Chandrashekhar Limit

Definition of Chandrasekhar limit : the maximum mass at which a star near the end of its life cycle can become a white dwarf and above which the star will collapse to form a neutron star or black hole : a stellar mass equal to about 1.4 solar masses What is the Chandrasekhar limit and what is its basis? Chandrasekhar limit is the maximum mass of a stable white dwarf star. Stable, in this case, refers to hydrostatic equilibrium—an equilibrium between the outward thermal force and the inward gravitational pull. Chandrasekhar limit is based on a quantum-mechanical effect rising from the Pauli exclusion principle, called electron degeneracy pressure. Pauli exclusion principle says that electrons can never occupy the same state; rather, they must occupy a band of energy levels. One can view an electron as a gas, since it is a reasonably accurate conception of its dual—particle and wave— nature. As stars reach the final stages of their cycle, their radiation pressure fades out and their gravitational pull dominates. This tips the hydrostatic equilibrium, and if the star is massive enough, it can compress its atoms to a level that the electrons can go into the nuclei through the process of K-capture. (Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell.) This compression takes place only when the star’s mass exceeds the Chandrasekhar limit. Its numerical value is 2.765 ×1030 kilograms or approximately 1.4 M☉ (solar mass). What is its significance in astrophysics? Since the life of a star is characterized by thermonuclear fussion, the Chandrasekhar limit plays a crucial role in studying stars.  Neutron stars — If a main sequence star does not shed enough mass to morph itself below this limit, it becomes a neutron star; the electron degeneracy pressure is not enough to keep this star from collapsing. Interestingly, this decrease in the gravitational potential energy releases a lot of energy, often in the order of 1046Joules.  Life — The Chandrasekhar limit is also known as the threshold that makes life possible. Heavier (than hydrogen and helium) elements—essential to life—like carbon, oxygen, and nitrogen are forever trapped in stars if it weren’t for supernova explosions. For rocky planets to form, it is required that get enough rocky material out into the universe and such stars can deliver that material in sizable quantities—through supernovae. In fact, Subrahmanyan Chandrasekhar was awarded a Nobel Prize in physics for his extensive insights into astrophysics.

Electron Degeneracy Pressure

The Pauli exclusion principle states that no two electrons with the same spin can occupy the same energy state in the same volume. Once the lowest energy level is filled, the other electrons are forced into higher and higher energy states resulting in them travelling at progressively faster speeds. These fast moving electrons create a pressure (electron degeneracy pressure) which is capable of supporting a star! In particular, electron degeneracy pressure is what supports white dwarfs against gravitational collapse, and the Chandrasekhar limit (the maximum mass a white dwarf can attain) arises naturally due to the physics of electron degeneracy. As the mass of a white dwarf approaches the Chandrasekhar limit, gravity attempts to squeeze the star into a smaller volume, forcing electrons to occupy higher energy states and attain faster velocities. At the Chandrasekhar limit, the pressure exerted by the electrons travelling at close to the speed of light becomes insufficient to support the star, and the white dwarf collapses into a much denser state. Electron degeneracy occurs at densities of about 106 kg/m3.