A star spends about 90% of its life on the main sequence. When the hydrogen in its core runs out, as described in main-sequence lifetimes, its life changes fast. For a star like the Sun, here is what happens next.
Why it works
With no fusion in the core, nothing supplies the heat that held it up, so gravity squeezes the core of helium; squeezing heats it. Hydrogen just outside the core now gets hot enough to fuse in a shell, faster than the core ever did. The extra energy pushes the star's outer layers outward, and the star swells to tens or hundreds of times its old radius. Its surface, spread over a far larger area, cools to about $3500$ to $4500$ K and glows orange-red: a red giant, cooler but far more luminous. When the core reaches about 100 million K, helium nuclei fuse into carbon and oxygen. Once the helium runs out, a Sun-like star cannot squeeze its core hot enough for the next step. Its outer layers drift off as a glowing planetary nebula (nothing to do with planets), and the bare core is left: a white dwarf.
Key idea
When core hydrogen runs out, a Sun-like star swells into a red giant, later fuses helium into carbon and oxygen, then sheds its outer layers. Its core remains as a white dwarf: about the Sun's mass packed into a ball the size of Earth, slowly cooling.
Worked examples
Worked example: How big is a red giant?
A red giant has $1000$ times the Sun's luminosity and $0.6$ of its surface temperature. Find its radius.
- $L = R^2T^4$, so $R = \frac{\sqrt{L}}{T^2} = \frac{\sqrt{1000}}{0.6^2} = \frac{31.6}{0.36}$.
- $R \approx 88$ solar radii, about $0.41$ AU: larger than Mercury's orbit.
Answer: About $88$ solar radii.
Worked example: A white dwarf's density
A white dwarf has $0.6$ solar masses ($1.19 \times 10^{30}$ kg) in a radius of $6000$ km. Find its density.
- Volume: $\frac{4}{3}\pi (6.0 \times 10^{6})^3 = 9.05 \times 10^{20}\ \text{m}^3$.
- Density: $\frac{1.19 \times 10^{30}}{9.05 \times 10^{20}} = 1.3 \times 10^{9}$ kg/m³.
- A sugar-cube-sized piece would have a mass of over a tonne. No fusion holds it up: the electrons are packed so tightly that they resist further squeezing.
Answer: About $1.3 \times 10^{9}$ kg/m³.
Common mistake
The Sun will not become a black hole or explode as a supernova; those fates need stars of more than about 8 solar masses. A white dwarf can hold up at most about 1.4 solar masses (the Chandrasekhar limit), and the Sun's core will be well under that. Check the path: red giant, planetary nebula, white dwarf, which is just what we see around many stars in our galaxy today.