Origin of the Elements

Overview: Where Do the Elements Come From?

The atoms around us were not created on Earth. Almost all atomic nuclei were formed long before the Earth existed, in different stages of the history of the universe and inside stars. Only a few very light nuclei were produced in the very early universe; almost all heavier ones are products of stellar processes and stellar explosions.

In this chapter, the focus is on which processes produced which elements and where they take place in the universe. Details of nuclear reactions, nuclear stability, and the general properties of nucleons are treated in other chapters and are not repeated here.

Key questions for this chapter:

• Which elements were formed in the Big Bang?
• How do stars build heavier elements during their lifetimes?
• How do stellar explosions (supernovae, neutron star mergers) and other environments contribute to heavy-element formation?
• How does this history explain the observed abundances of the elements?

Big Bang Nucleosynthesis: The First Few Minutes

Conditions in the Early Universe

Shortly after the Big Bang, the universe was extremely hot and dense. As it expanded, it cooled rapidly. In the first seconds to minutes:

• Matter consisted mainly of protons, neutrons, electrons, photons, and neutrinos.
• At very high temperatures, protons and neutrons were interconverted; as the universe cooled, neutrons became less stable and many decayed.
• When the temperature dropped sufficiently, protons and neutrons could start to bind into light nuclei.

Which Nuclei Were Produced?

The nuclear reactions in the first few minutes of cosmic history are called Big Bang nucleosynthesis. Under these conditions, only very light nuclei could be produced efficiently before the universe became too cool and dilute.

The main products:

• Hydrogen-1 ($^1\mathrm{H}$, a proton)
• Deuterium ($^2\mathrm{H}$ or D)
• Helium-3 ($^3\mathrm{He}$)
• Helium-4 ($^4\mathrm{He}$)
• Very small traces of Lithium-7 ($^7\mathrm{Li}$) and Beryllium-7 ($^7\mathrm{Be}$, which decays to $^7\mathrm{Li}$)

No significant amounts of heavier nuclei formed. The dominant primordial composition after Big Bang nucleosynthesis (approximately):

• About 75% hydrogen (by mass)
• About 25% helium-4 (by mass)
• Traces of deuterium, helium-3, and lithium-7
• Essentially no elements heavier than lithium

Why Heavier Elements Were Not Made in the Big Bang

Heavier nuclei require a sequence of reactions building up from lighter ones. In the rapidly expanding and cooling early universe there were two main obstacles:

1. Limited time and density
• The window of time where temperatures and densities were suitable for fusion was only a few minutes.
• After that, the universe expanded enough that collisions between nuclei became too rare.
2. Absence of stable nuclei with mass numbers 5 and 8
• There is no stable nucleus with mass number $A = 5$ or $A = 8$.
• Paths like
  $$^4\mathrm{He} + p \rightarrow ^5\mathrm{Li}$$
  or
  $$^4\mathrm{He} + n \rightarrow ^5\mathrm{He}$$
  lead to unstable nuclei that decay rapidly.
• Similarly, $^8\mathrm{Be}$ formed from two $^4\mathrm{He}$ is extremely short-lived.
• This blocks straightforward buildup to heavier elements under the conditions of the early universe.

Because of these limitations, the early universe left us mainly with hydrogen and helium plus tiny amounts of a few light isotopes. All heavier elements were synthesized later in stars and stellar explosions.

Stellar Nucleosynthesis: Element Formation in Stars

Once matter collected under gravity to form stars, new environments arose for nuclear reactions. Stellar interiors provide high temperatures and pressures for billions of years, enabling a variety of fusion processes that build up heavier nuclei.

The term stellar nucleosynthesis covers all element-forming reactions taking place during the life cycle of stars, from their birth to their final stages.

From Hydrogen to Helium: Main-Sequence Stars

Most stars, including the Sun during its current phase, are main-sequence stars. Their primary energy source is the fusion of hydrogen into helium in their cores.

