What is Stellar evolution?

We may see thousands of stars in the dark sky. Our universe consists of billions of stars. Stars may appear tiny to us but they are huge balls of gasses. Sun is a star of average size. Some stars are even a thousand times larger than the sun. The stars do not exist forever they have a certain lifetime. The life span of the sun is about 10 billion years. The star undergoes various changes during its lifetime, this process is called stellar evolution. The structure of the sun-like star is shown below.

Birth and death of stars

Stars are giant balls of gasses even though there are billions of stars of various sizes, almost every known star consists of hydrogen and helium gases. These gases are held together by a gravitational force. The stellar evolution can be studied using the concepts of thermodynamics and quantum physics.

Stages of stellar evolution

The stars undergo various stages during their lifetime the newly formed it is a protostar. The death of a star is the supernova explosion. The evolution depends upon various factors.

Birth of stars-protostar

In the initial stage of stellar evolution, stars are formed due to the collapse of clusters called molecular clouds which consist of hydrogen gas and other dust particles due to strong gravitational force. The collapsing cloud is about 100 light-years wide. During collapsing the clouds get condensed into a smaller volume while the gravitational energy is liberated as heat. At this stage, the clouds condense to a spherical shape while the stellar temperature and pressure of the star increase. At this instant, the star is called a protostar. It takes about thousands of years to form a typical protostar.

Main sequence stage

As the protostar collapses due to strong gravitational force the temperature at the stellar core increases. At some point, the temperature favors the stellar proton-proton nuclear fusion where hydrogen is fused to form helium. This stage is referred to as the main-sequence star. The main sequence stage is the longest stage for any star. The sun is presently at the main sequence stage. At this instant, the stars do not collapse further as the inward gravitational force balances the thermal pressure which exerts in the outer direction. Once the hydrogen present inside the core is completely converted to helium, the main sequence stage will end. After this stage, the hydrogen present in the outer shell is fused to form helium by nuclear reaction.

After the main sequence stage, the fate of the star depends upon its stellar mass.

The fate of low-mass stars-white dwarfs

In low-mass stars, once the hydrogen at the shell is exhausted there will not be a proper state to carry on nuclear reaction. The temperature decreases so that the condition does not favor the nuclear reaction. The star reaches to stage called the white dwarf stage. Hence, the low-mass stars collapse due to gravity to form white dwarfs. They have very low luminosity. The sun will shrink to the volume of the earth if it becomes a white dwarf. The white dwarf stars cannot collapse further as electron degenerate pressure prevents further collision. The white dwarf is smaller in volume compared to other stages.

The fate of average massive stars

Stars of average mass like sun reach stage called red giant once the hydrogen at the inner core is exhausted. At this stage, the outer hydrogen layer is used as fuel. The volume of the giant star increases tremendously. The radius of the sun will increase up to the revolution orbit of the earth if it reaches the red giant. During this stage, the inner temperature of the star core increases. This condition favors nuclear reaction where the elements like carbon, oxygen, and nitrogen are formed. The reaction continues till the iron is formed and no further element is formed after iron.

Neutron star and supernova

If the mass of the star is close to about three times of the sun, after the fuel at the inner core is finished there won’t be any fuel left. The thermal equilibrium is disturbed; hence, the star undergoes collapse due to gravity. In this case, the collapse cannot stop at electron-degeneracy pressure, as the gravitational force is way larger than electron pressure but the collapse stops at some point due to neutron degeneracy pressure. When neutron stars collapse the moment of inertia is conserved, hence the neutron stars spin rapidly and they eject radio waves.

The sudden collapse exerts huge pressure at the core. The neutron star explodes causing a supernova. Last known supernova which was observed directly happened in the year 1604 named Kepler's supernova.

The supernova produces huge energy. In some cases, the supernova tends to the formation of stellar black holes

Black holes

If the stellar mass is much greater than about three times the sun’s mass. Then the inwards gravitational force that collapses the high-star is much larger. During the gravitational collapse of massive stars, the neutron degeneracy pressure cannot stop the collapse, the massive stars collapse into a point called a singularity. The density at this point is infinite. At some distance from this point no object even a photon cannot escape from its gravitational force. This point is called a black hole. The region where no object cannot escape is called the event horizon of a black hole.

