The Neutron Stars And Their Birth

Rishabh Nakra

Admin and Founder of ‘The Secrets Of The Universe’ and former intern at Indian Institute of Astrophysics, Bangalore, I am a science student pursuing a Master’s in Physics from India. I love to study and write about Stellar Astrophysics, Relativity & Quantum Mechanics.

In the last article of the Basics of Astrophysics series, we discussed the evolution of Sun-like mid-sized stars. We saw how they become white dwarfs. In the seventeenth article of the series, let us learn about the evolution of massive stars and how they end becoming neutron stars or black holes.

There is a little difference between the evolution of mid-sized stars and the massive stars till carbon fusion. Instead of redirecting you to the previous article of the series, I will start afresh. So here we begin with the evolution of massive stars and their ultimate death as neutron stars. If you have read the previous article, you may skip to the Post AGB heading and continue reading the formation of neutron stars and black holes.

Read all the articles of Basics of Astrophysics here

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 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 gravity. This collapse continues for a long period 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:

In the core, hydrogen is being converted into helium by the PP chain or the CNO cycle which we discussed in the previous article. In Sun-like mid-sized stars, the 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 the temperature is high enough (15 million K). The surface temperature of the 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 the 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:

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 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.

The 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 (marked 1,2 and 3 in the image respectively). The heat from the core reaches the radiation zone directly via radiation. In the convection zone, the plasma is in convection currents.

Also watch: How will the Sun die?

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 carbon 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.

Also read in series:
Chapter 1 – What is Astrophysics?
Chapter 10 – The Hertzsprung Russell Diagram
Chapter 11: The Saha’s Equation

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 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

fter 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 the same luminosity (brightness, on the y-axis) across a horizontal branch of stars of different spectral types (surface temp, on the x axis). An HB star is characterized by the following: a helium-burning core followed by a hydrogen-burning envelope or shell.

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.

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.

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The concept of Hawking radiation from black holes
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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 a 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.

Post AGB Phase

The story ends here for the mid-sized stars as they do not have the potential to host a full-scale carbon fusion. However, massive stars easily reach the temperature required for carbon fusion. They go on to synthesize heavier elements by the nuclear reactions which we will discuss below.

Carbon Fusion

Carbon fusion begins at a whopping 500 million K. The common products of this reaction are neon, oxygen, sodium, and magnesium. Stars below 8 solar masses cannot host carbon fusion. Stars between 8-11 solar masses begin carbon fusion with a flash but this disrupts the star. The ones with mass above 11 solar masses go on to fuse even heavier elements.

The final product after carbon fusion at 500 million K is a core of Neon-Oxygen-Magnesium-Sodium mixed together.

Neon Burning

After fusing carbon, the core again becomes inert. When the temperature hits the mark of 1.2 billion K, neon burning begins. This reaction proceeds as shown above. During neon burning, oxygen and magnesium accumulate in the central core while neon is consumed. After a few years the star consumes all its neon and the core ceases producing fusion energy and contracts. Again, gravitational pressure takes over and compresses the central core, increasing its density and temperature until the oxygen-burning process can start.

Oxygen Burning

Oxygen burning begins when the core temperature reaches about 3 billion K. The major products of oxygen burning are silicon and sulphur. The silicon and sulphur that accumulates in the core undergo the last set of nuclear reaction known as the alpha ladder.

Alpha Ladder

Silicon has a mass number of 28. This is the number of protons and neutrons in the nucleus of silicon. Alpha particle or the helium nucleus has mass number 4. When it strikes silicon-28, it forms sulphur-32. See how the mass number is conserved (28+4=32). Subsequently, the next alpha elements with the mass number as multiples of 4 keep on forming as shown below.

The reaction sequence ends at Nickel-56. This is because Ni-56 peaks the binding energy per nucleon curve. In other words, the next nuclear reaction, Ni-56 to Zn-60 will consume energy rather than releasing. Hence it is not thermodynamically favorable. So at Ni-56, the core becomes inert. The alpha ladder is a very fast reaction owing to the tremendous temperature at which it takes place. Remember how it took about a billion years for the star to convert H into He? Well, the alpha ladder from Si to Ni ends in a single day!

In the absence of the core nuclear reaction, gravity again gains the upper hand and starts crushing the star.

Supernova

We had seen how shell burning started after the turnoff point. Well, that didn’t stop. Subsequent shells burnt heavier fusion elements and just after the alpha ladder ends, the internal structure of star looks like this:

The hydrogen-burning shell that was the first to be ignited has moved up just below the surface of the star. Now the collapsing gravitational force is so intense that even electron degeneracy pressure does not save the dying star. The electrons and the protons combine to form neutrons and the collapse is halted by the analogous neutron degeneracy pressure. This is because just like electrons, neutrons are also Fermions obeying Pauli’s exclusion principle.

Also read:
The experience of an internship at CERN’s Large Hadron Collider
8 interesting facts about neutrinos: Nature’s ghost particles
Understanding the Feynman diagrams in physics

The infalling outer envelope of the star is halted and flung outwards by a flux of neutrinos produced in the creation of the neutrons, becoming a supernova. The remnant left is a neutron star. If the remnant has a mass greater than about 3 Mo (3 times mass of Sun), it collapses further to become a black hole.

Neutron Stars

Neutron stars thus formed are very dense as the matter is degenerate. Just as we defined an upper mass limit, the Chandrasekhar limit (1.44 Mo) for white dwarfs, there is an analogous limit of stable neutron stars. This limit is known as the Tolman-Oppenheimer-Volkoff (TOV) limit. This lies between 1.4 and 3 M_o. Stars between 3 M_o and 5 M_o form hypothetical compact stars like quark stars while those greater than this form black holes.

Properties Of The Neutron Stars

Before ending this article, let us have a look at some eye-catching properties of neutron stars.

• The temperature of newly formed neutron stars is about 1 trillion K. As the neutrinos escape from it, the temperature falls to 1 million K over the course of a few years. At this temperature, neutron stars mainly emit X-rays.
• The density of neutron stars is of the order of nuclear density (10^17 Kg per cubic meter). A teaspoonful of its material will be 900 times heavier than the Great Pyramid of Giza.
• Neutron stars have an enormous magnetic field. There is a special class of neutron stars known as magnetars that have the field of the order of 1 trillion Tesla. Note that in laboratory conditions, we can generate a maximum magnetic field of the order of 100 Tesla. If a magnetar is placed at the position of the Moon, it has the capability to affect the magnetic strips of our credit cards.

So this was all about today’s lesson on neutron stars.

Author’s Message

We did it! This was the last “difficult” article of the Basics of Astrophysics series. My major aim was to show you that Astrophysics requires a wide range of Physics. The evolution of stars is one field I chose to show this. I tried my level best to explain stellar evolution in the simplest way. I hope you enjoyed the Stellar Astrophysics part of this series. From here on, we will be just ‘touching’ the other concepts of Astrophysics such as black holes, nebulae, galaxies, etc. There won’t be hardcore physics involved.

But before leaving, I want to share something. Many students ask me the way to pursue Astrophysics after they leave high school (Class 12). For them, I have one advice: “Don’t go for Astrophysics at such an early stage”. Yes! First you should master concepts of Physics. The subjects that you should master include Statistical Mechanics, Spectroscopy, Electrodynamics, Nuclear Physics, Optics, Quantum Mechanics, and Mathematical Physics among others. If you have a stronghold on these, Astrophysics will be a cakewalk for you.

Read all the articles of Basics of Astrophysics here