The Chandrasekhar mass limit is a fundamental concept in astrophysics, representing the maximum mass that a white dwarf star can possess while remaining stable against gravitational collapse. This limit is named after the Indian-American astrophysicist Subrahmanyan Chandrasekhar, who first calculated it in 1930, revolutionizing our understanding of stellar evolution. White dwarfs are the remnants of stars that have exhausted their nuclear fuel and expelled their outer layers, leaving behind a dense core primarily composed of electron-degenerate matter. In this state, electrons are packed so tightly that quantum mechanical effects, specifically the Pauli exclusion principle, create a pressure that counteracts the inward pull of gravity. This electron degeneracy pressure is independent of temperature, meaning that even when a white dwarf cools, it can remain structurally stable as long as its mass does not exceed a certain threshold.
Chandrasekhar approached the problem by applying principles of special relativity to the behavior of electrons in extremely dense stellar cores. At low densities, electrons are non-relativistic, and the degeneracy pressure is sufficient to support the star against gravity. However, as the mass of the white dwarf increases, the core density rises, causing the electrons to approach relativistic speeds. In this relativistic regime, the relationship between pressure and density changes in such a way that electron degeneracy pressure can no longer indefinitely support the star. Chandrasekhar calculated this upper mass limit to be approximately 1.44 times the mass of the Sun, a value that depends slightly on the chemical composition of the white dwarf’s core, particularly the ratio of protons to nucleons.
Exceeding the Chandrasekhar limit has profound consequences for stellar evolution. If a white dwarf accretes mass from a binary companion or merges with another dense star such that its total mass surpasses this threshold, the electron degeneracy pressure is insufficient to counterbalance gravity. The star then undergoes catastrophic collapse, leading to one of two possible outcomes depending on the mass and composition: a type Ia supernova or the formation of a neutron star. In a type Ia supernova, the white dwarf explodes in a thermonuclear reaction, producing immense luminosity and dispersing heavy elements into the interstellar medium. Alternatively, if collapse continues beyond nuclear densities, the object may become a neutron star, supported by neutron degeneracy pressure, or in extreme cases, a black hole.
The Chandrasekhar mass limit has implications beyond individual stars, influencing models of stellar populations, supernova rates, and galactic chemical evolution. Observationally, the existence of type Ia supernovae, which serve as standard candles for measuring cosmic distances, provides indirect confirmation of this limit, as these explosions typically occur in systems where the white dwarf approaches but does not significantly exceed the Chandrasekhar mass. Furthermore, the limit illustrates a profound intersection of quantum mechanics, special relativity, and astrophysics, showing how microscopic properties of electrons dictate macroscopic phenomena in the cosmos. Chandrasekhar’s work not only established a cornerstone of theoretical astrophysics but also highlighted the predictive power of applying fundamental physical laws to the extreme environments found in the universe.