The Mass-Luminosity Relationship
Luminosity
Proxima Centauri, the second closest star to Earth
In astronomy, luminosity is the brightness of a star, which is indicative of the total amount of radiation emitted by a star. The best indication of a star’s luminosity is a star's size and temperature. This can be measured using the star's absolute magnitude. This is the true brightness of the star. Many stars are very dim and are not easily seen. Stars are brighter if they are closer to Earth or very large in size. Apparent magnitude is the brightness of a star as it appears from the Earth. To people on Earth, the brightest star is the Sun because it is the closest star to Earth – a mere 150 million kilometers or 93 million miles away. The Sun is quite average in comparison to the other billions of stars. Its absolute magnitude, or true brightness, is lower than many other stars.
The second closest star to Earth is Proxima Centauri, which is 4.25 light-years away. You may remember that a light-year is the distance that light travels in one year, which is approximately 1.0x1015 meters. Proxima Centauri is extremely far away – around 4.25x1015 meters from Earth.
Because of its distance (relatively close to Earth),
it may seem like the Sun is the largest star in the sky,
but you know that there are stars much bigger
If all the stars stood the same distance away from Earth, the true brightness of the stars could be seen based on the intensity of the light they emit. Intensity is the measure of the light energy of a star. It is a measurable number. As you can imagine distance plays a huge factor in how you see the night sky. Just because something appears larger in the night sky, it does not mean that it is actually bigger. If spectral classes were based on the apparent magnitude, then you would assume that the Sun is the brightest star in the sky; however, you already know there are stars much bigger than the Sun.
Hipparchus, from The School of Athens by Raphael
The intensity of stars is specified with a magnitude system. Around 150 B.C., the astronomer Hipparchus devised the stellar classes. In total, he created six different stellar classes divided by brightness. By the 19th century, astronomers developed the technology to measure a star’s intensity. They set-up a magnitude scale to have an intensity of one hundred if two stars differ by a magnitude of five. If two different stars differ by only one magnitude, then the intensity ratio is the fifth root of one hundred or 2.512. This means that the light of one star is 2.512 times more intense. If they differ by two magnitudes, the intensity is 2.512 x 2.512, which equals 6.3 time more intense. If the differences are not simple like one or two, you will need to use the formula for intensity: the fifth root of one hundred to the power of the magnitude of one star minus the magnitude of the second star. Why did they develop this scale? Your eyes perceive equal ratios of intensity as equal intervals of brightness.
Say the magnitude of star A is 7.33 and the magnitude of star B is 1.01. What is the intensity ratio? The fifth root of one hundred equals 2.512. Next, find the difference between the magnitude of star A of 7.33 and the magnitude of star B of 1.01. The difference is 6.32. The intensity ratio, therefore, is 2.5126.32 , which equals 337. That means that the brighter star, star B, is 337 times more intense than star A. Remember, the smaller the magnitude number, the brighter the star. The diagram below represents some of the apparent magnitudes of common stars and objects.
Star Temperature
All stars generate energy through nuclear fusion. Fusion occurs when temperatures at a star’s core are high enough to literally fuse atoms together, creating new atoms of a higher atomic mass. For example, hydrogen fuses together to create helium, which is a process of star formation, along with condensation and gravitational compression of gas and dust. The more massive the star, the higher the temperature inside the star. Once formed, stars do not stay the same, and like a flame, they die out. A star’s mass influences how it evolves and how long it exists.
The temperature is directly connected to the color of the star. When you associate colors with temperatures, you may think of red as representing hot and blue as representing cold. With stars, though, the burning of their gases gives off specific colors. Cool burning gases are red in color and hot burning gases are blue. If you have ever seen a candle lit, it is relatively cool. It is reddish orange. If you have a gas stove or ever lit a butane burner, it is bluer in color because it is burning at a higher temperature; therefore, if a star is red in color it is a relatively cool star and a blue star is the hottest.
The Main Sequence Spectral Classes
Main sequence stars are starts that appear on a continuous and distinctive band when graphed based on their color and luminosity. You will learn more about this sequence of stars when you study the Hertzsprung-Russell (H-R) diagram. It is important to note that these stars are all in hydrostatic equilibrium, meaning that the thermal pressure produced in their cores is in balance with the force of gravity pushing in from their outward layers.
In astronomy, scientists divide main-sequence stars into spectral classes based on a number of characteristics. Spectral classes separate stars into the following classes: O, B, A, F, G K, and M. In this interactivity, click on each of the thumbnail images or the arrows in the lower right corner to learn the characteristics of each spectral class. Click the player to begin.
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The Mass-Luminosity Relationship Review
Now that you have studied the mass and luminosity of stars, check your knowledge in this non-graded activity. Read the directions associated with each question and provide the appropriate answer. Then, click SUBMIT to check your response. Click the player to get started.