive and very short-lived, as we’ve seen. Higher metallicity over time makes it possible for smaller clouds to cool into a protostar, and some of them, much smaller than their ancestors, will make it to star, status, although not all.
Below 1.25% of our Sun’s mass (\(0.0125 M_\odot\)), the cloud gets warmer and is called a sub-brown dwarf (not dissimilar from a gas planet, except that it’s not orbiting another star; that cutoff mass is 13 times the mass of Jupiter).
Betwen \(0.0125\) and \(0.08M_\odot\), hydrogen can be fused into deuterium at some point during the object’s lifetime. It is then called a brown dwarf.
Above \(0.08M_\odot\), the protostar’s core can become hot enough (\(>10^7\text{K}\)) for the nuclear fusion of hydrogen into helium to start. A static equilibrium is soon reached and the object is officially a star!
At this point, the star is said to enter its main sequence, which represents roughly 90% of its life. The temperature and luminosity of the star stay constant during that phase, although the parameters depend on its mass: heavy stars are shorter-lived, hotter and more luminescent (they "burn brighter" indeed). Our Sun will have been in its main sequence for about \(10^{10}\) years, so it is about half-way through it’s life. The largest known stars, about 100 times heavier, live only for a few million years. The smallest ones, right above the brown dwarf cutoff, have a theoretical lifespan of trillions of years, although in practice other cosmological events will put an end to their life before.
The ultimate fate of stars is almost entirely determined by their initial mass:
Below \(0.3M_\odot\), stars on the main sequence are called red dwarves. They simply burn down all of their hydrogen into helium. At that point there is no pressure from fusion anyomre, since it has entirely stopped. Gravitational collapse then proceeds unfettered, until the helium turns into a degenerate plasma where protons, neutrons and electrons move freely. Fermi-Dirac statistics predit that electron degeneracy pressure manifests, which re-stabilizes the objects and halts the collapse again: it has now become a white dwarf, whose low luminosity is just a consequence of thermal activity. In the absence of fusion, its temperature just slowly gets down, until it becomes a black dwarf: a lifeless husk of matter. That has not happened yet, given the current age of our universe.
Above \(0.3M_\odot\), a star that burns all the hydrogen in its core is large enough to enter the red giant phase: the core contracts and becomes much hotter, which triggers the burning of hydrogen in the star’s shell, resulting in a massive expansion (hundreds of time). Red giants are not in a stable equilibrium and become colder but more luminous as times go by. Red giants whose initial mass was below \(0.6M_\odot\) just become white dwarves once hydrogen shell stops to burn.
Above \(0.6M_\odot\), but below \(10M_\odot\), stars follow a different path after the initial red-giant phase. When the helium core finally collapses on itself, it doesn’t have time to become degenerate, as the temperature is high enough to trigger the fusion of helium into carbon and oxygen. The star enters a state of quasi-equilibrium for a while, before a new red-giant phase called the asymptotic giant branch kicks in: this time, fusion stops in the carbon and oxygen core but starts again in the helium shell, and the star becomes even more luminous.
The thermic conditions mean that the helium burning shell is very loosely held, and massive stellar winds end up exposing the core more and more, which ionizes the surrounding matter, creating a nebula. At the same time, a process of neutron capture, combined with the decay of unstable isotopes, creates nuclei heavier than oxygen, up to lead. Towards the end, the central core becomes a very bright white dwarf, surrounded by the nebula, marking the end of the star’s life (except in some cases, where it appears that white dwarves that are part of a binary system can still be disrupted enough that they end up exploding in a supernova, producing elements up to zinc).High-mass stars (above \(10M_\odot\)) evolve differently. Their transition to the giant state is smoother in the sense that helium fusion can start concurrently with hydrogen burning in the shell. The are called red supergiants. The increase in luminosity is then lesser, although they did start from a point of very high luminosity in the first place. When the carbon and oxygen core is massive enough, fusion can actually continue, producing neon, magnesium, silicon,... The end point is iron, although small amounts of nickel are also produced. Any heavier element would cost too much energy. When this unfusable core reaches a critical mass, it collapses, unable to support itself. The fusion of the whole carbon core into iron is so fast (hundreds of years) that the star looks unchanged and has no time to adapt and find a new equilibrium. It won’t evolve into a white dwarf. Instead, it will end in a supernova event.