Black holes do not emit any type of radiation they do not possess any luminosity. Hence, it is difficult to observe any black hole directly.

Characteristics of stars

There are billions of stars in space but they can be classified based on their characteristics such as brightness, color, etc. The observation of color is significant in astronomy. The temperature of the star decides the color of the star. The color of the star is associated with the wavelength emitted by the stars. The temperature T can be calculated using the following formula for the black body is,

$T=\frac{b}{\lambda }$

Where,

b is the wein’s displacement constant.

$b=2.897\times {10}^{-3}m K$

λ is the wavelength emitted by the star.

H-R diagram

H-R diagram or Hertzsprung-Russell diagram is a tool that is used to analyze the characteristics of stars. H-R diagram is a plot between the surface temperature and the luminosity of the star. If we know these two quantities of a star, the stage of the star can be predicted.

The different regions indicate different stages of the stars. The massive stars usually occupy the top region of the diagram.

The stars at the main sequence exhibit certain relation between temperature and luminosity. The sun is present in the middle region of the curve. The other stars at the main sequence occupy the s-shaped curve in the H-R diagram.  

The red giant stars occupy the upper region of the diagram. The red giant stars are bright stars with relatively lower temperatures. As the mass of the stars increases, the region in the H-R diagram shifts to the upper part.

The white dwarfs occupy the lower region in the diagram. These stars are not as bright as stars at the main sequence stage. Also, white dwarf stars have got lower temperatures compared to the main-sequence stage and red giants.

The stars Sirius and Sirius A are white dwarf stars. The mass of the white dwarf ranges is usually less than the stars in the main sequence.

Formulas

The surface temperature of a star can be calculated using,

$T=\frac{b}{\lambda }$

Where,

b is the wein’s displacement constant.

λ is the wavelength emitted by the star.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for Bachelors and masters in science (physics).

Practice problems

Question 1: If the wavelength emitted by a star is 579.4 nm, what is the surface temperature (in kelvin) of the star.

(a) 3000 K                        (b) 3600 K

(c) 5000 K                        (d) 6000 K

Answer: The correct option is c.

Given Data:

$\lambda =579.4 nm$

$L=100 L_{sun}$

Explanation: 

To find surface temperature:

$T=\frac{b}{\lambda }$

$T=\frac{2.897\times {10}^{-3}}{579.4\times {10}^{-9}}K$

$T=5000 K$

The surface temperature of the star is 5000 K.

Question 2: The stars produce a huge amount of energy by ______.

(a) Nuclear fission                             (b) Nuclear fusion

(c) Gravitational energy                    (d) Chemical energy

Answer: The correct option is b.

Explanation: Inside the star's core the hydrogen atoms fuse due to high pressure and temperature to form helium atoms which is a nuclear fusion reaction.

Question 3: In the main sequence stage of a star the inward gravitational force is balanced by the ______.

(a) Normal force (b) Thermal pressure

(c) Electron degenerate pressure (d) Neutron degenerate pressure

Answer: The correct option is b.

Explanation: At the main sequence stage huge amount of heat energy is radiated. This force prevents the further collapse of the star. At this stage, the magnitude of gravitational force is the same as the thermal pressure so that the star remains stable.

Question 4: The color of the star depends upon ___ of the star.

(a) Luminosity (b) Chemical composition

(c) Mass (d) Temperature

Answer: The correct option is d.

Explanation: The chemical composition of all the stars is the same. Stars are treated as black bodies hence the following equation holds good for the stars.

$T=\frac{b}{\lambda }$

Where T is the surface temperature and λ is the wavelength. Since the color depends upon the wavelength, the color of the star depends upon the temperature.

Question 5: In the H-R diagram, the lowest position is occupied by ______.

(a) White dwarfs (b) Red giants

(c) Main sequence stars (d) Neutron stars

Answer: The correct option is a.

Explanation: White dwarfs stars are the low mass and low luminous stars. The temperature of the white dwarf star is lower than any other stage of the star. Hence, the white dwarf's stars occupy the lowest region in the H-R diagram.