Chandrasekhar Limit

The Chandrasekhar Limit sounds like a big scientific term, but it reveals one of the coolest secrets of our universe: how stars die! Interestingly, stars shine for millions of years, but they eventually run out of fuel and begin to collapse. And here is the exciting part: not all stars collapse in the same way! 

Imagine a giant star, thousands of times bigger than our Sun, exploding into a supernova. Why do some stars end as calm white dwarfs while others become mysterious black holes? This article is a perfect guide to know the story of dying stars, collapsing cores, Chandrasekhar limit, and one of the most important limits in astrophysics!

Table of Contents

• Must-Know Facts Chandrasekhar Limit
• What is Chandrasekhar limit?
• Significance of the Chandrasekhar Limit
• Chandrasekhar limit Unit
• Applications of Chandrasekhar Limit

Must-Know Facts About Chandrasekhar Limit

The Chandrasekhar Limit is about 1.44 times the mass of the Sun and is the maximum mass a white dwarf can have before collapsing under its own gravity. If a white dwarf exceeds this limit, it can collapse into a neutron star, black hole, or trigger a supernova explosion. The Chandrasekhar Limit is used in the confirmation of the existence of Neutron Stars and Black Holes. It is supported by quantum mechanics and special relativity and depends on the chemical composition of the white dwarf. The Chandrasekhar Limit is important in astrophysics for understanding the end stages of stars and confirming the existence of neutron stars and black holes.

What is Chandrasekhar limit?

The Chandrasekhar Limit is the maximum mass a white dwarf can have while remaining stable.

In simple words:

• If a white dwarf is lighter than the limit, it stays a white dwarf.
•  If it is heavier than the limit, it cannot support itself and collapses further.

To understand this, there is one simple example. Consider a small table that can hold weight. If you put light books on it, it stands firm. But if you pile on heavy boxes past the table’s strength, the table breaks. The Chandrasekhar Limit is like the maximum weight the table can hold.

But who discovered the Chandrasekhar limit? Let's discuss this in detail,

This idea came from Subrahmanyan Chandrasekhar, a brilliant Indian-born astrophysicist. He showed the world that there is a clear mass limit for white dwarfs. 

If a leftover mass of a star after it dies is over that limit, the star can not stay a white dwarf; it must collapse further.

But one question arises here: why does it matter?

 So, the limit helps scientists understand how different dead stars turn into white dwarfs, neutron stars, or black holes. It explains why not all stars end their lives the same way.

The Chandrasekhar Limit is the maximum mass a white dwarf can have and still stay stable. E.C. Stoner and Wilhelm Anderson first discussed it, and it was later named after Subrahmanyan Chandrasekhar, who improved the calculations.

At first, scientists ignored this idea because it supported the existence of black holes, which seemed impossible then. A white dwarf stays stable due to electron degeneracy pressure, which pushes against gravity.

But if the star becomes heavier than the limit, about 1.39 times the mass of the Sun, and this pressure cannot hold it up anymore, the star collapses further. The limit that has been established these days is 1.39 M_☉.

This idea might sound difficult at first, so let's discuss it with a detailed explanation. 

Pauli’s exclusion principle is a rule in quantum physics that says no two electrons can stay in the same energy state. Electrons follow this rule because they are a type of particle called fermions.

Because of this rule, electrons must spread out across different energy levels. When the gas of electrons inside a white dwarf is squeezed into a smaller space, more electrons get packed into the same volume. This forces some electrons to move to higher energy levels.

As a result, the electrons push back and create a force called electron degeneracy pressure. This pressure helps the white dwarf stay stable and stops it from collapsing under its own gravity.

But if the pressure becomes extremely high, something else happens: the electrons get pushed so hard that they are forced into the nuclei of atoms. This process is called electron capture.

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Significance of the Chandrasekhar Limit 

• The Chandrasekhar Limit is about 1.44 times the mass of the Sun.
  A white dwarf below this limit remains stable indefinitely.
• A star exceeding this limit can explode as a supernova or collapse into a neutron star or black hole.
• It helps explain the properties and ultimate fate of white dwarfs.
• It is important for understanding the life cycle of stars and the evolution of galaxies.
• It is also used to confirm the existence of neutron stars and black holes.

Chandrasekhar limit Unit

The Chandrasekhar limit is the unit of measuring the maximum stable mass of a white dwarf star. This value is about 1.44 times the mass of the Sun. If a white dwarf grows heavier than this limit, it can no longer stay stable and may collapse into a neutron star or a black hole. 

Let's discuss what the Chandrasekhar limit is for a neutron star.

The maximum Chandrasekhar limit for a neutron star is 3M_sun, which means it can be up to three times the mass of the Sun before collapsing.

Applications of Chandrasekhar Limit

The Chandrasekhar Limit helps us understand what happens to stars when they run out of fuel. Its key applications are:

• When nuclei of lighter elements fuse to form heavier ones, they release heat. This heat stops the core of the star from collapsing.
• As the star uses up its fuel, its core becomes smaller, hotter, and more tightly packed.
• Fusion cannot produce energy from iron ions, so when iron builds up in the core, the star enters a dangerous stage.
• If the mass of stars is less than 8 times the mass of the Sun, its core will remain below the Chandrasekhar Limit.
• If the star is more massive, electron degeneracy pressure cannot hold it up forever. The core collapses further and may eventually turn into a black hole.
• During this collapse, electrons get captured by protons, creating neutrinos. These neutrinos carry away a huge amount of energy that's around 10⁴⁶ joules.

Till now, we have learnt that the Chandrasekhar Limit helps us understand how stars end their lives and why they become white dwarfs, neutron stars, or black holes. It is a key idea in astrophysics that explains the fate of dying stars and deepens our understanding of the universe.