Two main reaction chains produce helium from hydrogen, depending on the mass and central temperature of the star:

1. Proton–proton (pp) chain
   Dominant in stars with masses similar to or smaller than the Sun. In several steps, four protons ultimately combine to form one helium-4 nucleus, with the release of energy and neutrinos. Net reaction:
   $\,^1\mathrm{H} \rightarrow ^4\mathrm{He} + 2 e^+ + 2 \nu_e + \text{energy}$$
2. CNO cycle (carbon–nitrogen–oxygen cycle)
   Important in more massive, hotter stars. Carbon, nitrogen, and oxygen nuclei act as catalysts in a cycle of reactions that again converts four protons into one helium-4 nucleus. The catalysts are regenerated, so their overall abundance changes little.

In both cases, the main product is helium-4. These processes do not significantly change the amounts of heavier elements; instead, they transform part of the star’s hydrogen into helium while releasing energy that supports the star against gravitational collapse.

Helium Burning and the Production of Carbon and Oxygen

When the hydrogen in the core is largely exhausted, the core contracts and heats up. At sufficiently high temperatures, helium nuclei ($^4\mathrm{He}$, also called alpha particles) can take part in new fusion reactions.

The Triple-Alpha Process

A key reaction for the origin of heavier elements is the triple-alpha process, which overcomes the bottleneck caused by the absence of stable nuclei with $A=5$ and $A=8$:

1. Two $^4\mathrm{He}$ nuclei briefly form unstable $^8\mathrm{Be}$.
2. Before $^8\mathrm{Be}$ decays, a third $^4\mathrm{He}$ can collide with it to form stable $^{12}\mathrm{C}$.

Net:
$$3\,^4\mathrm{He} \rightarrow ^{12}\mathrm{C} + \gamma$$

This is the dominant way that carbon-12 is created in stars.

Formation of Oxygen-16

Once some carbon has formed, additional capture of helium-4 nuclei can occur:

$$^{12}\mathrm{C} + ^4\mathrm{He} \rightarrow ^{16}\mathrm{O} + \gamma$$

This step produces oxygen-16. Helium burning in red giant stars therefore explains why carbon and oxygen are among the most abundant elements after hydrogen and helium.

The relative amounts of carbon and oxygen produced depend sensitively on the temperature, density, and reaction rates in the star’s core.

Advanced Burning Stages in Massive Stars

In stars significantly more massive than the Sun, further contractions and temperature increases after helium burning allow additional burning stages. These create a sequence of heavier elements, predominantly with even mass numbers:

• Carbon burning
  Fusion reactions involving $^{12}\mathrm{C}$ nuclei can produce elements like neon, sodium, magnesium:
  $$^{12}\mathrm{C} + ^{12}\mathrm{C} \rightarrow ^{20}\mathrm{Ne} + ^4\mathrm{He}$$
  $$^{12}\mathrm{C} + ^{12}\mathrm{C} \rightarrow ^{23}\mathrm{Na} + p$$
• Neon burning
  At higher temperatures, neon can undergo photodisintegration and subsequent reactions, forming more oxygen and magnesium.
• Oxygen burning
  Oxygen-16 fusion produces elements such as silicon, sulfur, phosphorus.
• Silicon burning
  At extremely high temperatures, silicon and nearby nuclei undergo complex networks of reactions (including photodisintegration and reassembly) resulting in a mixture dominated by iron-group elements, particularly iron-56 ($^{56}\mathrm{Fe}$), nickel-56 ($^{56}\mathrm{Ni}$, which decays to $^{56}\mathrm{Fe}$), and cobalt isotopes.

These burning stages occur in shells around the core in the most massive stars, forming an onion-like structure: hydrogen burning in outer layers, helium burning inside that, then carbon, neon, oxygen, and silicon burning in successively deeper shells, with an iron-group core at the center.

Why Fusion Stops at the Iron Group

Fusion reactions involving light nuclei (up to roughly iron) generally release energy, because the binding energy per nucleon increases up to the iron region. Beyond the iron group, heavier nuclei have slightly lower binding energy per nucleon.

As a consequence:

• Fusing nuclei heavier than iron (e.g. $^{56}\mathrm{Fe}$ to $^{60}\mathrm{Ni}$) would consume energy rather than release it.
• In stellar cores, once an iron-dominated core has formed, no further energy-producing fusion is possible under ordinary conditions.

This marks the end of the star’s ability to support itself by nuclear energy production in its center. In massive stars, this leads to core collapse and a subsequent supernova explosion, which plays a crucial role in the creation and distribution of heavy elements.

