Where Does the Sun's Energy Come From?

Layers of the Sun — The different layers of the Sun: the core, the radiative zone, the convective zone, the photosphere, the chromosphere, and finally the solar corona. At the heart of fusion, one gram of hydrogen releases as much energy as 300 tons of oil.
Image source: astronoo.com (new window)

Scientific Summary

The article explains the Sun's energy source: the nuclear fusion of hydrogen into helium in its core, at 15 million K and under a pressure of 26 petapascals. This process converts 4.3 million tons of mass per second into energy (E=mc²), producing 4×10²⁶ W. The proton-proton fusion requires overcoming the Coulomb barrier, which temperature alone cannot achieve. The quantum tunnel effect makes fusion possible despite insufficient kinetic energy. The weak interaction converts a proton into a neutron, forming deuterium, then helium-3 and -4, releasing neutrinos and gamma radiation.

Where Does the Sun's Energy Come From and How Is Fusion Possible?

The Sun's energy comes from the nuclear fusion of hydrogen into helium in its extremely dense and hot core (15 million K). Every second, 627 million tons of hydrogen fuse, converting 4.3 million tons into pure energy according to E=mc². Fusion is possible thanks to a quantum phenomenon: the tunnel effect. It allows protons to overcome their electrical repulsion (Coulomb barrier) even if their temperature is insufficient. This process, called the proton-proton chain, releases immense amounts of energy and has sustained the Sun for 4.6 billion years.

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Energy Concentrates at the Center of the Sun

A Giant with Colossal Dimensions

The Sun is a massive star with a diameter 109 times that of Earth, or 3.6 times the Earth-Moon distance. Its volume is 1.3 million times that of Earth.

Crushing Gravity and an Extremely Dense Core

The gravitational force at the surface (274 m/s², 28 times that of Earth) of this enormous mass (1.989×10³⁰ kg) compresses matter at its center. Although its core has a diameter equal to the Earth-Moon distance, the core's volume represents only 1.5% of the total volume.

Nuclear Fusion: 627 Million Tons of Hydrogen per Second

Yet, in its core at about 15 million kelvins or degrees Celsius (1 K = -273.15 °C), every second, 627 million tons of hydrogen fuse to produce 622.7 million tons of helium. The mass difference (4.3 million tons) is converted into energy, 4×10²⁶ joules, or about 1.5×10¹⁹ kilowatt-hours (10 trillion trillion kWh).

For 4.57 billion years, the Sun has been consuming 4 million tons of hydrogen per second.

Extreme Pressure and Temperature Conditions

The gravitational pressure at the center of the Sun is 26 petapascals (26×10¹⁵ Pa), which is 260 billion times the atmospheric pressure on Earth's surface. At this pressure, 1 m³ of hydrogen weighs 150 tons. 1 m³ of hydrogen on Earth weighs 90 grams. There are therefore 1.6 million times more hydrogen atoms in 1 m³ at the center of the Sun than in 1 m³ of hydrogen on Earth (which is not as enormous as it seems).

The Triggering of Fusion and Its Immense Power

At this pressure and temperature (15 million kelvins), nuclear fusion can begin.
Hydrogen nuclei will fuse and form a helium nucleus, releasing enormous energy (15 times more than the nuclear fission triggered in our power plants).

The Quantum Probability at the Heart of Nuclear Fusion

Probability of Particle Fusion

The Probabilistic Nature of the Proton

The size or position of a proton is a probability density represented by a curve. The farther you move from the peak of the curve, the less likely the presence or size of the proton is. However, at the bottom of the curve, the probability of having two protons that fuse is low but not zero.

The Necessary Condition: Contact Between Protons

For the nuclear reaction to "ignite," protons (hydrogen nuclei) must come into contact. Then, one of the two protons transforms into a neutron.

Without radioactivity, this transformation would be impossible. Two protons, even in contact, are unable to overcome the Coulomb barrier; they repel each other.

The Rare Event That Triggers Fusion

But the proton can transiently transform into a neutron by emitting a particle (W boson). This W boson is immediately reabsorbed, and the neutron becomes a proton again.

Very rarely, the W boson decays into a positron and a neutrino, and at that moment, the neutron remains a neutron. It can then fuse with the other proton to form a deuterium nucleus and trigger the "proton-proton chain."

How to Fuse Two Protons?

The Coulomb Barrier: An Electrical Obstacle

For two protons to fuse, the distance between them must be very small, on the order of the nucleus (10⁻¹⁵ meters). To do this, the Coulomb barrier (the force of electrical interaction between two positively charged protons) must be overcome. This force is proportional to the product of the two charges and inversely proportional to the square of the distance between the two charges (which requires considerable energy to "stick" two protons together).

