Neutron Stars And Their Birth

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

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.

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Birth of Stars

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

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.

Neutron stars formation

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. Here stems the difference. The core of massive stars reaches this limit quicker and thus they have a short span of subgiant phase. 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 reaches SC limit, it contracts and starts heating up. 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 out of which the most important is dredge up (click to read about it in previous article).

Helium Flash

Once the core temperature reaches 100 million K, helium fusion begins. The major difference between the evolution of massive and mid sized stars here is that in the former, there is no explosive helium flash. We learnt in the previous article that helium fusion begins explosively in mid sized stars. However, in the massive stars, the core isn't degenerate so there is no flash.

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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.

Horizontal Branch

Becoming Neutron Stars

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.

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. The go on to synthesize heavier elements by the nuclear reaction which we will discuss below.

Carbon Fusion

Carbon Fusion Reaction In Massive Stars

I have written the five possible reactions in which carbon can fuse. Firstly, two carbon nuclei come together and form magnesium in excited state which decays in five possible ways as shown above. The first two reactions are strongly exothermic, as indicated by the large positive energies released, and are the most frequent results of the interaction. The third reaction is strongly endothermic, as indicated by the large negative energy indicating that energy is absorbed rather than emitted. This makes it much less likely, yet still possible in the high-energy environment of carbon burning. The fourth reaction is unlikely to occur because it proceeds via the electromagnetic interaction as indicated by the gamma photon. Finally, the fifth reaction involves three reaction products and is endothermic thus making it unlikely.

Also Read: Nuclear Reactions In Stars

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 strikes the mark of 1.2 billion K, neon burning begins. This reaction proceeds as shown below.

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 undergoes the last set of nuclear reaction known as the alpha ladder.

Alpha Ladder

Silicon has mass number 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, next alpha elements with mass number as multiples of 4 keep on forming as shown below.

Neutron Stars formation

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 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, alpha ladder from Si to Ni ends in a single day!

In the absence of the core nuclear reaction, the 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:

Neutron Stars formation

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 Fermion obeying Pauli's exclusion principle.

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 M (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 M) for white dwarfs, there is an analogous limit of stable neutron stars. This limit is known as Tolman-Oppenheimer-Volkoff (TOV) limit. This lies between 1.4 and 3 M. Stars between 3 M and 5 M form hypothetical compact stars like quark stars while those greater than this form black holes.

Properties of Neutron Stars

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

  • The temperature of a newly formed neutron star is about 1 trillion K. As the neutrinos escape from it, the temperature falls to 1 million K over the course of 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 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 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 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 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 strong hold on these, Astrophysics will be a cake walk for you.

4 thoughts on “Neutron Stars And Their Birth

  1. I wish to congratulate you on this wonderful series and thank you for your efforts. You have condensed extremely complex subjects into manageable slices as an introduction and incentive for further study.
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