What is Chandrasekhar Limit?
There is always a line of separation when it comes to a bang and a whimper. In the case of stars, these lines are known as Chandrasekhar Limit. In other words, this is the difference between dying supernaturally and going out in a slow fading on the verge of extinction. Here, in the universe, this line gives rise to a different cosmos formation where stars sow the seeds of life.
Chandrasekhar Limit Definition
A white dwarf star with the utmost mass limit that remains stable is known as the Chandrasekhar limit. EC Stone and Willhelm mentioned the discoveries on how to improve the preciseness of computation in papers. They named it after an Indian astrophysicist Subrahmanyan Chandrasekhar.
History of Chandrasekhar Limit
A decade before Chandrasekhar started his journey to England, i.e., by 1920, the astronomers had realised that Sirius B, a white dwarf companion to the bright star Sirius, had a million times more density than the Sun. This density could only be acquired by an object if the atoms forming the star were so firmly compressed that they were no longer separate entities. The gravitational pressures would compress the atoms so much that the star would consist of positively charged ions surrounded by a sea of electrons.
Before discovering quantum mechanics, physics didn't understand the force capable of supporting any star against such gravitational force. But a new way was suggested by quantum mechanics, for a star to hold against gravity. As per the quantum mechanics rule, no two electrons can be in the same state.
Explanation
With the help of thermonuclear fusion, a star is characterised, hydrogen merges to helium, helium merges to carbon, and so on, forming more massive and heavier elements. Still, thermonuclear fusion cannot create an element heavier than iron. Copper, gold, silver, and trace elements are created only by a supernova explosion, which is important for the process of life.
Oxygen, carbon, and nitrogen, which are lighter elements are also essential to life, but these elements will remain locked forever up in stars until a supernova explosion occurs. Similar to the iron-on earth that is locked up in the core, being heavier hydrogen and helium, which comprise most of the initial mass of the stars, they deposit to form the central core of the star.
If stars are destined to become white dwarfs, as Eddington believed, the elements will remain confined to the glamorous interior at best to be provided in minute quantities to the universe as a whole via solar winds. Rocky planet is required to form life as we know, and there is no simple method in which a large quantity of rock can be made available in the universe unless the stars can deliver the material in wholesale quantities, but supernovae can provide that.
Therefore, the Chandrasekhar limit is not just the upper limit for the maximum mass for an ideal white dwarf, but also the threshold. A star can no longer hoard its precious cargo of heavy elements once it crosses the threshold. As an alternative, it delivers them to the universe at large in a supernova. This allows the possibility of the existence of life but marks its death.
Chandrasekhar Limit Derivation
The value for the calculation of the limit depends on the nuclear composition of the mass. For an ideal Fermi gas, Chandrasekhar limit has provided the following expression which is based on the equation of the state: Chandrasekhar limit equation given as:
\[M_{limit} = \frac{\omega_{3}^{0} \sqrt{3 \pi}}{2} (\frac{\hbar c}{G})^{\frac{3}{2}} \frac{1}{( \mu_{0} m_{H})^{2}}\]
Where:
ħ is reduced Planck constant
c is the speed of light
G is gravitational constant
μe is the average molecular weight per electron. This solely depends on the chemical composition of the star.
mH is the hydrogen atom mass.
ω0
3 ≈ 2.018236 is a constant link with a solution to the Lane–Emden equation.
As √ħc/G is Planck mass, the threshold is of the order of :
\[\frac{M_{Pl}^{3}}{m_{H}^{2}}\]
This simple model requires adjustment for a variety of factors, including electrostatic interactions between electrons and nuclei and effects caused at nonzero temperature, for a more accurate value than a given range. Lieb and Yau give the thorough derivative of the limit from the relative multi-particle Schrödinger equation.
Fun Facts
In the beginning, the scientist community ignored this limit as it would mean legitimising the existence of a black hole. This was considered unrealistic at that time because the white dwarf stars oppose the gravitational collapse from the pressure of electron degeneration.
The Chandrasekhar limit is when the mass of the pressure from the degeneration of electrons is unable to balance the gravitational field's self-attraction of 1.39 M☉limit.
