Chandrasekhar limit

The Chandrasekhar limit is the theoretical upper limit for the mass of a white dwarf, derived in 1930 by the Indian-American astrophysicist and Nobel laureate Subrahmanyan Chandrasekhar. Independently of Chandrasekhar, the same upper limit was calculated earlier by Wilhelm Anderson (1929, Tartu) and Edmund Stoner (1930, Leeds).

After the extinction of its nuclear fusion processes a star collapses like the sun and forms a white dwarf. This is possible for all stars whose mass is below the Chandrasekhar limit. Otherwise, the degeneracy pressure in the star is not sufficient to stabilize the white dwarf. Depending on the mass, a collapse to a neutron star or black hole occurs instead.

White dwarfs are described using the concept of an ideal degenerate electron gas. The derivation of the Chandrasekhar limit is therefore based on statistical quantum mechanics, more precisely on Fermi-Dirac statistics, because electrons are fermions. Effects of general relativity are disregarded, since they play a role only for even more compact stars. For the limiting mass get:

Here the solar mass, and η gives the average number of nucleons per electron, assuming that white dwarfs are electrically neutral. The stellar matter is thereby composed of atoms with nucleons and protons.

Examples

For white dwarfs consisting essentially of the carbon isotope or the oxygen isotope valid:

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:

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.