Beyond Iron: Neutron Capture and Explosive Nucleosynthesis

Elements heavier than iron are mainly formed by neutron capture followed by beta decay, predominantly during late stellar evolution and in stellar explosions.

Neutron Capture: s-Process and r-Process

Two main types of neutron-capture processes are distinguished:

1. s-Process (slow neutron capture)
• “Slow” means that the time between successive neutron captures is generally longer than the beta-decay half-lives of unstable nuclei along the path.
• A nucleus captures a neutron to form a heavier isotope. If that isotope is unstable, it has enough time to undergo beta decay (a neutron turns into a proton) before capturing another neutron.
• Over long times, this creates a path of stable isotopes along the valley of nuclear stability.

Site: mainly in relatively quiescent phases of evolved stars, especially in asymptotic giant branch (AGB) stars, where moderate neutron fluxes exist.

Typical products: many isotopes of elements from strontium (Sr) and barium (Ba) up to lead (Pb) and bismuth (Bi).

2. r-Process (rapid neutron capture)
• “Rapid” means the neutron flux is so high that multiple neutron captures occur faster than beta decays.
• Nuclei are driven to very neutron-rich, unstable regions before they can decay. After the neutron flux ceases, these nuclei undergo a series of beta decays back toward stability.
• This process can build up very heavy and neutron-rich nuclei rapidly, including many rare-earth elements and actinides such as uranium (U) and thorium (Th).

Sites: require extremely high neutron fluxes and extreme conditions, associated with catastrophic astrophysical events, such as:

• Core-collapse supernovae
• Neutron star mergers

Both s- and r-process nucleosynthesis contribute to the detailed pattern of heavy elements found in the universe.

Other Nucleosynthesis Processes for Heavy Nuclei

Besides the s- and r-processes, several additional processes contribute more specialized components of the abundance pattern:

• p-Process
• Produces certain rare, proton-rich isotopes (p-nuclei) that cannot be made by ordinary neutron capture.
• Involves reactions such as proton capture or photodisintegration (gamma-induced reactions) on pre-existing heavier nuclei.
• Thought to occur mainly in supernova environments where high photon fluxes and temperatures are available.
• rp-Process (rapid proton capture)
• Occurs in extremely hot, proton-rich environments, such as on the surface of neutron stars during certain explosive events (e.g. X-ray bursts).
• Successive rapid proton captures and beta decays build up heavier proton-rich isotopes, though the process is usually limited to elements lighter than the heavy r-process region.

These processes are mainly relevant for explaining specific, often rare isotopes rather than the bulk of heavy elements.

Supernovae and Neutron Star Mergers as Element Factories

While stable stars build elements up to iron and some beyond via the s-process, the heaviest elements and many specific isotopes require extreme environments.

Core-Collapse Supernovae

In massive stars (above a certain mass threshold), the iron core becomes unstable and collapses under gravity. This triggers:

• A violent rebound and explosion (core-collapse supernova).
• Extremely high temperatures and densities, with intense fluxes of neutrinos and neutrons.
• Shock waves passing through the star’s outer layers, driving additional nucleosynthesis and ejecting material into space.

In such an explosion:

• Pre-existing elements are expelled into the interstellar medium, enriching the surrounding gas with metals (all elements heavier than helium).
• Additional elements can be formed through explosive burning and possibly through r-process nucleosynthesis in regions with high neutron densities.

Neutron Star Mergers

Binary systems of neutron stars, after losing energy via gravitational waves, can spiral in and merge. During this event:

• Extremely neutron-rich matter is ejected.
• Conditions allow for very efficient r-process nucleosynthesis, producing large amounts of heavy elements, including rare-earth elements and actinides.

Observations of electromagnetic signals (kilonovae) associated with neutron star mergers have provided strong evidence that these events are major sources of the universe’s heaviest elements such as gold, platinum, and uranium.

Distribution of Newly Formed Elements

The elements produced in stars and stellar explosions are dispersed by:

• Stellar winds (especially from evolved stars)
• Planetary nebulae (from low- and intermediate-mass stars)
• Supernova explosions and other violent events

This enriched material mixes into the interstellar medium. New generations of stars and planetary systems form from this chemically evolved gas. Thus, each stellar generation includes more heavy elements than the previous one, a process referred to as cosmic chemical evolution.

