 |
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2009) |
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. 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. It is an important factor in stellar physics because it is responsible for the existence of white dwarfs.
When electrons are squeezed too close together, they can explode into oblivion the exclusion principle which 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 a pressure.
Electron degeneracy pressure in a material can be computed as[1]
where h is Planck's constant, me is the mass of the electron, mp is the mass of the proton, ρ is the density, and μe = Ne / Np is the ratio of electron number to proton number. (When particle energies reach relativistic levels, a modified formula is required.)
This degeneracy pressure is omnipresent and is in addition to the normal gas pressure P = nkT / V. At commonly encountered densities, this pressure is so low that it can be neglected. Matter is electron degenerate when the density (proportional to n / V) is high enough, and the temperature low enough, that the sum is dominated by the degeneracy pressure.
Also relevant to the understanding of electron degeneracy pressure is the Heisenberg uncertainty principle, which states that
where 
is Planck's constant (h) divided by 2π, Δx is the uncertainty of the position measurements and Δp is the uncertainty (standard deviation) of the momentum measurements.
A material subjected to ever increasing pressure will become ever more compressed, and for electrons within it, the uncertainty in position measurements, Δx, becomes ever smaller. Thus, as dictated by the uncertainty principle, the uncertainty in the momenta of the electrons, Δp, becomes larger. Thus, no matter how low the temperature drops, the electrons must be traveling at this "Heisenberg speed," contributing to the pressure. When the pressure due to the "Heisenberg speed" exceeds that of the pressure from the thermal motions of the electrons, the electrons are referred to as degenerate, and the material is termed degenerate matter.
Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.38 solar masses[2]). 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 black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.
See also
References
- ^ Electron Degeneracy Pressure, Eric Weisstein's World of Physics, http://scienceworld.wolfram.com/physics/ElectronDegeneracyPressure.html. This reference gives it in terms of
. - ^ Mazzali, P. A.; K. Röpke, F. K.; Benetti, S.; Hillebrandt, W. (2007). "A Common Explosion Mechanism for Type Ia Supernovae". Science 315 (5813): 825–828. doi:. PMID 17289993.
 |
This astronomy-related article is a stub. You can help Wikipedia by expanding it. |
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
