The White Dwarf Stars

Abstract:

This article explores the evolution and formation of white dwarf stars, starting from the process of star formation in nebulas to the subsequent stages that lead to their creation. White dwarf stars are medium-sized stars that exhaust their nuclear fuel, much like our Sun. The article explains how these dense and compact stars are formed and details their cooling process over billions of years. Also, it discusses their unique properties, such as extreme heat and low luminosity compared to other stars. White dwarfs play a crucial role in understanding the future of our Sun and similar stars, providing valuable insights into stellar evolution and the overall dynamics of the universe.

keywords: White Dwarf Stars, Stellar Evolution, Star Formation, Chandrasekhar Limit, Planetary Nebula

Formation of Stars:

The Big Bang theory explains how the universe expanded from its initial state. As a result, atomic matter was formed. Stars, the basic building blocks of galaxies, began forming around 5 - 6 billion years ago. Our galaxy alone contains about 300 billion stars. Stars are celestial bodies that generate their own light and heat.

In the early universe, matter and density were not evenly distributed, which caused differences in gravitational fields. This uneven distribution pulled matter together. Galaxies began to form by accumulating hydrogen gas in large clouds called nebulas. As gravity pulled more matter into these clouds, the temperature and pressure increased, creating turbulence. This eventually led to the formation of high-density regions within the clouds.

Star formation starts when gravity overcomes the heat in these clouds, causing them to collapse. Collisions within the gas clouds cause them to expand, and the process of fragmentation leads to the contraction of the gas, forming what is known as a protostar—the early phase of a star. Not all the material from the cloud becomes part of the protostar; some of it forms planets, asteroids, and other celestial bodies.

As the gas cloud collapses, a dense, hot core forms, gathering more dust and gas. When the temperature reaches 10 million K, the protostar becomes a full-fledged star, a process known as stellar nucleosynthesis. During this time, hydrogen atoms fuse to form helium, a process that requires immense energy. Once fusion starts, stars produce and emit large amounts of energy.

The color of a star depends on its temperature: the hottest stars appear blue, warmer stars are yellow, and cooler stars are red. A star remains stable as long as the inward gravitational pull and the outward thermal energy from fusion are balanced. This stable phase is called the "main sequence," which accounts for about 90% of a star's life. The Sun is a main-sequence star, and stars that fail to sustain nuclear fusion due to insufficient mass are known as brown dwarfs.

?Hertzsprung–Russell diagram:

The above image shows the relationship between stars' luminosity and their surface temperature. The x-axis represents the stars' surface temperature, which decreases from left to right. The left side shows hot, blue stars (with temperatures of over 10,000 K), while the right side shows cooler, red stars. The y-axis represents the stars' luminosity. Stars with higher luminosity are at the top, and dimmer stars are placed at the bottom. Most stars are on the main sequence, including our Sun. Stars in this region are fusing hydrogen into helium in their cores. The giants and supergiants are found in the upper right portion of the diagram. They are cool but extremely luminous, indicating they are large in size. The white dwarfs are in the lower left corner. White dwarfs are very hot but dim because they are small in size. These stars are the remnants of stars like the Sun that have exhausted their nuclear fuel. Blue stars on the left side are much hotter, with temperatures over 10,000 K. Red stars on the right side are cooler, with temperatures below 3,500 K. Stars typically start on the main sequence when they are burning hydrogen. As they exhaust their fuel, they move off the main sequence to become red giants or supergiants. After shedding their outer layers, some stars become white dwarfs.

The Chandrasekhar Limit:

The Chandrasekhar limit is a key concept in astrophysics that defines the maximum mass a white dwarf can have while staying stable, around 1.4 times the mass of our Sun. White dwarfs are supported by electron degeneracy pressure, a force that prevents them from collapsing under their own gravity. This pressure is based on a quantum rule that says two electrons can't occupy the same space. If the star's mass stays below the limit, this force keeps it stable. However, if the mass exceeds 1.4 times, the stars become a black hole or neutron star. This limit was discovered by Indian-born astrophysicist Subrahmanyan Chandrasekhar in 1930. He used ideas from Einstein's theory of relativity and quantum mechanics to figure it out. The Chandrasekhar limit helps scientists understand how stars evolve and what happens to them after they die.

End of Stars:

Stars like the Sun have a lifespan of about 10 billion years. According to astronomers, our Sun has about five billion years left. The changes that occur in a star’s final stages depend on its mass. Massive stars burn through their energy faster than smaller ones.

