Question

Describe the mass, size, and density of a typical white dwarf. How does the size of a white dwarf depend on its mass?

Short answer

White dwarfs are dense, Earth-sized stars with masses like the Sun. Their size decreases as mass increases.

Step-by-step solution

Define a white dwarf

White dwarfs are stellar remnants left behind after a star has exhausted most of its nuclear fuel. They are the end-state for stars with a mass less than about 8 times that of the Sun.

Describe the mass of a typical white dwarf

A typical white dwarf has a mass that is approximately equal to the mass of the Sun, ranging from 0.5 to 1.4 solar masses. The Chandrasekhar limit, which is about 1.4 times the mass of the Sun, is the maximum mass a white dwarf can have before collapsing into a neutron star or other compact object.

Describe the size of a typical white dwarf

While the mass of a white dwarf is similar to that of the Sun, its size is much smaller. A typical white dwarf has a size comparable to that of Earth, with a radius of about 7,000-10,000 kilometers.

Describe the density of a white dwarf

White dwarfs are incredibly dense objects with densities averaging around 10,000 kg/cm³. Despite their small size, their mass is concentrated in a compact volume.

Explain the mass-radius relationship for white dwarfs

The size of a white dwarf inversely depends on its mass due to the phenomenon known as electron degeneracy pressure. As the mass of a white dwarf increases, it becomes denser and its radius decreases. This inverse relationship is a consequence of quantum mechanics at extremely high densities.

Key concepts

Stellar Remnants

Stellar remnants are fascinating endpoints in the life cycle of stars. They arise once a star has burnt through its nuclear fuel. The most common type of stellar remnant is a white dwarf, which forms from stars with masses less than about 8 times that of the Sun.

• White dwarfs are composed mainly of electron-degenerate matter.
• They do not undergo fusion reactions, having exhausted their nuclear fuel.
• Their core cooling gradually, which means they slowly fade over time.

These remnants provide insight into the life cycles of stars and the eventual fate of our own Sun, which will someday become a white dwarf.

Chandrasekhar Limit

The Chandrasekhar limit is a crucial concept in understanding white dwarfs and other compact objects. It represents the maximum mass a stable white dwarf can have, which is about 1.4 times the mass of the Sun. Beyond this limit, a white dwarf cannot support itself against gravitational collapse.

• If a white dwarf exceeds this limit, it will continue to collapse.
• The potential outcome is the formation of a neutron star or black hole.
• The limit is named after the Indian-American astrophysicist Subrahmanyan Chandrasekhar, who first calculated and predicted this phenomenon.

Understanding this limit helps astrophysicists predict the evolutionary paths of stars. It also enhances predictions about supernova explosions, which occur when a white dwarf exceeds this critical mass.

Electron Degeneracy Pressure

Electron degeneracy pressure is a quantum mechanical force that plays a vital role in supporting white dwarfs. It arises from the Pauli exclusion principle, which states that no two electrons can occupy the same state simultaneously.

• As gravity pulls matter inward, electrons are squeezed into higher energy states.
• This pressure prevents the star from further collapse, balancing the inward pull of gravity.
• The more mass a white dwarf has, the denser it becomes, increasing the degeneracy pressure.

Thus, an increase in mass leads to a decrease in size of the white dwarf due to increased density and pressure. This relationship is responsible for the inverse mass-radius relationship characteristic of white dwarfs.

Quantum Mechanics in Astrophysics

Quantum mechanics plays an indispensable role in astrophysics, particularly in understanding complex celestial phenomena like the behavior of stellar remnants. It describes the physical properties of nature at the smallest scales, such as electrons within atoms.

• In white dwarfs, it explains the electron degeneracy pressure that stabilizes these objects.
• Quantum mechanics also accounts for the spectral lines and emissions seen from other stellar phenomena.
• The principles are crucial for explaining the lifecycle of stars and the structure of matter under extreme conditions.

Such concepts allow scientists to model and predict the behaviors of stars and remnants trillions of miles away, providing a window into the fundamental workings of the universe.