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Issue 5.17

The Astrophysics Spectator

October 29, 2008

Most classes of self-supported objects in the universe are supported against gravity by a pressure generated through quantum-mechanical effects.  On the macroscopic level, in the world of our daily experiences that Newtonian mechanics describes so well, an object can have any kinetic energy, but on the microscopic level, in the world of the electron, energy is quantized, and an electron can only have very specific values for its kinetic energy.  This quantization occurs when electrons are bound within atoms, and it occurs when electrons are moving freely through space.  But this quantization of energy is not the greatest peculiarity seen on the microscopic level; the quantized energy states themselves cannot be occupied by more than 2 electrons.  This is the well-known Pauli exclusion principle, and it causes cold electrons at high densities to exert a considerable pressure, a pressure that supports objects as diverse as the giant gaseous planets such as Saturn and Jupiter, the brown dwarfs, the degenerate (white) dwarfs, and the neutron stars.

Degeneracy pressure sets the floor under the size of astronomical objects ranging in mass from Saturn and Jupiter to the heaviest neutron stars.  The higher floor is set by electron degeneracy found in the giant gaseous planets, the brown dwarfs, and the degenerate dwarfs.  The lower floor is set by proton and neutron degeneracy found in the neutron stars.  The fusion-powered stars of less than 10 solar masses are evolving down to one of these two floors.

As befits objects that are governed by microscopic physics, the range of masses over which they are degenerate is set by ratios of fundamental constants.  For electron-degenerate objects, the lower limit on mass is set by a combination of the gravitational constant, the proton's mass, and the electron's charge.  For both degenerate dwarfs and neutron stars, the upper limit on mass is set by the gravitational constant, the proton's mass, and the Planck constant.  The ratio of these two masses is set by the fine structure constant, which is a constant that arises in the description of the hydrogen atom.  All of these constants that describe the microscopic world are directly manifested in the cosmic world of the giant gaseous planets and the degenerate dwarfs.

Next Issue: The next update to the web site is planned for around November 12.

Jim Brainerd

Stars

Degeneracy Pressure.  Jupiter and Saturn have a fundamental link to the degenerate (white) dwarfs and neutron stars: all of these objects are supported against gravitational collapse by a pressure generated through the Pauli exclusion principle of quantum mechanics.  This pressure is called degeneracy pressure, and it acts through electrons in planets, brown dwarfs, and degenerate dwarfs, and through neutrons and protons in neutron stars.  It's existence is directly linked to existence of chemical elements with distinctive properties.  (continue)

The Masses of Degenerate Objects.  Objects supported by electron degeneracy pressure span a broad range of masses.  The low-mass end of this range, which is near the mass of Saturn, is set by the transition from pressure exerted by atoms to pressure exerted by degenerate electrons.  The high end of this range, which is 1.4 solar masses, is set by the gravitational instability that arises when the degenerate electrons have kinetic energies equal to the electron rest-mass energy.  These limits are given by several fundamental constants of physics.  Despite the neutron stars being supported by neutron and proton degeneracy pressure rather than electron degeneracy pressure, they have an upper mass similar to that of the degenerate dwarf.  (continue)

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