### Assignments:

Unfinished Assignment Study Questions for Lesson 47

### Lesson Objectives:

- What is a white dwarf?
- Composition, density, and size
- Close binary systems

As you recall, a white dwarf is the exposed, inert carbon core that is left after the low-mass star expels its outer layers in a planetary nebula.

A white dwarf is very dense -- it usually has a mass similar to that of our Sun but a size no larger than our Earth. Since it has so much mass in a small space, gravity is very strong near its surface. What keeps it from contracting further under this powerful force of gravity is called electron degeneracy pressure.

Basically, the idea of electron degeneracy pressure is that the subatomic particles in atoms can only be compressed into so small of a space before they resist. More specifically, the laws of quantum mechanics limit how closely electrons can be packed together. Once they reach this threshold, they exert an outward pressure called degeneracy pressure. In white dwarfs, this degeneracy pressure is enough to counter the inward crush of gravity and maintain the white dwarf's size even though its core is dead and it is not generating any energy through nuclear fusion.

The white dwarf left behind by a low-mass star is mostly made of carbon, since that is what is left over when low-mass stars fuse helium in the latter stages of their lives.

A typical white dwarf contains the mass of our Sun but is the size of Earth. More massive dwarfs are compressed into smaller sizes because greater mass means greater gravity which compresses matter further. For example, a white dwarf with 1.3 times the mass of our Sun would be half the size of our Earth. As they get more compressed, electrons get more excited, moving around faster.

Theoretical calculations indicate that the limit for a white dwarf is about 1.4 times the mass of our Sun since that is when the compressed electrons would reach the speed of light. Since nothing can travel faster than the speed of light, if a white dwarf's mass exceeds this limit, it will explode as a white dwarf supernova.

If a white dwarf has a main-sequence or giant star close enough to it, it can pull away some of that companion star's material, leading to a rapidly rotating disk of gas around the white dwarf called an accretion disk.

This hydrogen gas from the companion star accumulates on the surface of the white dwarf, pressure and temperatures rise from as this layer of hydrogen contracts, and eventually, it reaches 10 million Kelvin where nuclear fusion can occur on the surface, causing a nova. A nova is not nearly as bright as a supernova, but can still shine as brightly as 100,000 Suns.

If accretion causes a white dwarf to exceed 1.4 times the mass of the Sun or if two white dwarfs orbiting each other merge together and exceed that mass limit, the result is a white dwarf supernova.