It is worth remarking this story is a bit simplified. Very heavy stars, above \(40M_\odot\), cannot become red supergiants straight away. They burn so bright and are so hot that the intensity of the winds battering their shell won’t allow it. They may spend some time in that unstable blue supergiant phase, following which they will sometimes directly explode into a supernova. The mass loss from the shell may also allow them to enter the red supergiant track.
We’ve already encountered supernovae when discussing the end of hypermassive primordial stars. The mechanism was different though, triggered by pair instability. In modern, smaller, more metallic stars, the process is driven by the iron-nickel core collapse. The core will collapse in a fraction of a second, at a speed around 20% of the speed of light. The resulting shockwave then bounces back, transferring a massive amount of energy to the outer layers of the star, triggering fusion reactions that go beyond the iron peak, generating all the heavier elements that are known to naturally occur (up to the heaviest one, uranium). Meanwhile, the burst of energy drives a powerful explosion of radiation, and expels the matter at high velocities, bound to scatter the cosmos.
The remaining core continues its collapse. For stars with an initial mass below \(25M_\odot\), the collapse is finally stopped by neutron-degeneracy pressure when the radius is just around 30\(\text{km}\) and the surface temperature \(10^{11}\text{K}\). Electrons and protons have merged to form neutrons, and what remains is called a neutron star. An initial release of energy (about 10% of the object’s rest mass) in the form of neutrino-antineutrino pairs is called the neutrino pulse. An exotic event, the merger of neutron stars is now believed to have produced and ejected most heavy elements, from niobium to uranium.
For heavier stars, the final outcome depends on their mass and metallicity combination. Some will leave a neutron star remnant, while for others, neutron-degeneracy pressure cannot halt the collapse, which ends up in a black hole.
Level 6: Globes — 5 \(\text{billion}\) years
Macromolecules
Size: \(1 \text{nm}\)
Initial state: Heavy molecules
Production process: Water-based chemistry
Meta-stable equilibrium: Macromolecules
Stable future: Organic monomers
Planetary systems
Size: \(50 \text{AU}\)
Initial state: Galaxies
Production process: Dust accretion
Meta-stable equilibrium: Planetary system
Stable future: Post-chaotic system of geologically inert planets
The emergent concept at Level 6 is that of Globes. Perhaps an expected heading, since we will ostensibly introduce planets here. But as previous concepts, this doesn’t refer to a physical object. Before humans had a sense of what the earth really was in its physical characteristics, its insides or its composition, there was a clear notion that this thing under ouf feet was "the world". Note that I’ve refrained from using the term "world", which we’ve used in very foundational contexts around our metaphysics sections; I want to avoid any semantic uncertainty, so I may use "world" liberally after that caveat, but will stick to "globes" for the official heading, even though the spherical shape is not exactly the key point here.
Conceptually, a galaxy is a system and a "cocoon" in many ways; it then matches our definition of a mesosphere. But it is not a world. In a sense, a "world", or globe, is another (albeit symbolic) compactification. To small enough beings, it provides a board for the game of life that could seem infinite in its two-dimensional extension, with only a slice of the third dimension available. That illusion the presence of a solid layer of materials to serve as a ground.
It might be anthropocentric, or at least geocentric, that we’re insisting on this feature as a necessary stepping stone to what sentient beings can consider conceptually as "a world". It sure is, and everything will be from that point on. It is a very solid hypothesis physico-chemical structures as complex as living beings could not emerge outside of a planetary environment, but by no means is it possible for prove it.
It seems that the only objects that could fit the bill are the ones in planetary systems. Dust grains are solid, but too small to act a "solid ground" for anything, since even a hefty macromolecule could "circumnavigate" it in a moment. Most stellar objects and media are not solid: they can be gaseous (clouds, brown dwarfs...), plasma (stars) or degenerate matter (white and black dwarfs, neutron stars, exotic stars...).
