Chapter 14, Problem 13QFT

(a)

To determine

The theoretical physical circumstances that lead to the creation of a white dwarf star.

Answer to Problem 13QFT

Solution:

The white dwarf stars are the stars which appear whitish in color and are usually faint, but relatively hot. These stars are comparatively small, perhaps twice the Earth’s size. Due to their small size, the white dwarfs appear faint. After blowing off the outer shells, a red giant star becomes a white dwarf. At a later stage, a white dwarf explodes tremendously which marks the end of a star.

Explanation of Solution

Introduction:

All stars go through different stages of life. The journey of their life begins with protostar and then followed by stages including the main sequence star, a red giant and a white dwarf.

Explanation:

A white dwarf star during the red giant stage, the helium fusion reactions begin to occur in the core of a red giant. After millions of years, the helium core is gradually converted to a carbon core and fusion reactions of helium begin in the surrounding shells of a red giant core. The helium fusion reaction decreases the core as the star is now having a helium-fusing shell surrounded by a second shell where hydrogen fusions are taking place. This results in the release of the additional energy and the star expands again to a red giant for the second time.

Changes in temperature cause changes in pressure and, balance among the temperature, pressure and generation rate of internal energy. This led the star to expand outward due to heating. However, the expanded gases are cooled by the process of expansion and are pulled back to the star by gravity. The outer layers of star begin to pulsate in and out. A violent explosion finally blows off the outer layers of the star and leave a small, hot, dense, underluminous stars called ‘white dwarf’.

Conclusion:

White dwarfs are the stars which appear whitish in color and are usually faint, but relatively hot. These stars are relatively small, perhaps twice the Earth’s size. Due to their small size, the white dwarfs appear faint.

(b)

To determine

The theoretical physical circumstances that lead to the creation of a red giant.

Answer to Problem 13QFT

Solution:

The hydrogen in the core of main sequence star has been fused into helium under high-temperature conditions, the star begins to move towards its next stage called ‘red giant’. These stars are enormously bright for their temperatures. This is due to their enormous surface area that gives off a huge amount of light.

Explanation of Solution

Introduction:

All stars go through different stages of life. The journey of their life begins with protostar and then followed by stages including the main sequence star, a red giant and a white dwarf.

Explanation:

When the hydrogen in the core of main sequence star has been fused into helium under high-temperature conditions, the star begins to move towards its next stage called ‘red giant’. Less energy is released with fewer hydrogen fusion reactions and thus, less outward balancing pressure is produced. So, the star begins to collapse. This further heats up the core, which is primarily composed of helium and the hydrogen still exists in its surrounding shells.

The hydrogen in the shell undergoes fusion due to the increased temperature as a result of the collapse. This, in turn, causes increased release of energy leading to expansion of the outer layers of the star. The amount of radiation emitted per unit area is less as the surface area is increased now. Thus, the color of star turns reddish and the star is now referred to as the ‘red giant star’.

Conclusion:

Red giant stars are low-temperature, but bright stars. These stars are enormously bright for their temperatures. This is due to their enormous surface area that gives off a huge amount of light. After the main sequence stage, an average mass star expands to a red giant.

(c)

To determine

The theoretical physical circumstances that lead to the creation of a neutron star.

Answer to Problem 13QFT

Solution:

A neutron star is basically the collapsed core of a massive star. The neutron stars predominantly composed of closed packed neutrons. Sometimes, a core survives after a supernova whereas the outer layers of the huge massive star explode and materials are then ejected into space. If the remaining core has a mass between 1.5 and 3 solar masses, it contracts to form a super dense and tiny celestial object, also known as a neutron star.

Explanation of Solution

Introduction:

All stars go through different stages of life. The journey of their life begins with protostar and then followed by stages including the main sequence star, a red giant and a white dwarf.

Explanation:

The neutron stars are the celestial objects with very high density and very small radius of typically $30\text{km}$. They are predominantly composed of closed packed neutrons. If the core of a supernova has remaining mass $1.4$ times greater than that of sun, the gravitational forces of the remnants in addition to the compressional forces of the tremendous explosion are great enough to collapse the nuclei of remaining atoms in the core. The pressure thus forces the electrons and protons of the atoms together into neutrons, leading to the formation of the core of a neutron star.

Conclusion:

The neutron stars are made from the collapsed core of a massive star. They are predominantly composed of closed packed neutrons.

(d)

To determine

The theoretical physical circumstances that lead to the creation of a black hole.

Answer to Problem 13QFT

Solution:

The death of a massive star is marked by a tremendous explosion called a supernova. This further leads to the formation of a black hole at the place of the star in the universe. If the remaining core is much greater than 3 solar masses, then it collapses to form a black hole.

Explanation of Solution

Introduction:

All stars go through different stages of life. The journey of their life begins with protostar and then followed by stages including the main sequence star, a red giant and a white dwarf.

Explanation:

A black hole is often considered as the cosmic body of extremely intense gravity from which nothing can escape, not even the light. The death of a massive star with a core three times the mass of Sun is marked by a tremendous explosion called a supernova. This further leads to the formation of a black hole.

Conclusion:

When the remaining core has a mass equivalent to three times or greater than solar masses, then the gravitational force overwhelms all nuclear forces such as repulsive force between like charged particles. Nothing can stop the star to collapse at this point and the star will become so dense that it would be difficult for even the light to escape. Now, the star has evolved into a new stage called a black hole.

(e)

To determine

The theoretical physical circumstances that lead to the creation of a supernova.

Answer to Problem 13QFT

Solution:

When a star reaches its death stage after passing through all stages of life, it explodes in a tremendous way leading to the formation of a black hole at its place in space. The tremendous explosion or collapse of a massive star is commonly referred as a supernova, which is the largest blast occurring in space and marking the end of the star.

Explanation of Solution

Introduction:

The universe was born hot and dense after a big bang in space. Later on, the universe expanded quite rapidly. There are numerous elements that are commonly found in the universe. The source of all elements in the universe which are more massive than helium but less massive than iron is due to the nuclear fusion reactions. On the other hand, a supernova is mainly responsible for the all the elements produced in the universe that is more massive than iron.

Explanation:

The tremendous explosion or collapse of a massive star is commonly referred as a supernova, which is the largest blast occurring in space and marking the end of the star. Supernova is a violent explosion and can shine as brightly as an entire galaxy consisting of billions of the normal stars. A more massive star goes through a carbon fusing stage as the suitable temperature $600\text{million Kelvins}$ is reached. It will further lead to the production of new elements.

After the production of the iron element, energy is no longer released by the process of fusion and the star uses up all of its energy sources. The star is no longer able to maintain its initial temperature due to the lack of energy sources. Thus, the star collapses because it loses the outward pressure of expansion from high temperature, which had earlier balanced the inward pressure from gravitational attraction. After the collapse, the star rebounds like a compressed spring into a tremendous explosion called a supernova, producing a brilliant light in the sky which may last for months.

Conclusion:

When a star reaches its death stage after passing through all stages of life, it explodes in a tremendous way leading to the formation of a black hole at its place in space. The tremendous explosion or collapse of a massive star is commonly referred as a supernova, which is the largest

blast occurring in space and marking the end of the star.