Chandrasekhar Limit & Stellar Calculator

Calculate Chandrasekhar mass limit, white dwarf radius, and stellar remnant properties.

He/C/O: μe=2, H: μe=1
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Why White Dwarfs Have a Maximum Mass

A white dwarf is supported mainly by electron degeneracy pressure, a quantum-mechanical pressure that does not require the star to remain hot. As mass increases, gravity compresses the star, making the electrons more energetic. In ordinary nonrelativistic degeneracy, compression can provide enough extra pressure to balance gravity, but at sufficiently high density the electrons become relativistic and the pressure no longer stiffens fast enough to support arbitrary mass.

This leads to the Chandrasekhar limiting mass. A common composition scaling is MCh≈5.83/μe2M⊙, where μe is the average number of nucleon masses per electron. Carbon-oxygen and helium white dwarfs have μe≈2, giving a limit near 1.4M⊙. Detailed values depend on composition, rotation, temperature, general-relativistic corrections, and other physical effects.

MCh≈5.83/μe2 M⊙,   Rs=2GM/c2
SymbolMeaningWhy it appears / units
MChChandrasekhar limiting massUsually expressed in solar masses; maximum mass scale for a nonrotating electron-degenerate white dwarf.
μeMean molecular weight per electronDimensionless composition parameter; larger μe lowers the limit.
M⊙Solar massApproximately 1.988×1030kg.
RsSchwarzschild radiusm; horizon radius for a nonrotating uncharged black hole of mass M.

White dwarfs also show an unusual mass-radius trend: adding mass generally makes a degenerate white dwarf smaller. A simple R∝M−1/3 scaling can illustrate the nonrelativistic regime, but it is not accurate near the Chandrasekhar limit, where the radius falls more sharply. Neutron-star and black-hole outcomes require additional physics beyond the white-dwarf mass-limit formula.

Worked Examples

Example 1: White dwarf 1.0 M_sun, μe=2
Using this page's 5.87/μe² approximation: Chandrasekhar ≈1.47 M_sun — below limit
Result: R≈7000 km (Earth-size), ρ=10⁶ g/cm³
Stable white dwarf — our Sun's fate
Example 2: Black hole 10 M_sun
R_s=2GM/c²=2×6.674e-11×2e31/9e16
Result: 29.6 km Schwarzschild radius
Stellar black hole — event horizon
Example 3: Composition dependence
μe=2.15 → MCh≈5.87/(2.15)2M⊙
Result: MCh≈1.27M⊙
Because the limit scales as 1/μe2, even modest composition changes can shift the idealized mass limit.
Example 4: Solar-mass Schwarzschild scale
M=1M⊙ → Rs=2GM/c2
Result: Rs≈2.95km
A normal Sun-sized star is vastly larger than this; the Schwarzschild radius is a compactness threshold, not the radius of an ordinary star.

Common Mistakes

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Treating 1.44M⊙ as an exact universal number

The familiar value is an approximate scale for typical white-dwarf composition. Composition, rotation, temperature, magnetic fields, and more complete stellar physics can shift detailed limits.

⚠️
Using a simple M−1/3 radius law all the way to the limit

That scaling belongs to the nonrelativistic degenerate regime. Near MCh, relativistic electron behavior changes the mass-radius relation significantly.

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Assuming every object above the white-dwarf limit immediately becomes a black hole

Collapse can lead to explosive disruption, a neutron star, or a black hole depending on the stellar system, mass, composition, accretion history, and equation of state.

Frequently Asked Questions

What happens above Chandrasekhar limit?
Above the white-dwarf support limit, electron degeneracy pressure cannot maintain a stable white dwarf. The outcome is not determined by mass alone: accretion, composition, rotation, nuclear burning, stellar evolution, and the dense-matter equation of state can lead to thermonuclear disruption, a neutron star, or black-hole formation in different scenarios.
Type Ia supernova connection?
White dwarfs in binary systems can accrete mass up to Chandrasekhar limit → runaway nuclear fusion → Type Ia supernova. Same brightness everywhere → 'standard candles' used to measure cosmic distances and discover dark energy.
What provides pressure inside a white dwarf?
Electron degeneracy pressure arises from quantum statistics: electrons cannot all occupy the same quantum states. Compressing the star forces electrons into higher-momentum states, creating pressure even when thermal pressure is comparatively unimportant.
Why does a more massive white dwarf become smaller?
Stronger gravity compresses the degenerate matter more intensely. In the nonrelativistic regime the equilibrium mass-radius relation therefore trends roughly as R∝M−1/3. Near the Chandrasekhar limit, relativistic effects make the radius shrink even more steeply.
Is the Chandrasekhar limit the same as the neutron-star maximum mass?
No. The Chandrasekhar limit concerns support by electron degeneracy in white dwarfs. Neutron stars are supported by neutron degeneracy and strong-interaction effects, and their maximum mass depends on the uncertain dense-matter equation of state and relativistic stellar structure.
Why does μe matter?
μe measures how much baryonic mass is associated with each electron that provides degeneracy pressure. If there are fewer electrons per unit mass, electron pressure supports more mass less effectively, so the limiting mass decreases approximately as 1/μe2.

Formula Explorer connections

Interpretation: This relationship connects mass, distance, orbit or spacetime behavior through gravitation and astrophysical scaling. Assumption: Many calculations assume spherical bodies, point masses, circular orbits, weak fields or Newtonian gravity; relativistic regimes require the stated correction.

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