The concept of globe is then associated here, on the small scale, to the kind of materials that make up such solids, and on the large scales, to a planetary system as a whole: a system that includes a collection of globes. From where I stand, this relates more specifically to our Solar system, which indeed has been understood as a system of worlds for quite some time. In ancient Greece already, cosmological pluralists assume there were infinite worlds, a thesis whose statement by Anaxarchus supposedly reduced Alexander the Great to tears. But it’s only Galileo’s telescope that helped confirm without the shadow of a doubt that planets, up close, looked similar to our moon, and then probably to our earth. The moon, of course, much more visible, offered a prime example of an alternate world on which, perhaps, fantastic creatures roamed a strange land...
But let’s get back to it. The one factor that led our universe to harbor trillions of planets is the continued chemical enrichment stellar activity. Primordial stars were just surrounded by an ambient gas, similar to their native molecular cloud environment or to the interstellar medium (depending on their age). However, like our sun, they must have generated a heliosphere: that is the volume swept by stellar wind (plasma ejecta from the star). The heliosphere is likely shaped like the tail of a comet, since most stars are rotating around the center of their galaxies. The space within the heliosphere is already like a cocoon, preserved from the bulk of cosmic rays by the mechanical and magnetic effects of the stellar ejecta.
That space is where the future planetary system will be nested. But we’re still far from that state. We’ll place ourselves at the very start of a protostar’s life, when a molecular cloud starts its collapse. This has been happening continuously since the cosmic dawn, but the material composition of that cloud that would lead to planetary genesis has only been generalized since two billion years after the Big Bang. Our solar system, in comparison, was born 9.1 billion years after the Big Bang.
In what follows, for legilibity, we will periodize the different epochs in terms of the Sun Era (SE), starting from the sun’s birth, when an undistinguished volume from a molecular cloud starts to densify.
The nebular epoch : \(0\) to \(1\text{M}\) years SE
The transition from nebula to protostar to star has been discussed very quickly before. That is because in a largely non-metallic star, that stage is not extremely consequential. Now, the presence of elements heavier than helium and of cosmic dust is bound to change the dynamics at play. Every nebula starts with a certain angular momentum, which is due to density gradients and disturbances from the rest of the cloud. That angular momentum is conserved, so around the protostar, a protoplanetary disk will form, that gets faster and thinner over time. It represents about 1% of the protostar’s mass.
Initially, neither the protostar nor the disk would be visible, since they are surrounded by a wide envelope, one to ten thousand AU (Astronomical Units, the average sun-earth distance), which continuously discharge failling gas onto the center. The disk’s diameter at that point is a few hundreds AU. The envelope only becomes transparent after \(10^5\) years.
The disk epoch : \(1\) to \(10\text{M}\) years SE
Around the million-year mark, the envelope is cleared out and there’s an "empty" area surrounding the protostar, which then enters its "Tauri" phase. There’s still no nuclear burning, but a violent collapse leading to continous bipolar outflows perpendicular to the disk.
Meanwhile, in the disk, the accretion of dust starts. That process will ultimately give birth to the planets, but from that simple assertion it’s important to acknowledge the order of magnitude: sub-micron dust particle have gathered to constitute the earth with its \(6,000\text{km}\) diameter, a \(10^12\) factor.
The spinning disk is a fertile environment for this accretion. First of all, the physics favor a differentiation by mass whereby the biggest dust grain progressively migrate to the midplane of the disk. Huddled together, the grains are pushed against each other in frequent collisions by the thermal agitation and the variability in the disk’s spinning. At the same time, the fact they’re all spinning at almost the same speed means that the intensity of the shock stays moderate and rarely lead to the solid particles being crushed.
Initially, the rocky or icy dust grains aggregate atoms from the ambient gas one at a time via electrostatic forces. When the resulting pebbles are large enough, they start the accretion process and stick to each other. An object is called a planetesimal when it reaches a diameter around \(1\text{km}\). That is crucial threshold, as the moment when the object’s gravitational pull starts to be the dominant effect in attracting and holding on to smaller pebbles. As it keeps growing, the effect of gravitation increases, and the impact of aerodynamic forces to diminish.
