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.