Chandrasekhar Limit

Introduction

The Chandrasekhar Limit is the maximum mass that a stable white dwarf star can have before it collapses under its own gravity to form a neutron star or black hole. The limit is named after the Indian astrophysicist Subrahmanyan Chandrasekhar who calculated it in 1930.

Derivation

The Chandrasekhar limit is derived from the principles of quantum mechanics and stellar structure. It is based on the idea that the pressure from the electrons in the degenerate gas of a white dwarf star can resist the inward pull of gravity only up to a certain mass. Beyond this limit, the gravitational force overcomes the electron degeneracy pressure, leading to the collapse of the star.

The value of the Chandrasekhar limit is given by:

where is the Chandrasekhar limit and is the mass of the Sun.

Implications

The Chandrasekhar limit plays a crucial role in understanding the life cycle of stars. When a star like our Sun exhausts its nuclear fuel, it sheds its outer layers and leaves behind a white dwarf. If the mass of this white dwarf is below the Chandrasekhar limit, it can remain stable indefinitely. However, if the mass is above this limit (which can happen if the white dwarf is in a binary system and accretes matter from its companion), the star will undergo a catastrophic gravitational collapse, potentially leading to a Type Ia supernova explosion.

Recognition

For his work on the maximum mass of white dwarfs, Chandrasekhar was awarded the Nobel Prize in Physics in 1983. His contributions have profoundly influenced our understanding of the life and death of stars.

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