By the time a planetesimal is \(100\text{km}\) wide, it is totally insensitive to aerodynamic forces and is able to move freely within the disk under the sole influence of gravitation and mechanical constraints. We now call it a protoplanet. Since protoplanets are not part of the aerodynamical flow anymore, they tend to be faster than the disk itself, and tend to migrate closer to the star.
The protoplanetary epoch : \(1\) to \(10\text{M}\) years SE
An important radial border within the protoplanetary disk is the "snow line". Beyond that line, the disk is far enough from the star that CNO ices (methane, ammonia and water) can coalesce into icy dust, whilst within the "inner system", it stays diffuse as a part of the cloudy disk. Beyond the snow line, we also find silicates and metals, although in relatively low concentrations, since those tend to gravitate closer to the star. Be that as it may, most of the non-star mass of the system is in that area. Currently, the mass beyond the snow line is equivalent to \(350M_oplus\) (earth masses), versus only \(2M_oplus\) within.
The growth of protoplanets continues via oligarchic growth, meaning that a subset of large objects are the only one growing, and start to clear up their surroundings by absorbing shocks from planetesimals and smaller protoplanets, or by ejecting them from the orbit. When a critical mass of solid metal, rocks and ices of \(10 M_\oplus\) is attained, the object is officially a giant planet, large enough to attract surrounding gas (hydrogen and helium). The giant planets in our solar system are Jupiter, Saturn, Uranus and Neptune. A prominent hypothesis at the moment is that they formed on the same orbit, but then migrated according to their mass differential.
Five to ten million years after the protostar first appeared, the Tauri phase ended and the stellar object at the center of the system became a proper star, entering its main sequence of hydrogen burning. But before that, the strong solar winds characteristic of the Tauri phase had fully cleared out the disk from gas, debris and dust. Due to their mass, the giant planets held on to their gas (part of which had been compressed into a mantle of liquid and solid hydrogen/helium, surrounding the ice/rock/metal core). They also kept a ring of dust and pebbles, although it’s unclear if that’s a universal feature of giant planets.
As to the rest of the planetesimal-sized objects, they were cleared out into the asteroid belt that marks the border of the inner solar system (between Mars an Jupiter, 1.5 to 5 AU from the sun), into the Kuiper belt (beyond Neptune, 30 to 50 AU from the sun), or into the Oort cloud (a collection of icy, up-to-planetesimal-sized objects that have been thrown out by giant planets onto very eccentric orbits, way beyond the heliosphere, thousands to hundred thousands AU away, well into interstellar space when they approach the sun, we call them comets).
The planetary epoch : \(10\) to \(100\text{M}\) years SE
The formation of terrestrial (or "rocky" planets) follows a similar path. Icy grains are absent within the snow line, so the protoplanets in that area are entirely made of metals and rocks. The timing and nature of the formation process is still a subject of active research. It is generally assumed, at the time of writing, that rocky planet formation took much longer than giant planet formation, up to 100 million years, although the full extent is uncertain.
One frequent idea is that the inner solar system underwent an additional "chaotic phase", when it ended up hosting about 100 protoplanets of moon-to-mars size. Because of the more constrained space (at least 100 times smaller than the comparable band in the outer solar system), collisions are much more frequent, leading to catastrophic events, like the complete shattering of objects, potentially followed by re-assembly. It is likely that the already-formed giant planets, as well as the asteroid belt that their orbital "cleanup" had nourished around the frost line, were a major influence on rocky planet formation.
At the end of the process, we end up with the four planets known today: Mercury, Venus, the Earth and Mars. Given their physical features and they orbital dynamics, the end stages of their formation may have been very dramatic, for instance with a major protoplanet collision creating what is today the earth-moon system from two distinct objects of a similar size.
The Hadean epoch : \(100\) to \(500\text{M}\) years SE
When a rocky planet is formed, the Hadean ("hellish") epoch starts. Although a planet can be geologically active for billions of years, the features that we think of as constant are not in place before the Hadean ends. We could still talk of a planetary embryo at this stage.