The Insufficiency of Solar Temperature

The closer the protons get, the more energy is needed to "stick" them together. Even at 15 million kelvins, the energy is not sufficient to overcome the Coulomb barrier. Violent collisions between protons do not compress the strong nuclear interaction bubbles enough to "stick" two protons together.
Theoretically, protons would need to move at 20,000 km/s to reach a temperature of 5 billion kelvins. At 15 million kelvins, protons move at 600 km/s.

Classical Physics Condemns Fusion

However, 15 million kelvins is an average temperature. According to the Maxwell-Boltzmann distribution curve of particles as a function of temperature, protons are far from reaching 20,000 km/s, and thus fusion is impossible.

Quantum Physics: The Tunnel Effect

To achieve fusion, quantum physics must be invoked.
The size or position of a proton is a probability density represented by a curve. The farther you move from the peak of the curve, the less likely the presence or size of the proton is. At the bottom of the curve, the probability of having two protons that fuse is very low but not zero.
The property that allows a quantum object to cross a potential barrier even if its energy is less than the minimum energy required to cross this barrier is called the tunnel effect.

Overcoming the Coulomb Barrier

The Tunnel Effect: A Sufficient Probability at 15 Million Kelvins

Overcoming the Coulomb barrier is impossible at low temperatures, but with an average of 15 million kelvins, this is enough for the tunnel effect to become probable without having to reach 5 billion kelvins.

Endless Collisions and Fusion Opportunities

Every second, a proton undergoes 2×10¹⁵ collisions, and the tunnel effect occurs once every 10⁸ collisions. So each proton has 20 million opportunities to fuse.

The Exclusion Principle: Why Not Everything Fuses

So, why don't all the Sun's protons fuse in one second?
Because two protons, although united by the strong nuclear interaction, cannot coexist due to the exclusion principle of Wolfgang Ernst Pauli (1900–1958). Thus, each proton fuses with another proton 20 million times per second thanks to the tunnel effect and instantly separates (10⁻²¹ second).

Manufacturing a Helium Nucleus: Neutrons Needed

To manufacture a helium nucleus, it is necessary to fuse 2 protons and 2 neutrons.
Where do the neutrons come from?

Weak Nuclear Interaction: Proton → Neutron Transformation

The weak nuclear interaction (radioactivity) will intervene in our fusion. The weak nuclear interaction (100,000 times weaker than the strong nuclear interaction) allows a proton, with an extremely low probability (1 in 10²⁴), to transform into a neutron when it is in contact with another proton. When this happens, a deuterium nucleus appears, emitting a neutrino and a positron, which immediately annihilates with a surrounding electron, transforming matter into pure energy (E=mc²).

The Proton-Proton Chain: From Helium-3 to Helium-4

The deuterium will transform into helium-3, emitting pure energy (gamma rays) according to the same principle. Still with a low probability, then 2 helium-3 nuclei will give 2 helium-4 nuclei.

A Fragile Balance Maintained for 4.6 Billion Years

This process, called the "proton-proton chain," thanks to a very low probability of fusion, has been maintained for 4.6 billion years.

FAQ: Everything You Need to Know About the Sun's Energy

What is the physical condition required for nuclear fusion to start at the Sun's core?

Fusion requires extreme conditions: a temperature of about 15 million kelvins and a pressure of 26 petapascals (260 billion times Earth's atmospheric pressure). These conditions are met at the Sun's core due to the star's enormous mass compressing matter. The high temperature gives protons enough kinetic energy to get close, but it is the quantum tunnel effect that truly allows them to overcome the electrical repulsion barrier.

What is the role of the tunnel effect and weak interaction in solar fusion?

The tunnel effect is a quantum phenomenon that allows protons to overcome the Coulomb barrier (electrical repulsion) even without the required kinetic energy, making fusion possible at 15 million K. The weak nuclear interaction then allows, with a very low probability, the transformation of a proton into a neutron, forming deuterium. This step is crucial for helium synthesis and releases neutrinos and energy.

Why doesn't all the Sun's hydrogen fuse at once?

Fusion is an extremely unlikely process on an individual scale. Although each proton undergoes billions of collisions per second, the tunnel effect has only a 1 in 10⁸ chance of occurring. Furthermore, the formation of deuterium via weak interaction is even rarer (1 in 10²⁴). This statistical rarity ensures a slow and steady release of energy, preventing the Sun from exploding and allowing it to burn for billions of years.

Where Does the Sun's Energy Come From?

Scientific Summary