The Chandrasekhar Limit is a critical mass threshold in astrophysics that determines the fate of a star. Named after the Indian astrophysicist Subrahmanyan Chandrasekhar, this limit is approximately 1.4 times the mass of the Sun, or about 2.765 x 10^30 kilograms. Stars that exceed this limit are unable to support themselves against the force of gravity, leading to catastrophic events such as supernovae or the formation of black holes.
II. Why is the Chandrasekhar Limit important in astrophysics?
The Chandrasekhar Limit is crucial in understanding the life cycle of stars and the processes that govern their evolution. It serves as a fundamental boundary that dictates whether a star will end its life in a violent explosion or collapse into a dense, compact object. By studying the effects of this limit, scientists can gain insights into the mechanisms that drive stellar evolution and the formation of exotic celestial objects.
III. How was the Chandrasekhar Limit discovered?
The Chandrasekhar Limit was first proposed by Subrahmanyan Chandrasekhar in the 1930s while he was a graduate student at the University of Cambridge. Chandrasekhar’s groundbreaking work on the structure and evolution of stars led him to the realization that there was a maximum mass limit beyond which a star could no longer support itself through the pressure generated by nuclear fusion in its core.
Chandrasekhar’s findings were met with skepticism at first, but they were later validated through observational evidence and theoretical calculations. His work laid the foundation for our understanding of the processes that govern the behavior of stars and the formation of compact objects such as white dwarfs and neutron stars.
IV. What happens when a star reaches the Chandrasekhar Limit?
When a star reaches the Chandrasekhar Limit, it is no longer able to support itself against the force of gravity. The pressure generated by nuclear fusion in the star’s core is insufficient to counteract the gravitational collapse, leading to a catastrophic event known as a supernova. During a supernova explosion, the star releases an immense amount of energy and matter into space, enriching the surrounding environment with heavy elements and triggering the formation of new stars and planetary systems.
V. What are the implications of the Chandrasekhar Limit for stellar evolution?
The Chandrasekhar Limit plays a critical role in shaping the evolution of stars and determining their ultimate fate. Stars that are below the limit will eventually exhaust their nuclear fuel and shed their outer layers, forming white dwarfs or other compact objects. On the other hand, stars that exceed the limit will undergo a supernova explosion, leaving behind remnants such as neutron stars or black holes.
Understanding the implications of the Chandrasekhar Limit is essential for predicting the behavior of stars and the formation of diverse astronomical objects. By studying the effects of this limit, scientists can unravel the mysteries of stellar evolution and the processes that govern the dynamics of the universe.
VI. How does the Chandrasekhar Limit relate to supernovae?
The Chandrasekhar Limit is intimately connected to the phenomenon of supernovae, which are some of the most energetic events in the universe. When a star reaches the limit and undergoes a supernova explosion, it releases an immense amount of energy and matter into space, creating shockwaves that propagate through the interstellar medium and trigger the formation of new stars and planetary systems.
Supernovae are crucial for enriching the universe with heavy elements and shaping the evolution of galaxies. By studying the relationship between the Chandrasekhar Limit and supernovae, scientists can gain insights into the mechanisms that drive these explosive events and the role they play in the cosmic cycle of birth and death.
In conclusion, the Chandrasekhar Limit is a fundamental concept in astrophysics that governs the behavior of stars and the formation of exotic celestial objects. By understanding the implications of this limit, scientists can unravel the mysteries of stellar evolution and the processes that shape the dynamics of the universe. The discovery of the Chandrasekhar Limit has revolutionized our understanding of the cosmos and continues to inspire new discoveries in the field of astrophysics.
The solar mass ( M ☉) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes.
it (/ˌtʃəndrəˈʃeɪkər/) is the maximum mass of a stable white dwarf
white dwarf
A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to Earth's. A white dwarf's low luminosity comes from the emission of residual thermal energy; no fusion takes place in a white dwarf.
Chandrasekhar mass is the maximum mass of a white dwarf star which is 1.4 solar masses. If a white dwarf exceeds this mass, the pressure of the electrons in its interior becomes unable to withstand the pull of gravity and the star begins to collapse.
Chandrasekhar limit, in astrophysics, maximum mass theoretically possible for a stable white dwarf star. This limiting value was named for the Indian-born astrophysicist Subrahmanyan Chandrasekhar, who formulated it in 1930.
The Chandrasekhar limit determines if a star dies as a white dwarf, or has the mass to exceed this, launching a supernova to create a black hole or neutron star.
Stars below the Chandrasekhar limit become stable white dwarf stars, remaining that way throughout the rest of the history of the universe absent external forces. Stars above the limit can become neutron stars or black holes.
Supernovae are so powerful they create new atomic nuclei. As a massive star collapses, it produces a shockwave that can induce fusion in the star's outer shell. These fusion reactions create new atomic nuclei in a process called nucleosynthesis.
Very massive stars can undergo core collapse when nuclear fusion becomes unable to sustain the core against its own gravity; passing this threshold is the cause of all types of supernova except type Ia.
A simplified Chandrasekhar limit derivation begins by defining total energy as the kinetic energy of the degenerate Fermi electron gas plus gravitational potential energy. The degenerate Fermi gas's kinetic energy has a relativistic expression.
Beginning in the 1930s, Subramanyan Chandrasekhar formulated theories for the development that stars subsequently undergo. He showed that when the hydrogen fuel of stars of a certain size begins to run out, it collapses into a compact, brilliant star known as a white dwarf.
Chandrasekhar's most notable work is on the astrophysical Chandrasekhar limit. The limit gives the maximum mass of a white dwarf star, ~1.44 solar masses, or equivalently, the minimum mass that must be exceeded for a star to collapse into a neutron star or black hole (following a supernova).
Usually the “use polar coordinates” technique for evaluating limits of two variables works like this: Write f(x,y)=g(r,θ), and let r→0. If the limit still depends on θ, the two-variable limit lim(x,y)→(0,0)f(x,y) does not exist.
The ICH indicates that LOD (which they call DL, the detection limit) can be calculated as LOD = 3.3σ / S, and the limit of quantification (which they call QL, the quantitation limit) LOQ = 10σ / S. Here σ is the standard deviation of the response and S is the slope of the calibration curve.
LOD's may also be calculated based on the standard deviation of the response (Sy) of the curve and the slope of the calibration curve (S) at levels approximating the LOD according to the formula: LOD = 3.3(Sy/S).
The limit is approximately 1.4 times the mass of the Sun, or about 2.7 x 10^30 kg. Any white dwarf that exceeds this mass will inevitably collapse and explode as a Type Ia supernova.
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