Chapter 22: Problem 10

In what circumstances are degenerate electron pressure and degenerate neutron pressure incapable of preventing the complete gravitational collapse of a dead star?

Short Answer

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Degenerate electron and neutron pressures are incapable of preventing the complete gravitational collapse of a dead star if the star's mass exceeds the Chandrasekhar limit (approximately 1.4 solar masses) or the Tolman-Oppenheimer-Volkoff limit, respectively. Upon exceeding these thresholds, the stars could potentially collapse into black holes.

Step by step solution

Understanding the role of pressures

Pressure in stars is a result of the nuclear reactions occurring within, and this pressure works against the force of gravity, maintaining the star's stability. In dead stars, known as white dwarfs or neutron stars, nuclear reactions cease, but stability is maintained due to 'quantum degeneracy pressure'. In white dwarfs, this is because of electron degeneracy pressure - correlating to the Pauli Exclusion Principle, which states that no two electrons can occupy the same quantum state simultaneously. Neutron stars experience neutron degeneracy pressure, derived essentially from the same principle, but applied to neutrons instead of electrons.

Understanding the limitations: Chandrasekhar Limit and Tolman-Oppenheimer-Volkoff Limit

The Chandrasekhar Limit is the maximum mass that a white dwarf can have (approximately 1.4 solar masses) while being supported by electron degeneracy pressure. If its mass exceeds this limit, electron degeneracy pressure cannot prevent the star from collapsing under its gravity, leading to a supernova or forming a neutron star. The Tolman–Oppenheimer–Volkoff (TOV) Limit, although not precisely determined like Chandrasekhar's, is the equivalent mass limit for a neutron star, beyond which neutron degeneracy pressure also cannot prevent gravitational collapse, leading to the creation of a black hole.

Applying the limits

If a dead star's mass exceeds either the Chandrasekhar limit (making the electron degeneracy pressure inefficient) or the TOV limit (making the neutron degeneracy pressure inefficient), these phenomena cannot prevent the star's gravitational collapse. The star will then undergo further collapse into a black hole.

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In what circumstances are degenerate electron pressure and degenerate neutron pressure incapable of preventing the complete gravitational collapse of a dead star?

Short Answer

Step by step solution

Understanding the role of pressures

Understanding the limitations: Chandrasekhar Limit and Tolman-Oppenheimer-Volkoff Limit

Applying the limits

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