Chandrasekhar Limit Simulator: Maximum Mass of White Dwarf Stars

simulator intermediate ~10 min
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M_Ch = 1.44 M☉ — electron degeneracy pressure limit

For a carbon-oxygen white dwarf with electron fraction Y_e = 0.50, the Chandrasekhar limit is 1.44 M☉. A 0.6 M☉ white dwarf has a radius of about 8,700 km — roughly Earth-sized but 200,000 times denser.

Formula

M_Ch = (ℏc/G)^(3/2) × 5.83 / (μ_e m_H)²
R ∝ M^(−1/3) × (1 − (M/M_Ch)^(4/3))^(1/2)
P = K × ρ^(5/3) (non-rel) → K' × ρ^(4/3) (ultra-rel)

A Teenage Discovery

In 1930, nineteen-year-old Subrahmanyan Chandrasekhar, sailing from India to Cambridge, combined quantum mechanics with special relativity to derive a stunning result: white dwarf stars have a maximum possible mass. Above approximately 1.4 solar masses, the quantum pressure of degenerate electrons — the very force that supports white dwarfs — becomes insufficient against gravity. This discovery, initially met with fierce opposition from Arthur Eddington, eventually earned Chandrasekhar the 1983 Nobel Prize.

Electron Degeneracy Pressure

In a white dwarf, electrons are packed so tightly that quantum mechanics forbids them from occupying the same state (the Pauli exclusion principle). This creates an outward 'degeneracy pressure' independent of temperature. However, as the white dwarf mass increases, electrons are forced to higher momenta, approaching the speed of light. In this ultra-relativistic limit, the pressure equation of state softens from ρ^(5/3) to ρ^(4/3), and a maximum supportable mass emerges.

The Mass-Radius Paradox

Unlike normal stars, white dwarfs get smaller as they gain mass — the mass-radius relation runs backwards. Adding mass increases gravity, compressing the star further. Near the Chandrasekhar limit, the radius shrinks dramatically toward zero while central density soars toward infinity. This simulation visualizes this counterintuitive relationship and shows how the white dwarf structure changes as mass approaches the critical threshold.

Type Ia Supernovae

When a white dwarf in a binary system accretes matter from a companion star and approaches the Chandrasekhar limit, carbon ignites in the degenerate core. Unlike in a normal star where the gas would expand and cool, the degenerate material cannot expand — fusion runs away catastrophically, incinerating the entire white dwarf in a Type Ia supernova. These explosions synthesize about 0.6 M☉ of radioactive nickel-56 and serve as cosmological standard candles that revealed the accelerating expansion of the universe.

FAQ

What is the Chandrasekhar limit?

The Chandrasekhar limit (~1.44 M☉) is the maximum mass of a white dwarf star that can be supported by electron degeneracy pressure. Above this mass, the electrons become fully relativistic and degeneracy pressure can no longer balance gravity, leading to collapse. Subrahmanyan Chandrasekhar derived this limit in 1930 at age 19.

What happens when a white dwarf exceeds the Chandrasekhar limit?

If a white dwarf accretes matter from a companion star and approaches the Chandrasekhar limit, the carbon-oxygen core ignites in a runaway thermonuclear explosion — a Type Ia supernova. The entire white dwarf is destroyed, leaving no remnant. These explosions are used as standard candles to measure cosmic distances.

Why is the Chandrasekhar limit important for cosmology?

Type Ia supernovae, triggered when white dwarfs approach the Chandrasekhar limit, have nearly uniform peak luminosities. This makes them excellent standard candles for measuring distances across the universe. They were used to discover the accelerating expansion of the universe in 1998, leading to the concept of dark energy.

Does the Chandrasekhar limit depend on composition?

Yes. The limit is M_Ch = 5.83 × Y_e² M☉, where Y_e is the electron fraction (electrons per baryon). For pure carbon-12 or oxygen-16, Y_e = 0.5, giving 1.46 M☉. For iron-56, Y_e = 0.464, giving 1.26 M☉. General relativistic corrections reduce these values slightly.

Sources

Embed

<iframe src="https://homo-deus.com/lab/stellar-evolution/chandrasekhar-limit/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub