Stellar Physics
Chandrasekhar Limit
Maximum mass of a white dwarf — ~1.4 M_sun, beyond which gravity overwhelms electron degeneracy
The Chandrasekhar limit is the maximum mass a white dwarf can have before gravity overcomes electron degeneracy pressure. Value: ~1.4 M_sun. Above this, the star cannot remain stable — collapses to neutron star or explodes as Type Ia supernova. Discovered by Subrahmanyan Chandrasekhar in 1930 (~age 19, on a ship from India to England). Originally rejected by Eddington as impossible — Chandrasekhar later proved correct, won Nobel Prize 1983. Fundamental concept in stellar physics.
- Mass limit1.40 M_sun (more precisely 1.43)
- DiscoverySubrahmanyan Chandrasekhar, 1930
- Nobel Prize1983 — for stellar structure work
- Above limitNeutron star or Type Ia SN
- FormulaM_Ch ≈ 1.4 (μ/2)⁻² M_sun (μ = mean molecular weight)
- Originally rejectedEddington 1935; Chandrasekhar persisted
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Why Chandrasekhar matters
- Stellar end states. Determines what white dwarfs become.
- Type Ia supernovae. Origin and standardization.
- Cosmology. Type Ia distance measurements.
- Quantum statistics. Direct application of Pauli exclusion.
- General relativity. Demonstrates strong-field physics.
- Indian science. Chandrasekhar was first Indian Nobel in physics.
- Stellar structure. Most fundamental constraint on dense matter.
Common misconceptions
- Limit is exact 1.4 M_sun. Approximately; depends on composition.
- Above limit always becomes BH. Often neutron star or SN; not BH directly.
- Eddington's rejection ended the idea. Eddington was wrong; Chandrasekhar prevailed.
- Limit only applies to white dwarfs. Specifically — but parallel concept (TOV) for NS.
- Crossing limit is gradual. Catastrophic — once exceeded, structure fails fast.
- Sun reaches Chandrasekhar. No — Sun is too small to approach the limit.
Frequently asked questions
Why is there a maximum mass?
Electron degeneracy pressure (from Pauli exclusion) supports white dwarfs against gravity. Works at densities up to ~10⁹ kg/m³. At higher mass, electrons become relativistic — pressure increases more slowly with density. Eventually gravity wins. Critical mass: ~1.4 M_sun.
How was it derived?
Chandrasekhar combined Fermi-Dirac statistics for degenerate electrons with general relativity at high mass. Result: pressure ~ density^(4/3) for relativistic electrons (vs 5/3 for non-relativistic). This power law cannot support star above critical mass. Calculation (1930) was elegant; result fundamental.
What happens at the limit?
Two outcomes. (1) Type Ia supernova — carbon ignition triggers thermonuclear runaway; white dwarf disrupts. (2) Accretion-induced collapse — outer layers collapse; result depends on conditions. Generally Type Ia is preferred outcome for accretion onto C/O white dwarf.
How was it confirmed?
(1) Observation of white dwarfs — none above ~1.4 M_sun. (2) Type Ia SN luminosity uniformity — consistent with all from same mass. (3) Detailed binary observations — companion mass loss matches white dwarf approaching limit. Empirical evidence strong.
Why was it controversial?
Eddington (1935) publicly rejected the idea — couldn't accept stellar collapse. Said "I think there should be a law of Nature to prevent a star from behaving in this absurd way!" Eddington was mistaken — Chandrasekhar correct. Took years for community to accept. Nobel Prize awarded 1983.
Are there extensions?
Yes. Tolman-Oppenheimer-Volkoff limit — maximum mass for neutron star (~3 M_sun). Above this: black hole. Different physics (neutron degeneracy + GR effects). Chandrasekhar limit is for electron-supported objects; TOV for neutron-supported; both are upper bounds.
What's μ in the formula?
Mean molecular weight per electron. For pure ¹²C: μ = 12/6 = 2 (each ¹²C provides 6 electrons; 12 g/mol). For ⁵⁶Fe: μ = 56/26 ≈ 2.15. For pure He: μ = 4/2 = 2. White dwarf composition affects exact mass limit slightly. Typical C/O composition: M_Ch ≈ 1.4 M_sun.