16.3 The Solar Interior: Theory

Solar Structure and Stability

Hydrostatic equilibrium of the Sun

The Sun doesn't collapse under its own gravity, and it doesn't blow itself apart from the energy it produces. That's because of hydrostatic equilibrium: the inward pull of gravity is exactly balanced by the outward push of gas pressure and radiation pressure at every point inside the Sun.

This balance maintains the Sun's stable size and shape. If something disrupts the balance slightly, the Sun can undergo small pulsations or oscillations. These oscillations are actually useful: the field of helioseismology studies how sound waves travel through the solar interior, giving us a way to probe layers we can't directly observe.

Energy production in the solar core

Nuclear fusion powers the Sun. In the core, hydrogen nuclei fuse into helium through the proton-proton chain, which can be summarized as:

$4\text{H} \rightarrow \text{He} + 2e^+ + 2\nu_e + \text{energy}$

Four hydrogen nuclei combine to form one helium nucleus, two positrons, two neutrinos, and energy. A small amount of mass is converted to energy in the process (following $E = mc^2$), and that's what keeps the Sun shining.

Fusion requires extreme conditions. The core reaches about 15 million K with a density of roughly 150 g/cm³ (about 150 times denser than water). Only under these conditions can hydrogen nuclei overcome their electrical repulsion and fuse.

The energy produced starts as gamma rays and X-rays. These high-energy photons don't travel straight out of the Sun. Instead, they scatter off particles and get absorbed and re-emitted countless times as they work their way outward. Solar neutrinos are also produced as a byproduct of fusion. Unlike photons, neutrinos barely interact with matter and escape the Sun almost immediately, which makes them a direct probe of core conditions.

Solar Interior Layers and Energy Transport

Layers of the solar interior

The Sun's interior has three main layers, each defined by how energy moves through it:

• Core: The innermost layer, extending to about 0.25 solar radii. This is where nuclear fusion occurs, and it has the highest temperature and density.
• Radiative zone: Extends from the core boundary out to about 0.7 solar radii. Energy moves outward here primarily through radiation (photons bouncing around). Temperature and density both decrease as you move farther from the core.
• Convective zone: The outermost layer of the interior, from about 0.7 solar radii to the surface. Energy moves here through convection, where hot gas physically rises, cools, then sinks back down. This produces the granulation patterns visible on the Sun's surface, where each granule is the top of a convection cell roughly 1,000 km across. Larger-scale supergranules (about 30,000 km across) also form from deeper convective flows.
• Tachocline: A thin transition layer between the radiative and convective zones. This boundary is thought to play a key role in generating the Sun's magnetic field.

Radiative vs. convective energy transport

These two transport mechanisms dominate in different regions because of how the Sun's physical conditions change with depth:

• Radiative transport dominates in the core and radiative zone. Photons carry energy outward by being absorbed and re-emitted by surrounding matter. This process is slow (a photon can take tens of thousands of years to work its way out through the radiative zone) but it's efficient where density and opacity are high enough that the gas remains stable against convection.
• Convective transport takes over in the convective zone. Hot plasma rises, carries energy upward, cools near the surface, and sinks back down in cyclic convection cells. This kicks in where density and opacity are lower.

The transition happens at the depth where the temperature gradient (how quickly temperature changes with depth) becomes steeper than the adiabatic gradient (the rate at which a rising blob of gas would cool as it expands). When the actual gradient is steeper, a rising parcel of gas stays hotter than its surroundings and keeps rising. This is called convective instability, described by the Schwarzschild criterion. Below that boundary, the gradient is shallow enough that radiative transport keeps things stable.

Solar Magnetic Field and Energy Output

Solar dynamo and magnetic field generation

The Sun's magnetic field is generated and maintained by the solar dynamo mechanism. This arises from the interaction between two key processes in the convective zone: the churning convective motions of electrically conducting plasma, and differential rotation (the fact that the Sun rotates faster at its equator than at its poles). Together, these stretch, twist, and amplify magnetic field lines, sustaining the Sun's complex and changing magnetic field.

Solar energy output

Solar luminosity is the total energy the Sun radiates per unit time, roughly $3.8 \times 10^{26}$ watts. This output depends on conditions inside the Sun: the core temperature (which controls the fusion rate), the opacity of the solar interior (which affects how easily energy escapes), and the efficiency of the energy transport mechanisms in each layer.