Chandrasekhar Limit
The Chandrasekhar limit is the theoretical maximum mass (~1.4 solar masses) that a white dwarf star can possess and still be supported against gravitational collapse by electron degeneracy pressure. Below this limit, degenerate electrons exert sufficient quantum mechanical pressure to halt collapse; above it, gravity overwhelms this pressure, triggering a Type Ia supernova or collapse to a neutron star. The limit was derived by Subrahmanyan Chandrasekhar in 1930 using special relativistic corrections to the equation of state of a degenerate electron gas, earning him the 1983 Nobel Prize in Physics.
Key Formula
M_Ch ≈ 5.87 / μ_e² × (ℏc/G)^(3/2) / m_H² ≈ 1.4 × M_sun
LaTeX: M_{\rm Ch} = \frac{\omega_3^0 \sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^2} \approx 1.4\,M_\odot
| Symbol | Meaning | Unit |
|---|---|---|
| M_Ch | Chandrasekhar limiting mass | solar masses (M☉) |
| ℏ | Reduced Planck constant | J·s |
| c | Speed of light | m/s |
| G | Gravitational constant | N·m²/kg² |
| μ_e | Mean molecular weight per electron | dimensionless (~2 for C/O) |
| m_H | Hydrogen atom mass | kg |
Worked Example
Problem
A white dwarf accretes mass from a companion and reaches 1.38 M☉. Another 0.03 M☉ is accreted. Describe qualitatively what happens and why.
Solution
Step 1 — Check against the limit: 1.38 + 0.03 = 1.41 M☉ > 1.4 M☉ = Chandrasekhar limit. Step 2 — At M > M_Ch, electron degeneracy pressure can no longer balance gravity. Step 3 — The core contracts, raising temperature above ~5 × 10⁹ K, igniting runaway carbon fusion. Step 4 — Because degenerate matter does not expand on heating, a thermonuclear runaway (deflagration/detonation) destroys the star as a Type Ia supernova. Step 5 — The explosion releases ~1–2 × 10⁴³ J, briefly outshining the host galaxy.
Answer
The white dwarf undergoes a Type Ia supernova, completely disrupting the star with energy ~10⁴³ J.
Comparison of Stellar Remnant Types and Mass Boundaries
| Remnant Type | Typical Mass (M☉) | Support Mechanism | Density (kg/m³) | Stability |
|---|---|---|---|---|
| White Dwarf | 0.5–1.4 | Electron degeneracy pressure | ~10⁹ | Stable below limit |
| At Chandrasekhar Limit | ~1.4 | Limit of e⁻ degeneracy | ~10¹⁰ | Unstable — collapses |
| Neutron Star | 1.4–2.3 | Neutron degeneracy + nuclear forces | ~10¹⁷ | Stable below TOV limit |
| Black Hole | > 2–3 | No stable support | > 10¹⁸ | Collapse to singularity |
| Main-Sequence Star | 0.08–150 | Thermal gas pressure | ~10³–10⁵ | Stable during H fusion |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Stellar Nucleosynthesis
Stellar nucleosynthesis is the process by which nuclear fusion reactions inside stars create heavier atomic nuclei from lighter ones, releasing energy that sustains the star against gravitational collapse. Main-sequence stars primarily fuse hydrogen into helium via the proton–proton chain or CNO cycle, while more massive stars in later evolutionary stages fuse helium, carbon, oxygen, and silicon up to iron (Fe-56), the most tightly bound nucleus. Elements heavier than iron are synthesised through neutron-capture processes (s-process in AGB stars; r-process in neutron star mergers and supernovae), making stars the principal factories of the chemical elements in the universe.
Pulsar
A pulsar is a highly magnetised, rapidly rotating neutron star that emits beams of electromagnetic radiation from its magnetic poles; when these beams sweep across Earth like a cosmic lighthouse, observers detect precise periodic pulses ranging from milliseconds to seconds. Pulsars are the remnants of massive stars (>8 M☉) that exploded as core-collapse supernovae, leaving behind an object ~20 km in diameter but with a mass of 1.4–2 M☉ and a density (~10¹⁷ kg/m³) comparable to atomic nuclei. The extreme regularity of pulsar timing makes them natural clocks used to test general relativity, detect gravitational waves, and probe the interstellar medium.
Binary Star System
A binary star system consists of two stars gravitationally bound to each other, orbiting their common centre of mass (barycentre) under mutual gravitational attraction. Binary systems are remarkably common, accounting for roughly half of all star systems in the Milky Way, and are the primary means of directly measuring stellar masses through application of Kepler's third law. Depending on orbital geometry, binaries may be classified as visual, spectroscopic, eclipsing, or astrometric, each revealing complementary information about the stellar components.
Named after Indian-American astrophysicist Subrahmanyan Chandrasekhar (1910–1995), who derived the limit in 1930 at age 19 during his voyage from India to England. "Chandrasekhar" means "holder of the Moon" in Sanskrit.