Chandrasekhar limit

Author: Leandro Alegsa Creation date: November 13, 2022

The Chandrasekhar limit is the maximum mass of a stable white dwarf star. Building on work by others, the Indian physicist Subrahmanyan Chandrasekhar worked on the calculation. He published series of papers between 1931 and 1935. The Chandrasekhar limit is about 1.4 times the mass of the Sun.

The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is not enough to balance the star's own gravitational self-attraction. Then, white dwarfs with masses over the limit would gravitationally collapse into a neutron star or black hole. However, white dwarfs usually explode before they undergo collapse. Those with masses under the limit remain stable as white dwarfs.

Examples

For white dwarfs consisting essentially of the carbon isotope ${}_{{\ 6}}^{{12}}{\mathrm {C}}$ or the oxygen isotope ${}_{{\ 8}}^{{16}}{\mathrm {O}}$ valid:

$\eta =12/6=16/8=2$

This results directly in the mentioned critical mass of 1.457 solar masses. An example for such a star is SiriusB.

For white dwarfs with an iron core of , on the other hand, holds: ${}_{{26}}^{{56}}{\mathrm {Fe}}$

$\eta =56/26\approx 2{,}154$

Its limiting mass is therefore 1.256 solar masses. The Chandrasekhar limit is therefore not to be understood in such a way that it is the same for every star. It rather depends on the kind of stellar matter, which upper limit is present in each case.

Thermonuclear supernovae Ia are interpreted as a consequence of exceeding the Chandrasekhar limit mass. These supernovae show a rather uniform course of the light curve and in their absolute brightness. A subset of type Ia supernovae, those of the super-Chandrasekhar Ia supernovae, has a much higher luminosity, suggesting a collapsed white dwarf with a mass of up to 2.5 solar masses. Attempts have been made to model white dwarfs with high magnetic field densities, stabilizing the degenerate matter against collapse. However, Lorentz forces should prevent a large increase in Chandrasekhar's limiting mass.

Neutron stars and quark stars

For neutron stars there is an equivalent limit, the Tolman-Oppenheimer-Volkoff limit. Likewise, an equivalent limit is assumed for the hypothetical quark stars, but the equations of state of these exotic types of degenerate matter are not yet precisely known.

Questions and Answers

Q: What is the Chandrasekhar limit?

A: The Chandrasekhar limit is the maximum mass of a stable white dwarf star.

Q: Who worked on the calculation of the Chandrasekhar limit?

A: The Indian physicist Subrahmanyan Chandrasekhar worked on the calculation of the Chandrasekhar limit.

Q: When did Chandrasekhar publish a series of papers on the Chandrasekhar limit?

A: Chandrasekhar published a series of papers on the Chandrasekhar limit between 1931 and 1935.

Q: What is the value of the Chandrasekhar limit?

A: The Chandrasekhar limit is about 1.4 times the mass of the Sun.

Q: Why would white dwarfs with masses over the limit gravitationally collapse?

A: White dwarfs with masses over the limit would gravitationally collapse because the electron degeneracy pressure in the star's core would not be enough to balance the star's own gravitational self-attraction.

Q: What would happen to white dwarfs with masses under the limit?

A: White dwarfs with masses under the limit remain stable as white dwarfs.

Q: What usually happens to white dwarfs before they undergo collapse?

A: White dwarfs usually explode before they undergo collapse.