What is Electron Degeneracy Pressure and White Dwarfs ExplainedElectron degeneracy pressure is a result of Pauli exclusion principle where 2 fermions can't occupy the same quantum state at the same time.
This article is part of a series of articles. Please use the links below to navigate between the articles.
Electron degeneracy pressure is a fundamental concept in astrophysics that plays a crucial role in the evolution of stars. This pressure arises from the quantum mechanical properties of electrons and helps to support the structure of stars against the force of gravity.
Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. As a result, electrons in a dense gas or solid are forced into higher energy states, creating a pressure that resists further compression. In the context of stellar evolution, electron degeneracy pressure plays a crucial role in supporting the structure of white dwarfs and neutron stars against the force of gravity. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a neutron star or black hole.
Electron Degeneracy Pressure is an important factor in stellar physics because it is responsible for the existence of white dwarfs. When electrons are squeezed too close together, the exclusion principle requires them to have different energy levels. To add another electron to a given volume requires raising an electron's energy level to make room, and this requirement for energy to compress the material appears as pressure.
Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit of 1.44 solar masses. This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without usable nuclear fuel will continue to collapse to form either a neutron star or a black hole because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.
How does Electron Degeneracy Pressure Affect the Evolution of Stars?
Electron degeneracy pressure plays a critical role in the evolution of stars, particularly in the later stages of their lives. As a star exhausts its nuclear fuel, it begins to collapse under the force of gravity. However, electron degeneracy pressure prevents the star from collapsing completely, creating a stable structure known as a white dwarf. In more massive stars, electron degeneracy pressure is eventually overcome by gravity, leading to a catastrophic collapse and the formation of a neutron star or black hole. Understanding the role of electron degeneracy pressure is essential for predicting the fate of stars and the formation of exotic objects in the universe.
Electron Degeneracy Pressure Calculations
The equation for calculating Electron Degeneracy Pressure is given by:
Equation 38 - Electron degeneracy pressure
Where h is Planck's constant, me is the mass of the electron, mp is the mass of the proton, ? is the density, and ?e = Ne / Np is the ratio of electron number to proton number.
This pressure is derived from the energy of each electron and every possible momentum state of an electron within this volume up to the Fermi energy being occupied. This degeneracy pressure is omnipresent and is in addition to the normal gas pressure.
Equation 49 - Normal gas pressure
At commonly encountered densities, this pressure is so low that it can be neglected. The matter is electron degenerate when the density (n/V) is high enough, and the temperature low enough, that the sum is dominated by the degeneracy pressure.
Future Research and Implications of Electron Degeneracy Pressure
Further research into electron degeneracy pressure could lead to a better understanding of the evolution of stars and the formation of other celestial objects. It could also have implications for our understanding of the universe as a whole, as the behaviour of matter under extreme conditions is still not fully understood. By studying the properties of electron degeneracy pressure, scientists may be able to unlock new insights into the nature of matter and the fundamental forces that govern the universe.
