What is the Chandrasekhar limit for White Dwarf Stars?

Physics Explained

26 Aug 202148:48

EducationalLearning

32 Likes 10 Comments

TLDRThis is the story of the discovery of white dwarf stars and how they ultimately fade away. It begins with observations of the irregular motion of Sirius, leading astronomers to deduce it had an invisible companion, Sirius B. Further study revealed Sirius B to be extremely dense, giving rise to the concept of 'white dwarfs'. Physicist Subrahmanyan Chandrasekhar later combined quantum mechanics and relativity to demonstrate there is a limit to how dense a white dwarf can become before collapsing, with 1.4 solar masses being the threshold now known as the Chandrasekhar limit. This finding was initially rejected but is now fundamental to our understanding of stellar evolution.

Takeaways

😲 The story of the discovery of white dwarf stars reveals the fate of stars like our Sun when they die.
🔭 In 1834, astronomer Friedrich Bessel observed irregular wavy motions of Sirius, indicating it had an invisible companion star - later identified as a white dwarf called Sirius B.
🚀 Understanding the properties of Sirius B required combining quantum mechanics and Einstein's theory of general relativity to explain its high density.
👨‍🔬 In 1915, Walter Adams found Sirius B had a light spectrum identical to Sirius A, implying it was very dense rather than just cool.
💡 In 1926, Ralph Fowler showed that electron degeneracy pressure, arising from quantum effects, could support white dwarf stars.
🎓 In 1930 Chandrasekhar combined special relativity and quantum mechanics to prove white dwarfs have a maximum possible mass, now called the Chandrasekhar limit.
😡 astronomer Arthur Eddington initially dismissed Chandrasekhar's work as he disliked its implication that massive stars must collapse.
🌟 Observations have since confirmed that no white dwarf exceeds Chandrasekhar's predicted 1.4 solar mass limit.
🏆 Chandrasekhar was awarded the 1983 Nobel prize for this pioneering discovery, though it was controversial for over 20 years.
❤️ Chandrasekhar reflected that scientific truth aligns with beauty - the human mind can perceive deep truths about nature.

Q & A

What was the main mystery surrounding the star Sirius B when it was first observed?
-The main mystery was that Sirius B had an extremely low luminosity compared to the Sun, yet it had a mass similar to the Sun. Scientists couldn't explain this through differences in temperature or size alone.
How did the discovery of electron degeneracy pressure help explain the existence of dense white dwarf stars?
-Electron degeneracy pressure is a consequence of quantum mechanics that causes electrons to exert more pressure when compressed to small volumes. This outward pressure can balance the inward gravitational force in white dwarfs, preventing further collapse.
What was the key insight Chandrasekhar had that built upon Fowler's earlier work?
-Chandrasekhar realized that relativistic effects needed to be considered for the high electron velocities in white dwarfs. This put a fundamental limit on the maximum supportable mass, unlike Fowler's theory.
Why did the astronomical community, and Eddington in particular, react so negatively to Chandrasekhar's work at first?
-Chandrasekhar's mass limit implied that stars over a certain mass would inevitably collapse. This contradicted the accepted view that all stars ended as stable white dwarfs. The possibility of complete gravitational collapse disturbed many scientists.
What is the physical meaning of the Chandrasekhar mass limit?
-It is the maximum mass of a white dwarf star. Above this mass, the electron degeneracy pressure is insufficient to balance gravity, so collapse will continue.
How does the radius of a white dwarf star vary with its mass?
-The radius is inversely proportional to the cube root of the mass. So higher mass white dwarfs have smaller radii and thus higher densities.
What fundamental constants determine the numerical value of the Chandrasekhar limit?
-The limit depends directly on Planck's constant, the speed of light, Newton's gravitational constant, and the proton mass. Quantum mechanics, relativity and gravity all play key roles.
What evidence supported Chandrasekhar's predicted mass limit for white dwarfs?
-Astronomical observations have discovered hundreds of white dwarfs, with masses all less than 1.4 solar masses, matching Chandrasekhar's calculation.
How does the concept of an electron degeneracy energy differ from normal thermal energy?
-Electron degeneracy energy arises purely from quantum confinement principles. It depends only on density, not temperature. Thermal energy involves the kinetic energy from random motion of particles.
Why did Chandrasekhar temporarily leave the field of stellar structure research in the late 1930s?
-He was deeply discouraged by the negative reaction from the astronomy community, especially Eddington's vocal criticism. He didn't return until over 25 years later.

Outlines

00:00

😀 The Discovery of White Dwarf Stars

This paragraph introduces the video, which will tell the story behind the discovery of white dwarf stars. It highlights that this was one of the most important discoveries in physics history, as it revealed the fate of stars like our Sun. The story involves many colorful characters, controversies, calculations and is still unfolding today.

05:01

😮 The Mystery of High Stellar Density

This paragraph discusses the mystery behind the discovery that Sirius B had an extremely high density, unlike any material found on Earth. While some thought this was impossible, further evidence showed that Sirius B must indeed be an incredibly dense 'white dwarf' star.

10:02

😵 Understanding Degenerate Matter

This paragraph explains that theorists in the 1920s struggled to explain how white dwarf stars could exist, given puzzles surrounding how their density and energy behavior. A breakthrough came when Ralph Fowler applied new quantum principles to show how 'electron degeneracy pressure' could support white dwarfs.

15:03

🤯 Calculating the Electron Degeneracy Energy

This paragraph provides a simplified derivation of how to calculate the contribution of electron degeneracy energy, which relates to the electron degeneracy pressure supporting a white dwarf star. It walks through constraining electrons in boxes to build up an understanding.

