The Journey Of The Stars From Birth To A Black Hole

A star is born within a nebula due to the gravity compressing the interstellar matter together causing the gas atoms to gain enough kinetic energy to enable nuclear fusion!


The inwards collapse due to the gravitational force is in equilibrium with the thermal gas and radiation pressure outwards due to the random motions of the interstellar particles. This phenomenon is known as the Stellar Hydrostatic Equilibrium. The Elephant's trunk nebula is known as the "Star nursery" due to many star formations occurring there.

The Jeans criterion

The minimum required mass of a cloud of interstellar matter to for a star is known as the Jeans mass, MJ, and can only be possible if M > MJ which is temperature-dependent. In sum, the magnitude of the gravitational potential energy of the interstellar matter needs to be higher than the kinetic energy of its particles. The optimal condition for star formation in a nebula is low temperature and high particle density, which corresponds to a lower Jeans Mass.

Main sequence star

A newly-formed star has a 75% distribution of hydrogen, the rest helium as well as heavier elements within due to the supernovae and a hot dense core where the temperature provides enough kinetic energy for the fusion of hydrogen into helium. Considering Helium is denser than hydrogen, it collects at the center and eventually, as hydrogen runs out, so does the lifespan of the main-sequence star.

The star began collapsing inwards as the Stellar Hydrostatic Equilibrium is disturbed causing a higher rate of transfer from gravitational potential energy into kinetic causing an increase in temperature, enough for further hydrogen fusion. Eventually, the size increases, and the outer layer cools, turning the star into a red giant or a red supergiant.

Luminosity is in relation to its mass accordingly; L M^3.5 meaning the more massive the star gets, the more luminous it, in turn, will be. This is due to the greater gravitational potential energy transfer to kinetic that increases the rate of particle speed. Following the demonstrated equation, it is possible to know the lifetime of a star with the known mass.

The fusion of hydrogen to helium in smaller main sequence stars such as our own sun follows the "Proton-proton cycle". For larger main sequence stars the CNO cycle is followed due to the carbon, nitrogen, and oxygen involved.


Proton-proton cycle



1. Two protons are fused to make a deuterium nucleus and the result becomes the emission of a positron and an electron neutrino.

2. The deuterium nucleus fuses with another proton, forming He-3, emitting a gamma-ray photon. Two He-3 nuclei fuse making a He-4 and emitting two protons as a result. Then, the deuterium nucleus fuses with another proton to make He-3. In this process, a gamma-ray photon is emitted. 1 H + 1 H → 2 He + 0 γ .

3. Finally, two He-3 nuclei combine to make He-4. Two protons are released.

"Nucleosynthesis" is essentially the formation of larger nuclei from different elements of smaller nuclei and nucleons. For example, Red giants have larger masses and in turn, greater temperatures that overcome the repulsive forces between nuclei, leading to the fusion of carbon and oxygen at the same time as helium is formed in the outer layer. Red supergiants are capable of performing nucleosynthesis of heavier elements such as silicon and iron. There is an increased binding energy per nucleon with the emission of energy after each fusion. But this also means that the binding energy per nucleon reaches its max by iron and nickel and thus no heavier elements can not be fused.


In order to form heavier elements, the process of neutron capture is required. Since many neutrons are released during nuclear fusion in stars. Neutrons are uncharged and can, therefore, gain enough kinetic energy to get close to the nuclei as the strong nuclear force pulls it in. This causes the element to turn into an isotope, unstable, and probable yo decay by beta-negative emission to an element of higher proton number.


S and R processes for neutron capture

The rate of neutron capture to a beta negative decay can occur through to different processes.


  1. Slow neutron capture; occur in red giants due to the low neutron density and relative temperature. It may take hundreds of years before a beta decay occurs and any further neutrons are captured. Below is an example of an S process.

  2. Rapid neutron capture; occur only in supernovae due to the need for higher temperatures and neutron density. Many neutrons are captured by the nuclei and within minutes beta decay occurs. Heaviest of elements are formed such as cobalt-61 in this way.

  3. Rapid neutron capture; occur only in supernovae due to the need for higher temperatures and neutron density. Many neutrons are captured by the nuclei and within minutes beta decay occurs. Heaviest of elements are formed such as cobalt-61 in this way.

Type Ia

If the mass of the white dwarf reaches the Chandrasekhar limit reaching to a constant luminosity and gravitational attraction from within is strong enough to attract another star, the increase in mass may overcome electron degeneracy pressure resulting in type Ia supernova. Another name for it is "Standard Candle" since it is used to determine the distance to other galaxies.


Type II

Once fusion ends within a red supergiant, the outer layer of the star tears apart and rapid neutron capture occurs which results in the formation of heavier elements. The resulting core becomes a neutron star or a black hole.

Reference

Physics Book - John Allum and Christopher Talbot - Second Edition - Hodder 2017

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