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| Sirius A (center) and Sirius B, a white dwarf . Sirius B is the point in the bottom left. Hubble. |
You're right.
It is cool.
Imagine a star. Imagine a dying star, one with an incomprehensibly large number of atoms, of electrons.
Given the right star (a main-sequence star with a mass of 0.07 to 10 solar masses, over 97% of the stars in our galaxy) which expands to a red giant, loses its ability to fuse carbon, and sheds its outer layers, you are left with a dense core mostly of carbon and oxygen, supported against gravitational collapse only by its electron degeneracy pressure.
When electrons are compressed in tiny volumes, they gain a large momentum and kinetic energy, a repulsive force that prevents further compression.
The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time, so there is a resultant repulsive force manifested as a pressure against compression of matter into smaller volumes of space. To add another electron to a given volume requires raising an electron's energy level to make room; there is a requirement for energy to compress the material which appears as pressure.
Solid matter is...solid because of this degeneracy, instead of electrostatic repulsion. For stars which are sufficiently large, electron degeneracy pressure is not enough to prevent them from collapsing under their own weight once nuclear fusion has ceased, and then neutron degeneracy pressure prevents the star from collapsing further. In a nonrelativistic material, this is computed as:
This pressure is in addition to the normal gas pressure P = nkT / V, and neglected unless the density (proportional to n/V) is high enough and the temperature is low enough.
Another way of looking at it is through the uncertainty principle. The Heisenberg uncertainty principle
lets us see that as matter is condensed (uncertainty in position decreases) the momenta uncertainty increases and the electrons must be traveling at a certain speed. When the pressure due to this speed exceed that of the pressure from the thermal motions of the electrons, the electrons are degenerate.Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.38 solar masses). This pressure prevents a white dwarf from collapsing. After the limit, the star will collapse to either a neutron star or black hole (by gravity).
See also
- White dwarf, the wikipedia article
- Simulating a white dwarf supernova; popular article
- Apparently, Betelgeuse is predicted to cataclysmically explode! See the Fox article
Very interesting! Degeneracy pressure is a pretty confusing subject, and every time I think about it, there's something new to understand!
ReplyDeleteWhat do you mean by "Solid matter is...solid because of this degeneracy, instead of electrostatic repulsion"? Solid matter, as we know it in our day-to-day lives, is held up by electrostatic repulsion. But you are right in the sense that if you squeeze it and squeeze it eventually the last recourse to hold up the matter is not electrostatic repulsion but rather degeneracy pressure. It's a bit weird to think about since degeneracy pressure isn't one of the four fundamental forces, and yet it holds things up! 09ooooooooooooooo (whoops that was a short message from my cat :)