When a star’s hydrogen fuel runs out, it can no longer maintain the balance between gravity and energy production. As a result, the star begins to collapse. All stars eventually expand, cool, and change color, becoming red giants or supergiants.

When the Sun exhausts its nuclear fuel, it will become a white dwarf, a remnant with about half its original mass. Lighter stars also become white dwarfs, while heavier stars end their lives in massive explosions called supernovae. These explosions may leave behind neutron stars, or, if there’s enough remaining mass, black holes—regions of space with such strong gravity that not even light can escape.

However, the Sun is not massive enough to become a black hole. There are estimated to be over 100 million black holes in our galaxy.

Introduction to White Dwarf Stars:

White dwarfs are the leftover cores of medium-sized stars and represent the final stage of their life cycle for more than 95% of stars in the universe. These small, faint stars have run out of thermonuclear fuel, which means they can no longer produce energy through the high temperature fusion processes in their cores. As they cool down, white dwarfs help us understand what will happen to stars like our Sun when they reach the end of their lives.

White dwarfs form when stars with a mass below 1.44 times that of the Sun run out of nuclear fuel and shed their outer layers, leaving a dense core behind. During their active lives, these stars burn most of the hydrogen and helium in their core. White dwarfs mainly consist of a core made of carbon and oxygen, which makes up about 99% of their total mass. Around this core, there are thin layers of helium and an even thinner layer of hydrogen, which together contribute only a small part of the star's overall mass.

White dwarfs are very dense, with densities often exceeding 1 million grams per cubic centimeter. Despite their small size, they can have a mass similar to that of the Sun, but compressed into a volume like that of Earth. In these stars, electron degeneracy pressure, a quantum force, keeps them from collapsing under their own gravity. This pressure comes from the Pauli exclusion principle, which stops electrons from being squeezed into the same state. Because of their extreme compactness, white dwarfs are nearly a million times denser than water.

Unlike more massive stars that explode in a supernova at the end of their lives, white dwarfs cool down and become dimmer over billions of years. They give us important information about what happens to stars that don’t have enough mass to explode. By studying white dwarfs, we can learn about the final stages of stars’ lives and understand what will happen to most stars in the universe.

Sirius B is a white dwarf star in the Sirius binary system, recognized as the first white dwarf discovered. It represents the remnant of a once massive star that evolved and shed its outer layers, leaving behind a dense core.

Formation of White Dwarf Stars:

The formation of a white dwarf occurs during the final stages of stellar evolution for stars that do not have enough mass to end their lives in a supernova explosion. Initially, these stars spend billions of years in the main sequence phase, where hydrogen in the core fuses into helium. This fusion process produces a lot of energy in the form of heat and light, allowing the star to maintain a balance against its own gravity, known as hydrostatic equilibrium.

As the star evolves into the red giant phase, it undergoes many changes. The outer layers of the star expand significantly due to increased pressure and energy from ongoing nuclear fusion in the core. As fusion continues, the temperature and pressure rise, causing helium to convert into heavier elements like carbon and oxygen. During this phase, thermal pulsations can occur, which are oscillations in temperature and pressure within the star. These pulsations happen when changes in temperature and energy cause the outer layers to expand and contract. This instability can lead to the ejection of the star's outer layers, contributing to the formation of a planetary nebula.

Eventually, the star runs out of nuclear fuel and can no longer sustain fusion reactions. This lack of fuel causes the outer layers to be expelled into space, forming a structure known as a planetary nebula. The ejection of these outer layers happens through mechanisms driven by thermal instability and pulsations, which can vary among different types of stars.

What remains at the core is a dense remnant primarily made of carbon and oxygen, known as a white dwarf. This core is very hot and dense, with gravity pulling inward while electron degeneracy pressure prevents it from collapsing further.

After their formation, white dwarfs no longer engage in nuclear fusion. Instead, they gradually radiate their remaining heat into space over billions of years. As they cool down, they change appearance based on their temperature and composition. Eventually, they become very faint and dark.

Overall, the journey from a main-sequence star to a white dwarf involves significant changes, including expansion, fusion of heavier elements, and the shedding of outer layers, ultimately leading to a stable, dense core that cools over time.

?Cooling Process of White Dwarfs:

After forming from the remnants of a dying star, a white dwarf cools down extremely slowly over billions of years. At first, a newly formed white dwarf can be extremely hot, with surface temperatures over 100,000 Kelvin. During this stage, it shines brightly, emitting lots of light and heat. These hot white dwarfs are often classified as "DA" white dwarfs, which means their atmospheres are mostly made up of hydrogen, with very little or no helium or other elements visible. DA white dwarfs are the most common type of white dwarf.

