The Chandrasekhar limit is the maximum mass that a white dwarf star can have while still supporting itself against gravitational collapse through electron degeneracy pressure. This limit is named after the Indian-American astrophysicist Subrahmanyan Chandrasekhar, who first calculated it in 1930.
### Key Points About the Chandrasekhar Limit:
1. **Value of the Limit**:
- The Chandrasekhar limit is approximately 1.4 times the mass of the Sun (1.4 \( M_\odot \)).
2. **Electron Degeneracy Pressure**:
- White dwarfs are supported by electron degeneracy pressure, a quantum mechanical effect arising from the Pauli exclusion principle, which states that no two electrons can occupy the same quantum state. This pressure counteracts the force of gravity.
3. **Mass Threshold**:
- If a white dwarf's mass exceeds the Chandrasekhar limit, electron degeneracy pressure is no longer sufficient to prevent gravitational collapse. The star will collapse further, potentially forming a neutron star or a black hole, depending on the mass.
### Implications of the Chandrasekhar Limit:
1. **Type Ia Supernovae**:
- When a white dwarf in a binary system accretes matter from its companion star and its mass approaches the Chandrasekhar limit, it can trigger a runaway nuclear fusion reaction, leading to a Type Ia supernova. These supernovae are important standard candles for measuring cosmic distances.
2. **Stellar Evolution**:
- The Chandrasekhar limit helps determine the ultimate fate of stars. Stars with masses less than about 8 \( M_\odot \) typically end their lives as white dwarfs, while more massive stars can evolve into neutron stars or black holes.
3. **Stellar Remnants**:
- Understanding the Chandrasekhar limit is crucial for predicting the types of remnants left behind after a star exhausts its nuclear fuel. Stars with masses exceeding the limit will not remain as white dwarfs but will undergo further collapse.
### Mathematical Expression
The Chandrasekhar limit can be derived from the balance between gravitational force and electron degeneracy pressure. While the detailed derivation involves complex quantum mechanics and relativistic equations, the simplified expression for the limit is:
\[ M_{\text{Ch}} \approx 1.4 \, M_\odot \]
### Conclusion
The Chandrasekhar limit is a fundamental concept in astrophysics that defines the maximum mass a white dwarf can have before it undergoes further collapse. This limit has significant implications for the life cycles of stars, the formation of neutron stars and black holes, and the occurrence of Type Ia supernovae.
