What Are White Dwarfs & How Do They Form?

It is the time to harvest what we sowed in the past one month of this series. One by one, we learnt different concepts of Astrophysics. Today, it is the time to apply those concepts and study one of the most interesting branch of Astrophysics: Stellar Evolution. The Universe is filled with about a trillion trillion stars. We have already learnt the art of classifying them into 7 major types by using the knowledge of their surface temperature and EM spectrum. We are familiar with the Hertzsprung Russell diagram and the nuclear reactions in the stars. Using these previous concepts, today, we will be studying the evolution of Sun like mid sized stars. So in the eighteenth article of Basics of Astrophysics series, let us learn what are white dwarfs and how do they form?

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Birth of Stars

I'll be starting from the very beginning. The Universe is made up of two main elements and they are hydrogen and helium. There are huge clouds of dust and gas composed of these two elements. Over the time, these clouds come together. Their dimensions can be across light years. When a cloud of dust and gas becomes massive enough (crosses a critical mass limit called Jeans limit), it starts collapsing under its own gravity. This collapse continues for a long period of time and forms a rotating sphere of mass. This mass is shrouded by dust and gas. Its temperature keeps on rising. When it reaches about 15 million K, hydrogen fusion begins and a star is born. This star enters the main sequence on the Hertzsprung Russell diagram.

The Main Sequence Phase

The main sequence is a band of stars on the HR diagram that are fusing hydrogen into helium in their core. Our Sun is a main sequence star. The most peculiar property of the main sequence phase is that the star is happy. This means that it is in perfect hydrostatic equilibrium. Due to its massive size, gravity tries to crush it. This inward gravitational force is perfectly balanced by the outward gas pressure from the nuclear reaction in the core. This is illustrated in the image below:

Related image

In the core, hydrogen is being converted into helium by the PP chain or the CNO cycle which we discussed in previous article. In Sun like mid sized star, PP chain dominates. It is a slow reaction. This is why it will take about 10 billion years for the Sun to completely convert hydrogen into helium in its core. Note that the nuclear reaction is only taking place in the core region where temperature is high enough (15 million K). The surface temperature of Sun is just 6,000 K.

Turnoff Point

One day, all the hydrogen gets converted into helium in the core. The next nuclear reaction is helium to carbon via the triple alpha process but the problem is temperature. The core is at 15 million K and the temperature required to initiate triple alpha process is about 100 million K. In the absence of this high temperature, the core shuts down and becomes inert. This is known as the turnoff point. The star now exits the main sequence and proceeds to the subgiant branch.

Subgiant Phase

I will try to make it as easy as possible. When the star reaches turnoff point, there is no core reaction going on. Now, it begins fusing hydrogen into helium in a thick shell around the helium core as shown below.

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There is a mass limit of core known as the Schonberg-Chandrasekhar limit (SC limit). The concept is simple. If the mass of the core exceeds this limit, the core can no longer remain in a thermal equilibrium. A strong gradient of temperature starts developing i.e. the core becomes non isothermal. Due to the shell hydrogen fusion, the mass of the inert helium core starts increasing as the "ash" falls on it from above. Once the core mass increases the SC limit, it shrinks and starts heating up. Depending on the initial core mass, the time taken by the stars to reach this limit varies. This was the internal story. Outside, due to shell fusion, the star's external layers expand and cool.

Red Giant Branch

The star's core is heating up now. Outside, it's size is increasing and due to expansion, the surface is getting colder. In other words, the star is becoming a red giant and on the Hertzsprung Russell diagram, it moves to the right and it said to ascend the Red Giant Branch (RGB). There are many internal events that occur during this phase. The most important I want to discuss is dredge up.

Dredge Up

There are 3 main regions inside the star: The core, radiation zone and convection zone. Heat from the core reaches the radiation zone directly via radiation. In the convection zone, the plasma is in convection currents. Just imagine heating a pot of water. Similarly, hot plasma near the radiation zone rises up, comes to the surface, cools and falls back. In the RGB phase, this convection zone gets deeper near the core region. This causes heavy fusion elements such as helium and carbon to get mixed with it and finally come to the surface where they get detected in its spectrum. This phenomenon is known as a dredge up. A dredge up gives important insight into the internal reactions of the stars.

