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Chandrasekhar Limit

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Last updated date: 29th Mar 2024
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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 and what happens after it? 

The maximum mass of a white dwarf star that is stable, is known as the Chandrasekhar limit. The theory and concept related to it are extremely imperative as they help to shape our understanding of the evolution of the stars that exist in the universe. 


One of two things are most likely to happen after or beyond the Chandrasekhar limit - either the stars that are on the brink of their end explode into what is called a supernova, or they first explode and then collapse into a neutron star, and at times, even into a black hole. 

2. Explain the application of the Chandrasekhar limit in detail.

Some of the most significant applications of the Chandrasekhar limit are as follows: 

  • This theory plays a key role in the study of the stars and their evolution in the universe, considering how the life of a particular star tends to be characterized by thermonuclear fission. 

  • The Chandrasekhar limit is considered to be a threshold because of which life is possible. In the case of elements heavier than hydrogen, oxygen, helium, etc., they would have ended up getting trapped in the stars, had the supernova explosion not occurred. 

  • Utilizing the process of fusion to obtain energy is neither possible nor is it viable in the case of iron ions. And if the star happens to be less than eight solar masses, then soon enough, the mass will be lower than the Chandrasekhar limit.

3. What is a white dwarf?

In 1922, Willem Luyten coined the word “white dwarf”. Also popularly referred to as a degenerate dwarf, a white dwarf is mostly made up of electron-degenerate matter and are recognized to be in the final, evolutionary state of stars, the mass of which, is not high enough to either transform into a neutron star or to become a black hole. This tends to include about 97% of the other stars that exist in the Milky Way. No kind of fusion tends to take place in a white dwarf, as a result of which, the star holds no source of energy. 


A white dwarf also happens to be very dense. This is because it is only supported by electron degeneracy pressure as it is incapable of supporting itself. When it first forms, a white dwarf is extremely hot, but slowly and steadily, it cools down due to the absence of any source of energy. That will lead its radiation to lessen with time, making it appear redder. And over an even longer period of time, after cooling, its material will start to crystallise. Contrary to its name, gradually, it will just end up becoming a cold and black dwarf. 


Sirius B is the nearest known white dwarf and it is at 8.6 light-years.  

4. What happens if the iron core of a star ends up exceeding the Chandrasekhar limit?

The pace at which the infalling layers tend to collapse is so fast and agile that the layers end up bouncing off the iron ore, close to the speed of light and this rebound leads the stars to explode as what is known as a supernova. During this explosion, the energy that is released is so much that the particular star might just end up outshining the whole galaxy for about a couple of days. You can learn more about Chandrasekhar Limit in Vedantu. You will get different study materials on the Vedantu website and app which will help you to understand this topic better.

5. What is a neutron star?

A neutron star is basically the core of a massive supergiant star that has collapsed. Besides black holes, neutron stars are considered to be the smallest as well as the densest class of stellar objects. They have a mass of about 1.4 solar masses and a radius on the order of about 10 km. A neutron star is formed as a result of a supernova explosion of a big star along with gravitational collapse. According to research, it is said that there are about a billion neutron stars currently in the Milky Way. However, most of these neutron stars are either cold and old or both.

6. What is Chandrasekhar Unit?

In order to explain the maximum mass of a white dwarf star, the Chandrasekhar unit is used. This is equivalent to 1.44 solar masses. A black hole or neutron star came into existence when the limit was surpassed.

7. State the Chandrasekhar Limit for a Neutron star?

3 M sun is the maximum Chandrasekhar limit for a neutron star.

8. State the value of the Chandrasekhar Limit Value?

Chandrasekhar limit value- For a stable white dwarf star; it is the maximum mass. 1.4 M ☉ (2.765×1030 kg) is the currently accepted value for the Chandrasekhar limit.

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