# Chandrasekhar boundary

Chandrasekhar boundary

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

After its nuclear fusion processes have ceased , a star like the sun collapses 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 will not be sufficient to stabilize the white dwarf. Instead, depending on its mass, it collapses into a neutron star or black hole .

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 the general theory of relativity are disregarded, as these only play a role in even more compact stars. The limit mass is: ${\ displaystyle M _ {\ mathrm {krit}}}$

${\ displaystyle M _ {\ mathrm {krit}} = 1 {,} 45727 \ left ({\ frac {2} {\ eta}} \ right) ^ {2} M _ {\ odot}}$

Here is the solar mass, and indicates how many nucleons there are on average for an electron , assuming that white dwarfs are electrically neutral. The star matter is made up of atoms with nucleons and protons . ${\ displaystyle M _ {\ odot}}$${\ displaystyle \ eta = A / Z}$${\ displaystyle A}$${\ displaystyle Z}$

## Examples

For white dwarfs, which consists essentially of the carbon - isotope or the oxygen isotope exist, then: ${\ displaystyle {} _ {\ 6} ^ {12} \ mathrm {C}}$${\ displaystyle {} _ {\ 8} ^ {16} \ mathrm {O}}$

${\ displaystyle \ eta = 12/6 = 16/8 = 2}$

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

For white dwarfs with an iron core from the other hand, the following applies: ${\ displaystyle {} _ {26} ^ {56} \ mathrm {Fe}}$

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

Its limit mass is therefore 1.256 solar masses. The Chandrasekhar limit is therefore not to be understood to mean that it is the same for every star. Rather, it depends on the type of stellar matter which upper limit is present.

Thermonuclear supernovae Ia are interpreted as a consequence of exceeding the Chandrasekhar limit mass. These supernovae show a fairly uniform course of the light curve and in their absolute brightness . A subgroup of type Ia supernovae, the super Chandrasekhar Ia supernovae , has a significantly higher luminosity , which suggests 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, whereby the degenerate matter is stabilized against collapse. However, Lorentz forces should prevent a strong increase in the Chandrasekhar limit mass.

### Neutron stars and quark stars

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