Understanding the Chandrasekhar Limit

May 14, 2025

Chandrasekhar Limit

Definition

  • The Chandrasekhar limit is the maximum mass of a stable white dwarf star.
  • Accepted value: approximately 1.4 solar masses (2.765 x 10^30 kg).
  • Named after Subrahmanyan Chandrasekhar.

White Dwarfs & Electron Degeneracy Pressure

  • White dwarfs resist gravitational collapse through electron degeneracy pressure.
  • Main sequence stars resist through thermal pressure.
  • Above the Chandrasekhar limit, electron degeneracy pressure can't balance gravitational attraction.

Stellar Evolution

  • Stars below the limit become white dwarfs.
  • Stars above the limit can become neutron stars or black holes.
  • Process involves fusion of hydrogen into helium, then heavier elements, culminating in iron.

Theoretical Basis

  • Electron degeneracy pressure arises from the Pauli exclusion principle.
  • Electrons, being fermions, can't all occupy the same energy state, leading to pressure.
  • Compression increases electron energy, exerting pressure.
  • In strong compression, electron capture occurs, affecting stability.

Equation of State

  • Non-relativistic case: P = K_1 ρ^5/3, resulting in a polytrope of index 3/2.
  • Relativistic limit: P = K_2 ρ^4/3, resulting in a polytrope of index 3.
  • Fully relativistic treatment interpolates between non-relativistic and relativistic equations.

Historical Development

  • Ralph H. Fowler and Edmund Clifton Stoner contributed to initial models of white dwarf stars.
  • Wilhelm Anderson and Stoner made significant early discoveries on mass limits.
  • Subrahmanyan Chandrasekhar further developed these ideas, including the relativistic treatments.

Controversies

  • Arthur Eddington opposed Chandrasekhar's findings, leading to significant debate.
  • Proposed modifications to relativity to avoid collapse, not widely accepted.

Supernovae

  • Type Ia supernovae result from runaway nuclear fusion in white dwarfs near the Chandrasekhar limit.
  • Some observed supernovae exceed this limit, suggesting phenomena like rapid rotation or mergers.

Chandrasekhar's Recognition

  • Awarded the Nobel Prize in Physics in 1983 for his work on stellar evolution.

Related Concepts

  • Tolman–Oppenheimer–Volkoff limit: Governs the maximum mass of neutron stars.
  • Super-Chandrasekhar mass supernovae: Observations include supernovae exceeding the typical Chandrasekhar limit due to unique conditions like rapid rotation or merging events.