The Chandrasekhar limit was found in 1930 by Subrahmanyan Chandrasekhar, an Indian astrophysicist and he used Albert Einstein's special theory of relativity along with the principles of quantum physics to further prove his theory.
FAQs on Chandrasekhar Limit
1. What is the Chandrasekhar Limit?
The Chandrasekhar Limit is the theoretical maximum mass a stable white dwarf star can have. If a white dwarf's mass is below this limit, it is supported against gravitational collapse by a quantum mechanical effect known as electron degeneracy pressure. The limit is approximately 1.44 times the mass of our Sun.
2. What is the currently accepted value of the Chandrasekhar Limit?
The currently accepted value for the Chandrasekhar Limit is about 1.44 solar masses. A solar mass is a standard unit of mass in astronomy, equal to the mass of the Sun (approximately 2 x 1030 kilograms). Therefore, the limit is equivalent to about 2.765 x 1030 kg.
3. What happens to a star if its core mass exceeds the Chandrasekhar Limit?
When a star's core exceeds the Chandrasekhar Limit, the inward pull of gravity overwhelms the outward push of electron degeneracy pressure. This causes the core to collapse catastrophically. This collapse can trigger one of two main events:
- For a white dwarf in a binary system that accretes enough mass to cross the limit, it results in a massive explosion known as a Type Ia supernova.
- For a massive star at the end of its life, the core collapse can lead to the formation of a much denser object, either a neutron star or, if the initial star was massive enough, a black hole.
4. Why is the Chandrasekhar Limit important in our understanding of the universe?
The Chandrasekhar Limit is fundamentally important for several reasons:
- Predicts Stellar Fate: It helps astronomers predict the final evolutionary stage of stars. Stars with a final core mass below the limit will end their lives as white dwarfs, while those above it face a more violent end.
- Explains Supernovae: It provides the mechanism for Type Ia supernovae, which are crucial for cosmology as 'standard candles' to measure cosmic distances.
- Origin of Elements: These supernovae are responsible for creating and dispersing heavy elements throughout the universe, which are necessary for the formation of planets and life.
5. How does electron degeneracy pressure relate to the Chandrasekhar Limit?
In a white dwarf, atoms are compressed so tightly that electrons are stripped from their nuclei, forming a dense sea of electrons. According to the Pauli Exclusion Principle, no two electrons can occupy the same quantum state. This creates a powerful outward pressure called electron degeneracy pressure, which resists further gravitational collapse. The Chandrasekhar Limit represents the precise mass at which gravity becomes strong enough to overcome this fundamental quantum pressure, forcing the star to collapse.
6. Who discovered the Chandrasekhar Limit and why was it significant?
The limit was discovered by the Indian-American astrophysicist Subrahmanyan Chandrasekhar in the 1930s. Its significance lies in being one of the first theories to combine quantum mechanics and special relativity to describe the fate of stars. Initially met with skepticism, his work revolutionised our understanding of stellar evolution and the existence of neutron stars and black holes. For this and other contributions to the study of stars, he was awarded the Nobel Prize in Physics in 1983.
7. What is the difference between a white dwarf, a neutron star, and a black hole?
These three objects represent the different possible final states of a star, primarily determined by mass:
- White Dwarf: The remnant core of a low-to-medium mass star. It is supported by electron degeneracy pressure and its mass must be below the Chandrasekhar Limit.
- Neutron Star: The collapsed core of a more massive star. It is incredibly dense and supported by neutron degeneracy pressure, which is much stronger than electron degeneracy pressure.
- Black Hole: Formed from the collapse of the most massive stars. Here, the core's mass is so great that gravity overwhelms even neutron degeneracy pressure, causing a complete collapse into a point of infinite density called a singularity.
8. Does the Chandrasekhar Limit apply to neutron stars or black holes?
No, this is a common misconception. The Chandrasekhar Limit applies specifically to white dwarfs, defining the maximum mass supported by electron degeneracy pressure. Neutron stars are governed by a different, higher mass limit known as the Tolman-Oppenheimer-Volkoff (TOV) limit, which is supported by neutron degeneracy pressure. If a neutron star exceeds the TOV limit (estimated around 2-3 solar masses), it will collapse further, likely forming a black hole.