Most of what follows is grounded in the young planet’s thermal conditions. Earth today has three sources of energy:
One external source: solar energy, the radiant light and heat from the sun.
Two internal sources:
Radioactive heat, from the decay of radioactive isotopes.
Primordial heat, converted from incoming meteorites’ kinetic energy.
Today, the earth’s internal energy is tiny compared to its solar energy (the ratio is around 0.03%). It was always the case, although internal sources used to be much more powerful. Radioactive heat has undergone a predictable decline since the density of radionuclides follows a negative exponential law (this doesn’t account for atmospheric isotopes that are constantly replenished by cosmic rays, but only represent a negligible part of the earth’s overall natural radioactivity). Primordial heat’s used to be much higher than today during the earth’s embryo phase remember that to clean up its surroundings, a rocky planet needs to sustain impacts scores of planetesimals and perhaps dozens of protoplanets but then fell off a cliff due to the changes we’ll describe. Since then it has followed a regular decline, as the heat dissipates.
With a rocky planet being so hot in that phase, it’s not so much like a rock as like a big ball of molten lava. Materials inside are then free to move around, and under gravity’s influence, settle into layers based on their density. This is called the differentiation phase, and has given rise to the following structure for earth, which is thought to be fairly representative of rocky planets:
The inner core is a solid ball of mostly iron (some have suggested it was a pure, single iron crystal).
The outer core is a fluid made of iron and nickel (with fairly low viscosity, due to its high temperature).
The mantle is a solid layer of silicate rocks, although on geological timescales, it behaves like a viscous fluid. Silicates are salts that associate silicon dioxide (or silica: \(\text{SiO\_2}\)) with metallic oxides. Silica represents about 45% of the mantle mass, with magnesium, ferrous and aluminium oxides respectively at 39%, 8% and 4%.
The lower mantle is made of post-perovskite (closest to the core) and bridgmanite.
The transition zone is made of ringwoodite and wadsleyite.
The upper mantle is mostly olivine and pyroxenes.
The crust is the brittle, rocky, outermost layer of the earth.
Differentiation in itself leads to heat transfer that contribute a lot to cooling. It also initiates a number of key processes.
First, the existence of the magnetosphere is grounded in that of the outer core. Remember that the outer core ends up being a liquid, surrounded by two solid layers, one hotter (the inner core), one cooler (the mantle). This generates convection currents: the cooler, denser material sinks, while the warmer, less dense material rises. In addition the rotation of the earth plays a significant role in having these currents twist and loop in a specific fashion. Since the outer core is metallic, its electrons are free and shared between atoms, so the currents induce a magnetic field. That field ends up acting as a shield for the planet, deflecting most of the sun’s radiation.
Convection also started in the mantle, for similar reasons. Because of its temperature at the time, viscosity was much lower than today, leading to much stronger convection current. Progressively, minerals with the highest melting-point temperatures made their way towards the surface, and enough heat dissipated for those to crystallize and solidify, forming the crust. However, they were still unstable slabs, soon to melt all over again, when magma (molten rock) finds its way from deeper in the mantle to the surface.
All of this activity also gave rise to the earth’s atmosphere. Like other sizable rocky planets, the earth had a first atmosphere of dihydrogen and helium captured from the protoplanetary disk, but as we’ve seen, that was blown away by solar winds. Earth’s second atmosphere comes from the inside: the constant magma cooling and rock melting leads to a continuous emission of vapor and steam, that builds up to a proper atmospheric layer. Why wasn’t that one blown away? First of all, solar winds were not as powerful as during the Tauri phase; but more crucially, the magnetic shield around the earth offers such a degree of protection that the atmosphere has been very resilient to solar radiation. It is still being peeled off, but at a vaninshingly low pace. The early atmosphere had a different composition from the modern one, with a 89/10 split between nitrogen and carbon dioxide (today it is 78/21 between nitrogen and oxygen).
Lastly, it is possible that the Hadean earth has water oceans already. Indeed, the temperature was much higher, but pressure was too (around 27 times today’s pressure): those are conditions under which water can exist in a liquid state. That water may have come from internal sources (dissipation from the mantle), or from external ones (ice deposits from countless comet impacts during that era).