Chandrashekhar Limit and Tolman-Oppenheimer-Volkoff limit

In my article on electron degeneracy, I mentioned about the Chandrashekar limit which was proposed by an Indian astrophysicist Subrahmanyan Chandrashekhar at the age of 20 in 1930.

As I explained earlier that, white dwarfs resist gravitational collapse through electron degeneracy. But after the Chandrashekhar limit it cannot resist more.

Subrahmanyan Chandrashekhar

Chandrashekhar limit is about 1.4 solar masses, which is approximately 2.765 x 10^³⁰ kg. Beyond this limit, the star’s core cannot resist more and either forms a neutron star or a black hole depending upon the mass.

Electron degeneracy pressure is a quantum-mechanical effect arising from the Pauli exclusion principle. Since electrons are fermions, no two electrons can be in the same state, so not all electrons can be in the minimum-energy level. Rather, electrons must occupy a band of energy levels. 

Compression of the electron gas increases the number of electrons in a given volume and raises the maximum energy level in the occupied band. Therefore, the energy of the electrons increases on compression, so pressure must be exerted on the electron gas to compress it, producing electron degeneracy pressure. With sufficient compression, electrons are forced into nuclei in the process of electron capture, relieving the pressure.

M_limit = {(ωo₃√3π)/2} ( c/G)^^3/2{1/(µ_em_H)}

Where,

ħ is the reduced Planck constant

c is the speed of light

G is the gravitational constant

μ_e is the average molecular weight per electron, which depends upon the chemical composition of the star.

m_H is the mass of the hydrogen atom.

ωo₃ ≈ 2.018236 is a constant connected with the solution to the Lane–Emden equation

Tolman-Oppenheimer-Volkoff limit

Just like the work done by Chandrashekhar Limit for white dwarfs, Tolman-Oppenheimer-Volkoff limit do for Neutron stars. In neutron stars, the gravitational collapse is stopped by Neutron Degeneracy which I explained in my previous article. After this limit, even Neutron degeneracy cannot stop further collapse and form black holes.

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