The Solar Interior: Theory

Core Concepts

Hydrostatic equilibrium: the Sun holds itself up

Picture the Sun as a stack of thin spherical shells. Each shell feels two competing forces:

• Gravity pulls it inward, toward the center.
• Pressure from the hotter, denser gas below pushes it outward.

In hydrostatic equilibrium these balance exactly at every depth: the pressure difference across each shell supports the weight above it. The Sun is in a delicate, self-correcting balance. If fusion suddenly produced more energy, the interior would heat and expand, cooling the core and slowing fusion; if fusion slowed, gravity would compress the core, heating it and speeding fusion up. This built-in thermostat keeps the Sun's luminosity remarkably steady.

Temperature, pressure, and density rise toward the center

To support the weight of the overlying layers, deeper gas must be hotter and denser — just as air pressure increases down a deep mine shaft. The standard solar model predicts (commonly cited reference values):

• Core temperature: ~1.5 × 10⁷ K (15 million K)
• Core density: ~150 g/cm³ — about 150 times the density of water
• Core pressure: ~2.5 × 10¹¹ bar — 250 billion times Earth's sea-level pressure

Compare the surface: the photosphere is only ~5,800 K, with density a million times thinner than air. Over most of the Sun's volume the gas behaves close to an ideal gas, so pressure ≈ density × temperature.

Energy generation: the proton–proton chain

Fusion occurs only in the core — very roughly the inner quarter of the Sun's radius — because only there is the temperature high enough (~10⁷ K) for protons to overcome electrical repulsion and get close enough for the strong force to bind them. The Sun's pathway: the proton–proton chain:

1. Two protons fuse to make deuterium (²H), releasing a positron and a neutrino. This first step is extraordinarily slow because a proton must convert to a neutron via the weak interaction — exactly why the Sun lasts ~10 billion years instead of burning out quickly.
2. Deuterium + proton → helium-3 (³He) + a gamma ray.
3. Two helium-3 nuclei → helium-4 (⁴He) + two protons.

Net result: 4 H → He + 2 positrons + 2 neutrinos + ~26.7 MeV (commonly cited). The positrons promptly annihilate with electrons, adding their mass-energy. The neutrinos barely interact and escape in seconds — the key observational probe in the next topic.

Energy transport: radiation zone and convection zone

Energy generated in the core must travel ~700,000 km to the surface, in two very different ways:

• Radiation zone (from the core out to about 0.7 R☉). Photons are constantly absorbed and re-emitted by the dense gas, performing a random walk: they move at light speed between absorptions but keep changing direction, so crossing takes a very long time — commonly cited as ~100,000 years or more. The sunlight we see today began its journey long before human history.
• Convection zone (the outer ~30% of the radius, from about 0.7 R☉ to the surface). Here the gas is cool and opaque enough that radiation cannot carry the energy efficiently. Instead, hot gas rises, cools, and sinks — like water boiling in a pot. This churning is visible at the surface as granulation — bright rising cells and dark sinking lanes.

The standard solar model

The standard solar model is a theoretical construction: given the Sun's mass, composition, and age, plus the laws of hydrostatic equilibrium, energy transport, and nuclear reaction rates, it computes pressure, temperature, density, and energy generation at every depth. It is not a guess — it is a set of coupled equations solved numerically — and it makes sharp predictions (core temperature, neutrino rate, convection-zone depth) that can be checked. The next topic shows how sound waves and neutrinos did exactly that.

Common Confusions