Chandrasekhar Limit
The Chandrasekhar limit is the maximum mass of a stable, non-rotating white dwarf, approximately 1.4 solar masses (1.44 for a carbon–oxygen composition); above this mass, electron degeneracy pressure cannot balance gravity, because the electrons become relativistic, and the star must collapse or explode.
Curious
A white dwarf is held up not by heat but by a quantum effect: electrons cannot be squeezed into the same state, so they resist compression (degeneracy pressure). Counterintuitively, heavier white dwarfs are smaller. As mass rises, the electrons are squeezed so hard that they move near the speed of light, and then the support stops growing fast enough to match gravity.
In 1930, the 19-year-old Subrahmanyan Chandrasekhar worked out this limit on a sea voyage from India to England. It determines which stars end as white dwarfs and which go on to become neutron stars or black holes, and it underlies Type Ia supernovae.
Exploring
| Quantity | Value |
|---|---|
| Limit (C/O white dwarf) | ~1.44 M☉ |
| Limit with μe = 2.15 | ~1.26 M☉ |
| Typical observed white dwarf mass | ~0.6 M☉ |
Deep Dive
Origin of the scaling. For a polytrope of index 3, which describes the fully relativistic degenerate electron gas, the equilibrium mass becomes independent of the central density: M = (√(3π)/2)(ℏc/G)3/2 (μemH)−2 × 2.018 ≈ 5.83 μe−2 M☉. Fundamental constants fix the number, so the result is a statement about nature rather than about any particular star. Rotation and strong magnetic fields can raise the effective limit; hypothetical super-Chandrasekhar white dwarfs have been proposed to explain a few unusually luminous Type Ia supernovae, but this remains debated.
The 1935 dispute. At a Royal Astronomical Society meeting in January 1935, Arthur Eddington publicly dismissed Chandrasekhar's result, arguing that nature must forbid such behaviour. Most physicists, including Bohr and Rosenfeld, privately sided with Chandrasekhar, but the objections of the most influential British astrophysicist delayed acceptance for years. The limit was fully accepted as the physics of neutron stars and supernovae developed, and Chandrasekhar shared the 1983 Nobel Prize in Physics with William Fowler.
Consequences. When a white dwarf accretes matter from a companion and nears the limit, a thermonuclear runaway can produce a Type Ia supernova, whose fairly uniform peak brightness is used to measure cosmic distances (see Dark Energy). The exact progenitor channels (single-degenerate versus double-degenerate mergers, with sub-Chandrasekhar explosions also proposed) are an active research question.
Concept Relationship Map
Requires: white dwarfs, quantum mechanics (Pauli exclusion)
Enables: Type Ia supernovae, neutron stars
Commonly confused with: the neutron-star mass limit (TOV limit)
Sources
- Chandrasekhar, S. (1931). The Astrophysical Journal, 74, 81–82.
- Chandrasekhar, S. (1935). “The highly collapsed configurations of a stellar mass (second paper).” Monthly Notices of the Royal Astronomical Society, 95, 207–225.
- Miller, A.I. (2005). Empire of the Stars. Houghton Mifflin.