II. Telescopes &
III. The Solar System
IV. The Sun
V. Stars
VI. Stellar Structure &
VII. Our Galaxy &
    Interstellar Matter
VIII. External Galaxies
IX. Cosmology
HOME > Syllabus and Guides > VI. Stellar Structure & Evolution
  Stellar structure can be understood based on the principles of statics equilibrium, the ideal gas equation, the method of energy transfer, and the nuclear fusion reaction in the center, and such physical descriptions offer us a theoretical explanation of stellar structure and evolution. The elements that compose the majority of the stars are hydrogen and helium, and nuclear fusion reactions in the center result in changes to the chemical composition. This change in the chemical composition is the key to comprehending stellar evolution. All stars evolve according to an identical series of stages, while the specific evolutionary stage for each differs according to the mass of the star. Through such stellar evolution, we can understand how a star’s luminosity and temperature changes over time.
The Stages of Stellar Evolution
  All stars follow the same sequence of evolution, following the stages of protostar, pre-main sequence star, main sequence star, and post main sequence star. Stars are created from a cloud composed of gases and dust, and the gravitational contraction of the star results in the temperature rising to a level that causes nuclear fusion reactions, and thus a single star is born. The star in this state preceding the moment of the star’s creation is referred to as the proto-star. The stage between the proto-star stage and the point immediately preceding the nuclear fusion that occurs upon the birth of the star is the pre-main sequence, and the stage in which the star reaches statics equilibrium and undergoes nuclear fusion in its center is the main sequence. The majority of stars spend most of its life span in the phase of the main sequence. The nuclear fusion that occurs in the center at this time differs according to the mass of the star, which also leads to markedly differing developments in the evolutionary stages thereafter.
The Evolution of Stars with Small Mass
  In the main sequence stage of stars with a mass similar to the sun, a nuclear fusion reaction that changes hydrogen into helium occurs in the core region. As the hydrogen changes in to helium, the chemical components are transformed, and the star’s structure also changes accordingly. When the hydrogen is depleted in the core, the nuclear fusion reaction ceases, and the star contracts. As the star contracts, the nuclear fusion reaction of hydrogen takes place in the crust layer outside the core rather than in the core, and the star reaches a stage in which its core region contracts while its external region expands. At this time, a convective flow occurs near the surface of the star. This stage is referred to as the red giant star phase. During the red giant star phase, the density in the core is extremely high and the electrons exist in a degenerated state, and when the temperature reaches a certain level in the core, helium nuclear fusion reaction occurs, which become explosive due to the degenerated electrons.? This is referred to as the helium flash. When the temperature in the core reaches above a certain level due to the helium flash, the degeneracy of the electrons recedes and the core area is greatly expanded, reducing the surface temperature by a large margin.
Evolution of High-Mass Stars
  By contrast, while large stars with masses 5 times or more than the sun also undergo a nuclear fusion reaction that changes hydrogen into helium in their cores, carbon functions as a catalyst in this reaction. This reaction requires an extremely high temperature in the core, and to counteract the gravity arising from the star’s mass, a larger quantity of hydrogen participates in the nuclear fusion reaction. For this reason, the nuclear fusion reaction in the core takes place over a much shorter time compared to stars with masses similar to the mass of the sun. Once the nuclear fusion reaction is complete, the core area contracts, and the hydrogen in the crust area begins nuclear fusion. The convection layer on the surface gradually develops and the star ultimately enters the red giant star stage. Unlike stars with masses similar to the sun, such heavy stars do not experience a helium flash because the internal temperature in the core reaches a level sufficient to cause a helium nuclear fusion reaction before the degeneracy of electrons.
The Final Stage of Stellar Evolution
  After undergoing these stages of evolution, the star faces the final phase of its life span. There are three forms that a star can assume in its final stage, namely a white dwarf star, a neutron star or a black hole. In the case of stars with core masses that are less than 1.4 times that of the sun, after the helium nuclear fusion reaction in the core, the star fails to reach the degree of temperature required for the next stage of carbon nuclear fusion reaction and the core continues to contract, while in the crust area the helium nuclear fusion reaction occurs, consuming helium. In this process, the star moves in pulsating motion, and the crust area is blown away from this pulsation. As a result of this process, a planetary nebula appears and the carbon nuclear core is exposed by the loss of the crust: this is referred to as a white dwarf star.

In stars with a core mass that is around greater than 1.4 times and less than 3 times that of the sun, protons and electrons combine in the core to form neutrons, resulting in a core composed only of neutrons. When even these neutrons contract, the star’s structure suddenly collapses, and the exterior area of the star collides with the core to cause intense explosions. This is referred to as a supernova. The star that is composed only of neutrons that remains after this explosion is called a neutron star. Meanwhile, in stars with a core mass 3 times greater than the sun, the strong gravity causes the volume of the core to continually contract, ultimately forming a black hole in the core.
  1. Explain the fundamental reasons why stars evolve.
2. Explain the reason why stars with greater mass evolve with greater speed than stars with smaller mass.
3. In the sun that we observe, hydrogen is in the process of changing into helium in the center. When this nuclear fusion reaction is over, the core will contract while the outer area will expand. Explain the reason for this occurrence.
4. The phenomenon of helium flashes that occur in stars with a mass similar to the sun does not occur in stars with large mass. Explain the reason for this difference.
5. Jupiter’s mass is around 320 times larger than the mass of the earth. Explain why Jupiter failed to become a star like the sun.
6. Explain why stars in the red giant star stage, despite the fact that they do not undergo nuclear fusion reactions in their cores, have a much higher luminosity compared to stars in the main sequence.
7. There are two stars, star A and star B. The average molecular weight of the gas that composes A is larger than the average molecular weight of B, how would the surface temperature and luminosity of A compared to those of B and why? Explain using the ideal gas equation.
8. A hydrogen nuclear fusion reaction is occurring in the core of star located in the main sequence and having a mass similar to the sun. Use the ideal gas equation to explain how the star’s radius will change in the main sequence as it undergoes such a nuclear fusion reaction.
9. In a white dwarf star, the pressure of the substances that undergone nonrelativistic degeneracy is proportional to the density to the? 5/3 power. Based on this information, demonstrate that the radius of the white dwarf star is in inverse proportion to cube root of its mass.
10. There is a star with mass M and an object with mass m that is moving in a circular orbit around this star. Find velocity equation for the object with mass m to escape from this star. Also, based on this information, explain the meaning of the Schwarzschild's radius in a black hole.
Find the kinetic energy of a planetary nebula that makes the sun’s mass move at a velocity of? 40km/s.