The Chandrasekhar Limit (1931): How Massive a White Dwarf Can Be

The Chandrasekhar limit is the largest mass a white dwarf can have, about 1.4 times the Sun’s mass. Subrahmanyan Chandrasekhar derived it in 1931, aged about 20. Above the limit a dead star’s core cannot hold itself up and collapses into a neutron star or black hole.

The question

A white dwarf is the hot, dense core left behind when a star like the Sun runs out of fuel: roughly a star’s mass squeezed into a ball the size of a planet. Nothing is burning inside it, so what stops gravity from crushing it further? Quantum mechanics had an answer in the 1920s. Electrons packed this tightly resist being squeezed, a push called electron degeneracy pressure. Without relativity, this pressure seemed able to hold up a white dwarf of any mass. Chandrasekhar asked what happens when the electrons inside move close to the speed of light.

What the paper found

• When the electrons in a white dwarf move at relativistic speeds, degeneracy pressure stops growing fast enough to match gravity. There is a maximum mass it can support.
• His first estimate of that limit was about 0.91 solar masses.
• Later work with an exact equation of state and updated composition gives about 1.4 solar masses, the value quoted today.
• Above the limit, a stellar core has no stable white dwarf state and must collapse further.

How he did it

The paper is pure theory. Chandrasekhar combined Einstein’s special relativity with the quantum statistics of electrons to work out how pressure depends on density in a white dwarf. Adding relativity changes the answer qualitatively: the heavier the star, the more its electrons are forced toward light speed, and the weaker their resistance becomes compared with gravity. He worked on the problem on the ship from India to England, on his way to the University of Cambridge in 1930, and sent the paper to The Astrophysical Journal in November that year.

Why it mattered

The limit is one of the key numbers in astrophysics. It decides the fate of a dying star: below about 1.4 solar masses the core settles as a white dwarf; above it the core keeps collapsing. That opened the door to Baade and Zwicky’s 1934 idea that supernovae make neutron stars and to Oppenheimer and Snyder’s 1939 description of collapse into a black hole.

Acceptance was slow. In 1935 the eminent astronomer Arthur Eddington publicly rejected the idea, and his authority delayed it for years. Chandrasekhar shared the 1983 Nobel Prize in Physics for his theoretical studies of the structure and evolution of stars.

What we know now

The limit is standard physics. It also explains why type Ia supernovae, explosions of white dwarfs, are similar enough to serve as cosmic yardsticks, the tool behind the 1998 discovery that cosmic expansion is accelerating. In the far future, cooling white dwarfs will be among the main objects left in the Degenerate Era. Our guide to stars covers how stars end up as white dwarfs, neutron stars or black holes.

Who wrote it

Subrahmanyan Chandrasekhar was a young physicist from Madras, India, traveling to Cambridge on a scholarship when he did this work. He went on to a long career in astrophysics, and NASA named its flagship X-ray telescope, the Chandra X-ray Observatory, in his honor.

Questions people ask

What is the Chandrasekhar limit?

The Chandrasekhar limit is the maximum mass of a stable white dwarf, about 1.4 times the mass of the Sun. Above it, electron degeneracy pressure cannot resist gravity. Subrahmanyan Chandrasekhar first derived the limit in 1931, with an initial estimate of about 0.91 solar masses that later work refined.

What happens if a white dwarf exceeds the Chandrasekhar limit?

A stellar core above the Chandrasekhar limit cannot stay a white dwarf, because the pressure of its electrons can no longer balance gravity. It must collapse further, into a neutron star or a black hole. White dwarfs pushed toward the limit are also linked to type Ia supernovae.

Who opposed the Chandrasekhar limit?

Arthur Eddington, then one of the most respected astronomers in the world, publicly rejected Chandrasekhar’s result in 1935. His authority delayed acceptance of the limit, but later work confirmed it, and Chandrasekhar shared the 1983 Nobel Prize in Physics.

Read the original

Chandrasekhar, S. (1931). “The Maximum Mass of Ideal White Dwarfs.” The Astrophysical Journal 74, 81. doi:10.1086/143324

Free to read: a scanned PDF on NASA ADS.