The Limit Keeper: Chandrasekhar Limit
Cosmology & the Sky arc, page 148 of 193. Back to The Pixelated Physics Universe
Who they are
Meet The Limit Keeper, guardian of the heaviest white dwarf. A white dwarf is held up not by heat but by electrons that refuse to share quantum states. In 1931 Subrahmanyan Chandrasekhar showed that when those electrons move close to the speed of light, their pressure can no longer beat gravity above a certain mass: about 1.4 times the mass of the Sun for a carbon-oxygen star. The work was part of his 1983 Nobel Prize. The Limit Keeper on a pixel-art unisex tee; equations, symbols and sources in the physics panel below."One point four, and not a grain more."
The Limit Keeper is a character of the Cosmology & the Sky arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
In a white dwarf, electrons refuse to share quantum states and push back, holding the star up. But when the star is heavy enough the electrons move near light speed and that pressure can no longer win. Above about 1.4 times the Sun's mass, gravity always does.
$$ \begin{gathered} M_{\mathrm{Ch}} = \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^{2}} \approx \frac{5.8\,M_\odot}{\mu_e^{2}} \\ \mu_e = 2 \;\Rightarrow\; M_{\mathrm{Ch}} \approx 1.44\,M_\odot\ \text{(ideal)},\ \approx 1.4\,M_\odot\ \text{(real white dwarfs)} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $M_{\mathrm{Ch}}$ | Chandrasekhar limit, maximum mass of a cold white dwarf | kg |
| $\omega_3^{0}$ | constant from the n = 3 Lane–Emden solution, ≈ 2.018 | 1 |
| $\hbar$ | reduced Planck constant | J·s |
| $c$ | speed of light | m/s |
| $G$ | Newtonian gravitational constant | m³ kg⁻¹ s⁻² |
| $\mu_e$ | mean molecular weight per electron (nucleons per electron; 2 for carbon and oxygen) | 1 |
| $m_H$ | mass of a hydrogen atom | kg |
| $M_\odot$ | solar mass, ≈ 1.989×10³⁰ kg | kg |
Sources
- Chandrasekhar (1931) The Maximum Mass of Ideal White Dwarfs, ApJ 74, 81
- NobelPrize.org — The Nobel Prize in Physics 1983
- NIST CODATA 2022 — Newtonian constant of gravitation
Crossovers
The Limit Keeper meets Exclusor (Pauli Exclusion Principle / Degeneracy Pressure). Exclusor's rule gives a white dwarf its degeneracy pressure. The Limit Keeper shows where that pressure stops being enough: once the electrons become relativistic, gravity wins above about 1.4 solar masses.
The Limit Keeper meets Spaghetta (Black Hole Physics / Spaghettification Stretch). The Limit Keeper says how heavy a white dwarf can get. Spaghetta adds that the tidal stretch near a compact object grows as one over distance cubed. Near a small black hole it can pull a body apart before it crosses the horizon.
Wear the lore
- Chandrasekhar Limit Tee: 1.4 M☉
- Related infographic poster: Chandrasekhar's Limit – Plate 067 Physics Poster
Concept keywords: Chandrasekhar Limit, The Limit Keeper, Cosmology & the Sky, physics lore, Pixelated Physics