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Subrahmanyan Chandrasekhar showed, while still in his twenties, that a white dwarf star cannot be heavier than a certain mass, about 1.4 times the mass of the Sun according to his Nobel lecture. Above that, the star cannot hold itself up. The idea was publicly challenged in the 1930s, and the white dwarf work was highlighted when he won the 1983 Nobel Prize in Physics. Here is the physics in plain terms, and an estimate of the limit you can do with a few constants.
Who was Chandrasekhar?
The Nobel Prize facts page records that he was born on 19 October 1910 in Lahore and died on 21 August 1995 in Chicago. The Chandra X-ray Center's biography, written for the NASA telescope named after him, gives the timeline: B.Sc. physics at Presidency College, Madras (1925-1930), Ph.D. at Cambridge under R. H. Fowler (1930-1933), and papers on white dwarf stars in 1931-32. The same page notes that he guided over fifty students to their Ph.D.s and edited the Astrophysical Journal for 19 years.
What is a white dwarf, and what holds it up?
The 1983 Nobel press release describes a white dwarf as what a star of around the Sun's mass becomes at the end of its life. Its matter is so compressed that one cubic centimetre weighs around 1,000 kilograms. The atoms' electron shells are crushed, leaving nuclei and an electron gas.
Gravity is not balanced by heat in such a star. In his Nobel lecture, Chandrasekhar explains R. H. Fowler's earlier resolution: the electrons are highly degenerate under Fermi-Dirac statistics. Electrons are fermions, so no two can share a state, and squeezing them forces them into higher-momentum states. That produces pressure even when the star is cold. (For the difference between fermions and bosons, see our post on S. N. Bose.)
Where does the limit come from?
Fowler's picture, Chandrasekhar's lecture continues, predicted a stable white dwarf for any mass. But in heavier white dwarfs the electrons move so fast that relativity matters. For a white dwarf of one solar mass, the lecture gives a central density of 4.19 × 10^6 g/cm^3 and electron speeds of about 0.63c.
When the electrons become fully relativistic, pressure grows more slowly as the star is squeezed. Chandrasekhar showed that the mass of the configuration is then fixed by the constant in the pressure-density relation, which is built from constants of nature, so there is an upper limit. Stars above it cannot end as white dwarfs. The Chandra biography says the result "shows that stars much more massive than the Sun must either explode or form black holes." His lecture puts the mass of a fully relativistic degenerate core, close to the limiting mass, at "approximately 1.4" solar masses. His 1931 paper was titled "The Maximum Mass of Ideal White Dwarfs."
The result was challenged. The Chandra timeline lists a "Battle with Eddington" at the Royal Astronomical Society on 11 January 1935. He shared the 1983 physics prize with William Fowler; Chandrasekhar's half was "for his theoretical studies of the physical processes of importance to the structure and evolution of the stars."
Worked example: estimating the limit with dimensional analysis
The mass limit depends on ħ (quantum mechanics), c (relativity), G (gravity) and the mass carried per electron. A natural combination of these with units of mass is:
M ~ (ħc / G)^(3/2) / (μe mp)^2
Here μe is the number of nucleons per electron. For helium, carbon or oxygen, μe = 2, the value the Nobel lecture uses. Constants from NIST's CODATA values: ħ = 1.0546 × 10^-34 J s, G = 6.6743 × 10^-11 m^3 kg^-1 s^-2, mp = 1.6726 × 10^-27 kg, c = 2.998 × 10^8 m/s.
ħc = 3.16 × 10^-26 J m.
ħc / G = 4.74 × 10^-16 kg^2.
(ħc / G)^(3/2) = 1.03 × 10^-23 kg^3.
Divide by mp^2 = 2.80 × 10^-54 kg^2: about 3.7 × 10^30 kg, or 1.85 solar masses, using the NASA Sun fact sheet value of 1.988 × 10^30 kg.
Divide by μe^2 = 4: about 0.46 solar masses.
The full calculation, which needs the solution of the Lane-Emden equation (the lecture quotes a constant of 2.018 from it), gives about 1.4. Dimensional analysis lands within a factor of about three. That is the point of the method, as our guide to dimensional analysis checks explains: it gets the scale right and shows how the answer depends on each constant.
What students can take from Chandrasekhar
Combine theories. The limit appears only when quantum statistics, relativity and gravity are used together.
Check the regime. Fowler's model worked until the electrons got fast; always ask if your assumptions still hold.
Estimate before computing. Five constants and a careful exponent gave the right scale.
For how astronomers read a star's temperature in the first place, see Meghnad Saha and the ionisation equation. If degeneracy pressure or the Pauli principle is still fuzzy, the Fermi Concept Library has a lesson for every concept in physics and shows where it sits in the map, so you can see which ideas come first.
