E.5 Fusion and stars

A star is essentially in a constant tug-of-war between two opposing forces. Gravity relentlessly pulls all of the star's mass inward, trying to crush it into a point. At the same time, radiation pressure , generated by nuclear reactions in the core , pushes outward. When these two forces are perfectly balanced, the star is said to be in hydrostatic equilibrium.

Hydrostatic Equilibrium: The stable state of a star in which the inward gravitational force is exactly balanced by the outward radiation pressure from nuclear fusion in the core.

This balance is not permanent , it depends entirely on the star having enough fuel to sustain fusion. As long as hydrogen is available, the star remains stable on what astronomers call the main sequence. Understanding what happens when that fuel runs out is the key to understanding stellar evolution.

Deep inside a star's core, conditions are extreme: temperatures reach tens of millions of kelvin, and pressures are almost incomprehensibly high. Under these conditions, hydrogen nuclei (protons) collide at enormous speeds. Although the Coulomb (electrostatic) repulsion between like-charged protons normally prevents them from getting close, the extreme kinetic energies allow protons to approach within the range of the strong nuclear force, which then binds them together.

Nuclear Fusion: A nuclear reaction in which two light nuclei combine to form a heavier nucleus, releasing energy due to the conversion of a small amount of mass into energy.

The net reaction for hydrogen fusion in stars can be written as:

$4{}_1^1\text{H}\to {}_2^4\text{He}+\text{energy}+\text{neutrinos}+\text{positrons}$

The helium-4 nucleus produced has less mass than the four protons that went in. This "missing" mass , called the mass defect , is converted into energy according to Einstein's famous equation:

$E=m{c}^2$

where $E$ is the energy released (in joules), $m$ is the mass defect (in kg), and $c=3.0\times 10^8{\text{m s}}^{-1}$ is the speed of light.