As time passes, the white dwarf loses heat and becomes less bright. Initially, it cools fairly quickly, but over time, the cooling slows down as it begins to lose heat more by radiation than by convection. The mass and composition of the white dwarf also affect how quickly it cools, with larger white dwarfs taking longer than smaller ones.

After millions or billions of years, white dwarfs can cool down to below 10,000 Kelvin, becoming "cool white dwarfs." If they keep cooling for an even longer time, they could eventually become dark, cold objects called "black dwarfs." However, the universe is not old enough yet for any black dwarfs to exist since it would take trillions of years for them to form.

The formation of crystals in white dwarfs is an intriguing aspect of their cooling. As they cool, the material inside white dwarfs begins to crystallize, similar to how water turns into ice. This crystallization process releases extra energy, which slows down the cooling even further. Scientists have observed this in white dwarfs, helping them to understand the star's age more accurately.

Temperature and Luminosity:

Temperature

White dwarfs start off extremely hot when they are first formed, with temperatures often above 100,000 Kelvin (around 179,500 degrees Fahrenheit). This initial heat arises from the intense gravitational pressure exerted by the core, which compresses the remaining stellar material. As a white dwarf no longer undergoes nuclear fusion, it gradually loses this thermal energy by radiating it into space. This cooling process is extremely slow, relatively taking billions of years for a white dwarf to cool.?

?After about a billion years, the temperature may drop to around 30,000 Kelvin, and after ten billion years, it could further decrease to about 10,000 Kelvin. Eventually, in the distant future, a white dwarf may reach temperatures close to 1,000 Kelvin or even lower, transitioning into a theoretical state known as a black dwarf. As mentioned earlier, the universe is young; therefore, currently we haven’t found any black dwarf yet.

Luminosity

The luminosity of white dwarfs is initially quite high, often comparable to that of the Sun, due to their elevated temperatures and the inherent energy they radiate light as they cool. This relationship between temperature and luminosity is governed by the Stefan-Boltzmann Law, which states that a star's luminosity is proportional to the fourth power of its temperature.

As white dwarfs cool, their luminosity diminishes significantly. Within a billion years, the luminosity can decrease to less than 0.01 times that of the Sun, and after several billion years, it may fall below 0.001 times solar luminosity when temperatures reach around 10,000 Kelvin.

Hertzsprung-Russell diagram In Fig. 2, which shows stars by their temperature and brightness, white dwarfs are found in the bottom left, showing they are hot but not very luminous. Over time, as they cool, their brightness fades and they become redder. Eventually, they will stop glowing and turn into cold, dark black dwarfs.

Although white dwarfs are incredibly hot, their brightness is quite low due to their small size. Unlike other stars, they don’t generate new energy through nuclear fusion; instead, their light comes from the leftover heat they radiate. From the second figure Hertzsprung-Russell diagram, which shows stars by their temperature and brightness, white dwarfs are found in the bottom left, showing they are hot but not very luminous. Over time, as they cool, their brightness fades and they become redder. Eventually, they will stop glowing and turn into cold, dark black dwarfs.

What about our SUN?

The Sun is currently in the main stage of its life cycle, known as the main sequence. This stage began 4.6 billion years ago and will last for about another 5 billion years. During this time, the Sun is stable because it is in a balance called hydrostatic equilibrium. In this state, the Sun converts hydrogen into helium through nuclear fusion, which releases a huge amount of energy. This energy creates outward pressure that balances the force of gravity pulling inward, keeping the Sun stable.

Once the Sun runs out of hydrogen in its core, nuclear fusion will stop. The core will shrink, and the outer layers will expand, making the Sun much larger and turning it into a red giant. In this phase, the Sun could grow large enough to swallow planets like Mercury, Venus, and possibly Earth. The red giant phase will last for a few hundred million years.

After the red giant phase, the Sun will shed its outer layers, leaving behind a dense core. This core will shrink into a white dwarf. At first, this white dwarf will be extremely hot, with temperatures over 100,000 Kelvin, and it will shine brightly, similar to the Sun. However, over billions of years, it will slowly cool down and eventually become a cold, dark object called a black dwarf, although this will take trillions of years.

Conclusion:

In conclusion, white dwarfs play a vital role in our understanding of stellar evolution. They are the final stage for many stars, including those similar to our Sun, and help illustrate what happens as stars exhaust their nuclear fuel. By studying white dwarfs, we gain insights into the long-term changes in stars and the overall dynamics of galaxies. Their cooling process over billions of years not only reveals the fate of stars but also opens up possibilities for further research in astrophysics.

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