Chandrasekhar Limit - White Dwarfs and Black HolesThe Chandrasekhar limit is an upper limit on the mass of stars where the electron degeneracy pressure and gravity balance out.
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The Chandrasekhar limit is an upper bound on the mass of bodies made from electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of electrons.
The Chandrasekhar Limit is named for Subrahmanyan Chandrasekhar, one of the great child prodigies. Chandrasekhar graduated with a degree in physics before reaching his twentieth birthday. He was awarded a Government of India scholarship to study at Cambridge, and in the fall of 1930 boarded a ship to travel to England. While aboard the ship - still before reaching his twentieth birthday - he did the bulk of the work for which he would later be awarded a Nobel Prize.
The Chandrasekhar limit is the maximum non-rotating mass which can be supported against gravitational collapse by electron degeneracy pressure. Electron degeneracy pressure is a result of the Pauli Exclusion Principle, which states that 2 fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without collapsing it into a neutron star or a black hole. It is accepted as being 1.44 solar masses. As white dwarfs are composed of electron-degenerate matter, no non-rotating white dwarf can be heavier than the Chandrasekhar limit. The Chandrasekhar limit is analogous to the Tolman-Oppenheimer-Volkoff limit for neutron stars.
White dwarf stars are the end products of the stellar evolution of low to medium-mass stars like our Sun. For white dwarf stars with masses greater than the Chandrasekhar Limit electron degeneracy pressure is not enough to prevent gravity from collapsing the star further into a neutron star or black hole.
Stars produce energy through nuclear fusion, producing heavier elements from lighter ones. The heat generated from these reactions prevents the gravitational collapse of the star. Over time, the star builds up a central core which consists of elements which the temperature at the centre of the star is not sufficient to fuse. For main-sequence stars with a mass below approximately 8 solar masses, the mass of this core will remain below the Chandrasekhar limit, and they will eventually lose mass as planetary nebulae) until only the core, which becomes a white dwarf, remains. Stars with higher mass will develop a degenerate core whose mass will grow until it exceeds the limit. At this point the star will explode in a core-collapse supernova, leaving behind either a neutron star or a black hole.
The use of the Chandrasekhar limit is fundamental in analyzing the evolution and demise of stars.
How is the Chandrasekhar limit calculated?
Chandrasekhar's limit is calculated by using a thermodynamic equation relating state variables. But this is a non-relativistic case due to which it does not account for the consequences of electrons approaching the speed of light.
The detailed evaluation of the state variables, as visible from the graph pictured above, sets the limit at 1.4 times the mass of the Sun.
What is the significance of Chandrasekhar Limit for astrophysics?
Since the life of a star is characterized by thermonuclear fission, the Chandrasekhar limit plays a crucial role in studying stars.
Chandrasekhar Limit for 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 1046 Joules.
Chandrasekhar Limit and 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.