Cosmic Chemical Evolution and Element Abundances

The varying origins of elements and the successive generations of star formation shape the observed abundance pattern of elements in the universe.

General Features of Elemental Abundances

Measured abundances (for example, in the Sun, in cosmic rays, and in distant stars) show characteristic patterns:

• Dominance of light elements
• Hydrogen and helium are by far the most abundant elements, reflecting their origin in Big Bang nucleosynthesis and stellar hydrogen burning.
• Deuterium, helium-3, and lithium-7 occur at much lower levels but are important cosmological tracers.
• High abundances of C, N, O, Ne, Mg, Si, S, Fe
• These are mainly products of stellar fusion and supernova nucleosynthesis.
• Carbon and oxygen are particularly abundant from helium burning and subsequent processes.
• Pronounced patterns among heavier elements
• Peaks at certain element groups (e.g. iron group, elements near barium and lead) correspond to the conditions of s- and r-process nucleosynthesis and nuclear stability.
• Odd–even effects: elements with even atomic numbers ($Z$) are generally more abundant than their odd-$Z$ neighbors, consistent with nuclear binding trends.

Metallicity and Stellar Generations

Astronomers often call all elements heavier than helium metals. The metal content of a star is described by its metallicity.

• First generation (Population III) stars
• Formed from primordial gas containing essentially only hydrogen and helium.
• Likely very massive and short-lived.
• Their supernovae initiated the first enrichment with heavy elements.
• Later generations (Population II and I stars)
• Formed from gas already enriched with heavy elements from earlier stars.
• The Sun is a Population I star with relatively high metallicity, reflecting billions of years of prior nucleosynthesis.

Over cosmic time, repeated cycles of star formation and stellar death increase the abundance of heavy elements in galaxies. This ongoing process determines the composition of interstellar gas, new stars, planets, and, ultimately, living organisms.

Connection to the Composition of the Solar System and Life

The elements that make up the Earth and living organisms have diverse nuclear origins:

• Hydrogen in water and organic molecules: mainly primordial from Big Bang nucleosynthesis.
• Helium: mainly primordial, with additional production in stars; on Earth, much helium in gas reservoirs originates from radioactive decay of heavy elements.
• Carbon, nitrogen, oxygen: primarily formed in stars (helium burning and subsequent stages).
• Silicon, magnesium, iron, nickel: produced in advanced burning stages of massive stars and in supernova explosions.
• Trace heavy elements (e.g. silver, gold, iodine, uranium): formed mainly via neutron-capture processes (s-process and r-process) in late-stage stars, supernovae, and neutron star mergers.

The material that eventually coalesced into the solar system was already enriched by many previous generations of stars. The atoms in rocks, oceans, air, and biological molecules thus carry a record of the universe’s nuclear history.

Summary: A Layered Origin Story

The origin of the elements can be viewed as a sequence of stages, each adding new components to the cosmic inventory:

1. Big Bang nucleosynthesis
• First few minutes after the Big Bang.
• Produced mainly hydrogen, helium-4, and trace amounts of deuterium, helium-3, and lithium-7.
2. Stellar nucleosynthesis in ordinary stars
• Over billions of years.
• Hydrogen burning (pp chain, CNO cycle) → helium.
• Helium burning (triple-alpha and related reactions) → carbon and oxygen.
• In massive stars, advanced burning stages (carbon, neon, oxygen, silicon) → elements up to the iron group.
3. Neutron capture and explosive nucleosynthesis
• In evolved stars, supernovae, and neutron star mergers.
• s-Process in relatively stable stellar environments → many heavy isotopes up to lead and bismuth.
• r-Process and related mechanisms in extreme, neutron-rich environments → very heavy elements, including many rare-earths and actinides.
4. Cosmic recycling
• Stellar winds and explosions disperse newly formed elements.
• Subsequent generations of stars and planetary systems incorporate this enriched material.

Understanding these stages links nuclear reactions at the smallest scales to the large-scale chemical evolution of the universe and to the elemental composition of planets and life.