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Stellar Nucleosynthesis [Review]

Author: Lakshmi Shanmukha Valli Mankala


Introduction

There are vast regions in space called nebulae (star-forming nurseries). Nebulae are filled with dust, gases like molecular hydrogen, helium and others. The other elements are produced by stars after a certain period of their lifetime. Nebulae fragment into gravitationally bound cores, most of which evolve into stars. Factors such as geometric bending and magnetic fields control the fragmentation. These collapsed regions become dense and hot over time, favoring the start of nuclear fusion which leads to a star’s birth.


1 History of Stellar Nucleosynthesis

The idea of nuclear fusion in stars has been around for over a century now. Fred Hoyle, the father of nucleosynthesis, developed the steady state theory. This theory states that our universe is constantly expanding in order to maintain a constant average density. It suggests that newer atoms and particles are being synthesized in the core of stars at the same rate as the old matter is becoming unobservable, because of their increasing velocity of recession and distance. With reference to stars, hydrogen and helium are continuously being created in the universe, in opposition to the big bang theory.


2 The Birth of the First Stars in the Universe

The first stars were born when the dense regions of gas and dust in the protogalaxies collapsed at the nodes of their network of filaments. We believe that the first protons in the universe were formed when the QGP (Quark Gluon Plasma) of the early universe lost sufficient energy leading to the bonding between the quarks. Hydrogen is the simplest atom in the universe. Helium atoms are formed when hydrogen nuclei are fused together.

After the formation of the first two elements in the universe, hydrogen and helium, a few regions had a greater density than the others, which started attracting nearby gases and dust by the gravitational force of attraction. These regions started to grow in size and mass as well. The atoms are in their ionic state within stars, which leads to a repulsive force between them. Nuclear fusion could overcome this force, but for that to happen, these gases need to have a temperature of at least 10 million degrees Celsius. This temperature is needed to overcome the Coulombic force of repulsion between like-charged nuclei. Intense pressure and sufficient density are also needed, which lead to super high kinetic energy of gases. The kinetic energy of nuclei in stellar interiors range from between a few keV to a few 100 keV.


3 The Relative Kinetic Energy between the Interacting Particles

The charge-induced cross-section (σ) as a function relative kinetic energy (E) between the interacting particles is given by the formula:

σ(E)=(1/E)G(E)S(E)

Here, G(E) is barrier penetration factor, S(E) is a function known as the astrophysical S-factor. S(E) varies with the kinetic energy of the interacting nuclei in the absence of resonance. Under these conditions, the protons fuse, producing a lot of energy and newer, heavier atoms. This energy is what makes stars shine, in a way keeping it alive.


4 Hydrogen Burning


The Proton-Proton Cycle

This is the first stage of burning in every star. In main sequence stars (like our Sun), ordinary hydrogen nuclei are burnt through a chain of nuclear reactions which finally produce He-4 nuclei.

The pp (proton-proton) chain proceeds through two reactions. The first reaction is an exothermic fusion of two protons into deuteron d (which consists of a proton and neutron) (refer 1).


(1)

After the formation of deuteron, the next reaction takes place rapidly. The next step has two alternatives called the pp1 and pp2 chains. Mostly pp1 chain takes place (85%) (refer 2). Here, two helium (H-3e) nuclei fuse into H-4e nucleus and also produce two protons.


(2)

In the pp2 chain, He-3 nucleus fuses with a He-4 nucleus producing a Be-7 nucleus and a photon, γ (refer 3).


(3)

After that, an electron is captured and a neutrino is emitted, thereby converting a Be-7 nucleus into Li-7. This is followed by the capture of a proton, creating two He-4 nuclei (refer 4).




(4)

The branching into pp-3 happens very rarely, with its probability being less than 1% (refer 5).






(5)

The final net reaction of three pp-chains is:


(6)

This reaction’s product is He-4 nucleus, giving rise two positrons e+ and two neutrinos ν and energy of 26.73 MeV. A part of the total energy released is carried away by neutrinos which leave the star as they are.


The CNO Cycle

This process is favored over the pp-chain in stars with mass two times greater than that of our Sun. The temperature must be greater than 15X10^6 K.













The early stars contain mostly only helium and hydrogen. In these stars, CNO cycle cannot take place, due to the lack of the prerequisite carbon, nitrogen and oxygen atoms.


5 Helium Burning

As long as there is hydrogen in the stars, it will continue to fuse into helium. When all the hydrogen in the star gets exhausted, helium starts to fuse into heavier elements. Before that, the star would have undergone gravitational collapse and the temperature of its core rises by 10^8 K, hence favoring helium burning. In the first reaction of helium burning, two He-4 nuclei fuse to form Be-8 nucleus. Be-8 has a life of 10^-16 then it decays back into two He-4 nuclei (refer 7).


(7)

Next, a Be-8 and a He-4 nucleus may form C-12 (refer 8).


(8)

The reactions (7) and (8) are known as triple alpha capture because three He-4 nuclei (particles) are required for the formation of C-12. The C-12 produced converts into O-16 (refer 9). Almost 50% of the carbon gets converted into oxygen. Helium burning usually ends with oxygen.


(9)


6 Carbon Burning

In stars with a mass of about 8 solar masses at birth, helium burning is followed by carbon burning. The minimum temperature required is 5X10^8 K and density must be greater than 3X10^9 kg/m^3. In the first step, two carbon nuclei fuse to form Ne-20 or Na-23 nuclei.




Later, at 10^9 K the photons disintegrate Ne-20 and produce He-4, which in turn reacts with the undissociated Ne-20 to form Mg-24.





Oxygen starts to burn at 2X10^9 K, to produce silicon.




7 Nucleosynthesis beyond Iron


There are two processes that lead to the formation of heavier nuclei (of elements beyond Fe). They are the r-process (rapid neutron capture) and s-process (slow neutron capture).


7.1 Slow Neutron Capture

In the s-process, a seed nucleus undergoes neutron capture to form an isotope with a higher atomic mass. If the produced isotope is stable, a series of increase in mass can occur; if it is unstable, it will undergo beta decay, hence producing an isobar. This process is slow because there is sufficient time for the reaction to take place before another neutron capture.


7.2 Rapid Neutron Capture

In this process, nuclei are bombarded with neutrons. Neutrons can be absorbed until the neutron separation energy is less than or equal to zero. This is called the neutron drip line. Neutron rich isotopes are unstable and lead to beta decay. After beta decay, the new nucleus will have a new neutron drip line and, in most cases, will be able to capture more neutrons.


Conclusion

After millions of years, when all the hydrogen and helium in the stars will have fused into higher elements and the stars having lost their heat, they will steadily become brighter and inert. The nature of the death of a star depends on the type of the star. Massive stars die much more violently. They would have developed an iron core toward the end of their lifetime and it begins to contract into an extremely high density, turning it into a ball of neutrons.

A supernova (triggered when massive stars die) releases more energy in a week than our Sun would release in its entire lifetime. The shockwave is super powerful and spews out material even out of the galaxies.

When medium sized stars die they continue to get hotter, redder and bigger as they turn into red giants. Our Sun would reach the orbit of the Earth when it becomes a red giant. When it dies, it also emits dust and gas which form nebulae and its core is called a white dwarf.


Bibliography

  • Principles of Stellar Evolution and Nucleosynthesis by Clayton, D. D.

  • Origin of the Chemical Elements by T. Rauscher and A. Patkos.

  • Neutron capture chains in heavy element synthesis by Clayton, D. D.; Fowler, W. A.; Hull, T. E.; Zimmerman, B. A.

  • Why the stars shine? by Selle, D.

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