Ⅴ. Stars


A fixed star (or star) is a mass of gases gathered together had having energy sources (nuclear fusion energy) that self-generate light and that maintains equilibrium of gravity and pressure (statics equilibrium) in space. Rather than identifying individually differentiated features of each star, we systematically categorize the stars according to criteria based on specific physical quantities. Physical quantities that can distinguish stars include the star’s age, magnitude, mass, radius, surface temperature, luminosity and chemical components, etc. and these physical quantities can be identified through observations and theoretical methods based on the observational data.

Magnitude and Color Index of Stars

When we actually look at the night skies, we observe that the colors of the light emitted by the numerous stars are various, and these differences in color are due to the fact that each star has a different temperature. Stars with a higher temperature on the surface will emit blue or white light and in opposite cases, the light is yellow or red. The criterion for categorizing the color of the star is defined by the magnitude (strength) of the light emitted from two wavebands and is referred to as the color index. This can be identified using a detector that reacts only in specific wavebands. The most commonly used color magnitude system is the UBV magnitude system, where U stands for ultraviolet rays, B for the blue color, and the V for the waveband in the range of visible light.

The strength of the light emitted from across the entirety of the star is referred to as luminosity. This expresses the strength of stellar light according to a system of magnitude, with the magnitude being smaller in value the brighter the light. For example, a star with a magnitude of 1 is 100 times brighter than a star of magnitude 6. The surface temperature, radius and luminosity of a star are correlated according to specific formulae, and this is referred to as the Stefan-Boltzmann Law.? The larger the radius of the star and the higher the temperature, the brighter the star’s luminosity. Stars are categorized according to the size of their radius into dwarf stars, giant stars, and supergiant stars.

Absolute magnitude expresses the star’s intrinsic property of luminosity, while the apparent magnitude expresses the star’s observed luminosity. In general, the brightness of the light darkens in inverse proportion to the square of the distance. Therefore, even when stars have the same luminosity, the star that is farther away will appear darker, and inversely, this phenomenon can be applied as a method for determining the distance to the star.

The Spectrum and Spectral Types of Stars

A star emits various lights ranging from very short wavelengths to very long wavelengths, and the spectrum encompasses the lights from these various wavebands. By analyzing these lights, we are able to identify the chemical components, namely the elements that constitute the star. As light passes through the surface of the star,? specific molecules, atoms and ions absorb the lights of particular wavelengths, and therefore the quantity of observed light will be significantly less in the wavelengths that correspond to the light that is thus absorbed. Using this principle where by spectral lines become apparent, we can deduce the chemical components of the star. Also, by measuring the degree of migrations in these lines, we can determine the relative speed of the star. Astronomers have used such spectral observations to learn that stars each have a specific spectral type (i.e. the form of the spectrum), and categorized the types into 7 stages, which are alphabetically expressed as OBAFGKM. Stars that are closer to the first stage of “O” are early types stars, and those closer to the last stage of “M” are late type stars.

The Hertzsprung-Russell Diagram (H-R Diagram)

Hertzsprung and Russell expressed the absolute magnitude of observed stars according to spectral type in a two dimensional diagram, and this is the Hertzsprung-Russell (H-R) Diagram well known to astronomers. Since the spectral type of the star and its color are closely correlated, the H-R diagram can also be expressed using the star’s color and magnitude. Based on the H-R diagram obtained by observing stars in the vicinity of the sun, astronomers have learned that there tend to be a greater number of late type stars and that the point where the star is located on the diagram forms a specific shape. Meanwhile, early type stars tended to be notably less in number. Here, the specific shape of the locations of stars on the H-R diagram is referred to as main sequence.

Star Populations

Stars can be categorized into two distinct populations. In astronomy, elements that are heavier than hydrogen and helium are collectively referred to as metals, and stars that have an abundance of metals and are young in age is categorized as Population I stars. By contrast, old stars with a deficiency in metals are referred to as Population II stars.

Star Clusters

Based on much observation, astronomers have determined that the majority of observed stars form a binary system or a? multiple star system, and a large number of stars compose a star cluster. A star cluster refers to a group of stars that have been created at nearly the same time period and exercise gravitational force on one another. Such clusters can be divided into two categories, namely open clusters where stars are gathered together but are dispersed without any specific form, and globular clusters where stars are gathered into a spherical form. If we assume that the distances to all stars within the cluster are the same, we are able to compose an H-R diagram using the color and apparent magnitude of each star within the cluster. Using the H-R diagram, it has been identified that in an open cluster, the majority of stars are young and bright, while by contrast in a globular cluster, the majority of stars are old and dark. Also, we use the term OB stellar association to refer to regions where, though the stars are not as densely gathered as in a star cluster, there is a concentration of stars with O and B spectral types. The stars that exist in the OB stellar association are very young astronomical objects that have been created a short period ago. By this observing, researching and understanding the observable stars, we gain the foundation for comprehending the structure and history of our galaxy.


  1. When the absolute magnitude is defined as the magnitude when the star is at a distance of 100 pc, give the equation expressing the mathematical relation between the absolute magnitude and the apparent magnitude.
  2. If we assume that the distance of the sun from the earth is 1 pc, how much greater will the apparent magnitude of this hypothetical sun be compared to the apparent magnitude of the actual sun
  3. Variable stars are stars that change in luminosity at specific time intervals. Assuming that the highest luminosity of a variable star is two times greater than its lowest luminosity, calculate the difference in magnitude.
  4. Calculate the combined magnitude of a binary system consisting of two stars with apparent magnitudes that are respectively 3.0 and 5.0.
  5. The V magnitude of the two stars A and B were observed to be 6.0, while the B magnitudes were respectively ?and . Which of these two stars are bluer in color? Which star has a higher surface temperature? Which star is closer to a late type star?
  6. An open cluster is a stellar cluster mainly consisting of Population I stars, while a globular cluster mainly consists of Population II stars. Based on the spectral type observation of the sun, it has been found that the sun has a strong spectral emission for ionized calcium. By contrast, stars in an open cluster with high metal content give almost no spectral line emissions for ionized calcium. Explain the reason for this difference.
  7. Two stars, one with spectral type O and one with spectral type M, both show a weak spectral line for hydrogen. Explain the reason for this weakness in each star.
  8. Explain why stars with larger mass are difficult to observe on the H-R diagram for globular clusters.
  9. When composing an H-R diagram of a star cluster, the region where the main sequence meets the area beyond the main sequence is referred to as the turn-off point. Given that a star located on the turn-off point is aged 10 billion years, determine the age of this globular cluster and explain the reasoning behind your calculation.
  10. Explain the conditions in which hydrogen exists within the OB stellar cluster.
  11. There are two stars located on the H-R diagram. If these two stars have the identical surface temperature, and star A has luminosity 100 times stronger than star B, what is the comparative length of the radius of star A in relation to the radius of star B