Helium Flash

Once the core temperature reaches 100 million K, helium fusion begins in a runaway fashion. This is known as helium flash. It is such an explosive event that 6% of the core gets converted into helium instantaneously. The star then starts fusing helium into carbon via the triple alpha process.

On the RGB, the star was not in hydrostatic equilibrium. In the absence of the core nuclear reaction, gravity had gained the upper hand and was crushing the star. The core was heating up by this crushing force. But why didn't gravity crush the star? After all there were about 2 billion years for this on the RGB. The answer is the electron degeneracy pressure. We all know that electrons are Fermions and they obey Pauli's exclusion principle. So no two electrons can occupy the same quantum state. When we try to crush the matter, electrons start occupying the lowest quantum states and further crushing results in an outward pressure from these electrons, known as the degeneracy pressure. This degeneracy pressure is due to the Pauli's exclusion principle.

Hence the core becomes degenerate and the enormous energy released from the helium flash is used to lift this degeneracy. Note that not all stars become degenerate before the flash and hence for massive stars, no flash occurs.

Horizontal Branch

Becoming white dwarfs

After the helium flash, the core becomes active again. Now the core is converting helium into carbon via the triple alpha process. The star contracts and its surface temperature increases. So it moves to the left on the HR diagram. The name horizontal branch is given because of the presence of stars with same luminosity (brightness, on y axis) across a horizontal branch of stars of different spectral types (surface temp, on x axis). A HB star is characterized by the following: a helium burning core followed by a hydrogen burning envelope or shell.

White dwarfs

Asymptotic Giant Branch

The star one day runs out of helium in its core. All the helium has been converted into carbon and the core becomes inert yet again. This is because carbon fusion requires a temperature of whooping 500 million K. In this scenario, the shell that was fusing hydrogen into helium now starts burning helium into carbon. A new shell next to this shell begins burning hydrogen into helium as shown below.

Structure of star before white dwarf

The star again moves to the right of the HR diagram as its surface temperature drops. This is parallel to the previous RGB and hence this new branch is known as the Asymptotic Giant Branch (AGB). AGB stars are massive. They are characterized by an inert carbon core followed by a helium burning shell and a hydrogen burning shell. The former swells the star and its radius may be as large as 1 AU. In these stars, a second dredge up occurs. This is the reason why cool and massive AGB stars show strong carbon lines in their spectrum.

Sun like stars do not have the potential to host a full scale carbon fusion in the core. They will expel most of their outer material as planetary nebula and the Carbon-Oxygen core will be left exposed. This is responsible for the carbon oxygen white dwarfs. The white dwarfs do not have any nuclear reaction going on. In such a situation, their collapse is halted by the electron degeneracy pressure that we discussed above.

White Dwarfs

The white dwarfs are the end points of small to mid sized stars. They are extremely dense because the matter that forms the white dwarfs is degenerate. Even a teaspoonful of its material can outweigh the heaviest object on Earth. At this point it is important to discuss a term related to white dwarfs: Chandrasekhar limit, Coined by the Indian Astrophysicist, S.Chandrasekhar at the age of 19. Chandrasekhar limit is the maximum mass of white dwarfs that can be supported by the electron degeneracy pressure. If the mass crosses this limit, the electron degeneracy pressure will be insufficient to halt the tremendous gravitational collapse. As a result, neutron stars or black holes can form.

White dwarfs on HR diagram

On the HR diagram, white dwarfs are at the lower left corner. This means that they have a very high surface temperature but owing to their small size, their energy output or luminosity is less.

Author's Message

I tried my level best to explain the evolution of small to mid sized stars in the simplest way. Now you can easily see why the articles on spectral classification of stars, the Hertzsprung Russell diagram and the nuclear reactions in stars were so important. Stellar Astrophysics is a very prominent branch of this field. It involves so many concepts of Physics. Writing this article was quite difficult for me because it involved a lot of simplification. In the next article, we will be studying the evolution of massive stars that end up becoming neutron stars and black holes. Stay tuned!

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