20:05

😶 Summing Over All Electron States

This paragraph continues the calculation by considering electron energy states in terms of shells and uses Pauli exclusion principle. It sums over all shells to derive a final equation for total electron degeneracy energy.

25:06

🧐 Adding Gravitational Potential Energy

This paragraph derives an expression for the gravitational potential energy of the star, which must be balanced by the electron degeneracy pressure. It arrives at a combined equation for total energy by adding the gravitational and degeneracy terms.

30:07

🔬 Finding the Most Stable White Dwarf Radius

This paragraph discusses the strategy of minimizing total energy to identify the most stable white dwarf configuration. It takes the viewer through the mathematical steps of finding the radius at which energy is minimized.

35:09

😮 The Chandrasekhar Limit

This paragraph introduces Chandraskhar's realization that special relativity must be incorporated to properly understand electron velocities. This leads to a relativistic equation and demonstration that white dwarfs have a maximum possible mass.

40:10

🚀 The Maximum White Dwarf Mass

This paragraph finishes the relativistic derivation to arrive at Chandraskhar's famous formula for the maximum white dwarf mass. It explains the physical meaning and that this places a limit on the electron degeneracy pressure.

45:11

👏 Honoring Chandraskhar’s Achievement

This closing paragraph recounts how Chandrasekhar faced objections from leading astronomers about white dwarf collapse, which took decades to resolve. It honors Chandrasekhar’s profound achievement in making an incredible discovery about nature.

Mindmap

Keywords

💡White dwarf star

A white dwarf star is the remains of a low-mass star after it has exhausted all its nuclear fuel. It is extremely dense as it has collapsed under its own gravity. White dwarf stars play a key role in the script as it discusses their discovery, properties, and stability.

💡Electron degeneracy pressure

This refers to the quantum mechanical pressure exerted by electrons when confined to a very small space inside a white dwarf star. This outward pressure balances the inward gravitational force, allowing white dwarfs to be stable.

💡Chandrasekhar limit

This is the maximum possible mass for a stable white dwarf star, above which it would collapse. It was first calculated by Subrahmanyan Chandrasekhar to be around 1.4 times the Sun's mass.

💡Quantum mechanics

The laws of physics that govern small, atomic-scale objects. Concepts like electron degeneracy pressure arise from quantum mechanics. The script discusses how quantum mechanics was key to understanding white dwarfs.

💡Gravitational collapse

The process by which an object shrinks and densifies under the force of its own gravity. The script explores when and why this collapse halts for white dwarfs versus continues indefinitely for more massive stars.

💡Heisenberg's uncertainty principle

A foundational quantum concept stating that complimentary properties like position and momentum cannot be precisely measured at the same time. This underlies the increasing electron velocity and pressure when squeezed to small volumes.

💡Pauli exclusion principle

States that no two electrons can occupy the same quantum state. Leads to a much greater electron degeneracy pressure as more electrons are forced to occupy higher energy states.

💡Degenerate matter

Matter in an extremely dense state only possible due to quantum mechanical effects. The high densities make white dwarfs and neutron stars possible.

💡Black hole

The video discusses how the inevitability of gravitational collapse for sufficiently massive stars led to the concept of black holes as the final state.

💡Stellar evolution

The life cycle of stars, from birth to eventual death. The video revolves around developing an understanding of the final stages of low mass stars - as white dwarfs.

Highlights

The discovery of white dwarf stars is a story about the ultimate fate of our Sun and what happens when a star like it dies.

Sirius B was found to have a mass comparable to the Sun but its luminosity was less than 1/400th that, presenting a puzzle about its nature.

Eddington suggested white dwarfs are extremely dense ionized gas stars, but realized this posed a problem about how they could then cool down without gaining energy.

Ralph Fowler used the new quantum mechanics to show electron degeneracy pressure could support white dwarfs, suggesting any star could form one.

Chandrasekhar realized Fowler neglected relativity and for very dense stars electrons would approach light speed, requiring both quantum and relativity.

Chandrasekhar showed no white dwarf can exceed 1.4 solar masses, the famous Chandrasekhar limit and one of physics' greatest discoveries.

The Chandraskhar limit gives the maximum possible mass of a white dwarf. Above this, electron degeneracy pressure cannot withstand gravity.

Eddington objected to the limit as he disliked the idea stars above this mass would completely collapse, possibly forming black holes.

Due to Eddington's objections, over two decades passed before Chandrasekhar's theory was fully accepted.

Observations have since confirmed that no white dwarfs exceed 1.4 solar masses, matching Chandrasekhar's prediction.

The conflict with Eddington discouraged Chandrasekhar so much he abandoned white dwarfs for over 25 years before returning.

The Chandrasekhar mass depends only on fundamental constants like Planck's constant, c, G, and proton mass.

The theory matches observation - all measured white dwarfs have masses under the limit.

Eddington failed to embrace the significance of Chandrasekhar's discovery and the possibility of black holes.

Chandrasekhar turned his back on white dwarfs in 1939 and didn't return for a quarter century due to the controversy.

Chandrasekhar remarked that the human mind perceives beauty in what it deeply understands, matched in external nature.

Transcripts

Browse More Related Video

White Dwarfs & Planetary Nebulae: Crash Course Astronomy #30

Sizes of Stars and Sub-Stellar Objects: From Brown Dwarf to Red Hypergiant

Low Mass Stars: Crash Course Astronomy #29

Journey to the Andromeda Galaxy [4K]

What if the Sun Exploded + More OUT OF THIS WORLD Questions! | COLOSSAL QUESTIONS

Stars: Crash Course Astronomy #26