Stellar Evolution, Red Shift and Hubble's Law

Stellar Evolution

Birth of star:

The inter-steller space contains an enormous amount of dust particles and gas, which come closer and closer due to the gravitational force of attraction and a cloud is formed. Within the cloud large clumps are formed, which attracts more mass and they get heat up due to contraction. The temperature of the central core heats up with the occurrence of nuclear fusion of hydrogen. During fusion of hydrogen atoms helium atom is produced with the release of energy. The gravitational force of attraction towards the centre of the star, due to its own mass is balanced outward pressure due to the heat generated due to the nuclear fusion.

Death of a star:

When the central core is completely converted into helium, there is no more production of heat. There is no outward pressure to balance the inward gravitational pull. So, star contracts and temperature increases causing the outer layer of the star to expand. Due to expansion outer layer is cooled and after certain time star looks red. The red star is called red giant. Due to further contraction, the temperature may rise to such high value, that fusion of helium will take place, forming heavier elements. Once again, the fuel will be exhausted and then there will be a violent explosion, called a supernova. Due to this explosion, a large portion of star’s envelope is thrown into interstellar space and this is the death of a star.

White dwarf:

For stars like the sun, the gravitational compression will leave the core, composed of protons and electrons, flying around a gas-like phase, called the electron gas. The electron gas is able to withstand the inward gravitational pull. Under this situation, the star is called white dwarf. White dwarf starts cooling and changes its color from white to yellow and yellow to red. Finally, it becomes a black dwarf, without emission of any radiation.

Black hole:

If the original mass of the star is greater than 5 solar mass, the gravitational pull inward will be so high that the core contracts to a radius R given by R = 2GM/c², where M is the mass of the star and c is the velocity of light. After meeting above criteria, a black hole is formed. The gravitational pull, within this, is so strong that even a light photon cannot escape from it.

Neutron Star

If the mass of the star is between 1.4M₀ and 5M₀ the core may end up as a neutron star. When the mass is greater than 1.4 solar mass, due to gravitational compression, the electrons are forced into the nuclei by the process called the inverse b-decay. In this process, the electrons and protons combine to form neutrons. Since the core contains only neutrons, it is called a neutron star.

Supernova:

When the neutron star is formed, the compression of the core produces a tremendous amount of gravitational energy. Due to the release of energy, the outer layers of the star explode. The phenomenon of the brightness of the star sharply increasing for some time and then decreasing is called a supernova.

Galaxy:

Galaxy is a large collection of a group of stars and is the building block of the universe. The galaxies are of different shapes, like a spiral, elliptical or irregular. Normal galaxies emit an only little amount of radio waves, but radio-galaxies give out million times more radio waves than normal galaxies. Our galaxy is a milky way and Andromeda is the nearest galaxy to us.

Redshift and Expanding Universe

On the basis of observations on the galaxies the distant galaxies are receding from us and also away from each other at a very high speed. According to Doppler effect in light, if source of light is receding from an observer, its wavelength appears to increase \(\left ( \lambda _0 = \lambda _s \sqrt {\frac {c + v}{c – v}} \right ) \), that is the light emitted by it appears to have a longer wavelength than when it was at rest. Thus, a receding source of light should show a shift towards longer wavelength region in the lines of its spectrum. This phenomenon is called the red shift.

If a radiation of particular wavelength l emitted by a star/galaxy is observed through a electroscope, then due to velocity v of the star/galaxy with respect to the earth, the wavelength recorded or observed will be l₀ which is quite different from the real wavelength l. Then the red dhift is denoted by z and is defined by

\begin{align*} z &= \frac {\lambda _0 - \lambda }{\lambda } = \pm \frac vc \\ \text {or} \: z &= \frac {\Delta \lambda }{\lambda } = \pm \frac vc \\ \end{align*}

Where positive sign means star/galaxy is receding away from the earth and negative sign means moving towards the earth.

Hubble’s law

This law states that the speed of recession of the galaxy is proportional to its distance from us. If v is the speed with which a galaxy recedes and r is its distance from earth,

\begin{align*} \text {Then} \: v &\propto r \\ \text {or} \: v &= H_0r \end{align*}

where H₀ is called Hubble constant. Its value is 2.3 ´ 10^-18 s^-1.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.