Professional astronomers, amateurs or anyone who has looked up in the nighttime sky has probably noticed the star Sirius. Located in the constellation Canis Major, Sirius is the brightest star visible on Earth, aside from the Sun. However, this does not mean that Sirius generates the most energy nor is the largest or hottest star. Compared to Earth's Sun, Sirius is only 1.7 times larger in radius. On the other hand, Rigel, a star in the Orion constellation, is nearly 80 times larger in radius than Earth's Sun but is only the 7th brightest star in the nighttime sky. How is one star so much smaller but able to shine so much brighter? The answer lies in perception.
The brightness of an object is the quality of the light that appears to shine from it and is influenced by the observer's distance to the object, For example, Sirius is only located 8.6 light years away from Earth while Rigel is quite a bit father at 863 light years away. Therefore, Rigel appears to be more dim because of the greater distance between the star and Earth. In order to accurately measure the amount of light from a star, scientists developed an equation that measures luminosity. Luminosity is the intrinsic or actual amount of light given off by an object. Specifically, luminosity in the total amount of electromagnetic energy released by a star per unit of time. Rigel's luminosity is 120,000 times brighter than the Sun while Sirius' luminosity is only about 25 times brighter than the Sun. Since Sirius is so much closer to Earth than Rigel, it appears much brighter even though it is smaller, cooler and produces less energy.
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The luminosity of a star has a direct correlation with its temperature. Many stars in the Milky Way use nuclear fusion to generate energy. Nuclear fusion occurs under intense pressure when the lighter nuclei of atoms combine to form heavier atoms. When this nuclear reaction occurs, energy is released, which in turn generates the temperature of the star. Earth's Sun has less luminosity than Sirius or Rigel. Which star would then have the greatest temperature? Earth's Sun has a surface temperature of about 6,000 Kelvin or over 10,000 degrees Fahrenheit. Sirius has a surface temperature of 9,940 Kelvin or about 17,000 degrees Fahrenheit. Astonishingly, Rigel's surface temperature is double that of the Sun's and has a temperature about 12,000 Kelvin or around 21,000 degrees Fahrenheit.
To calculate the luminosity of a star using brightness, astronomers use the formula:
| Symbol | Meaning |
|---|---|
| L | Luminosity |
| 3.14 | Pi, a mathematical constant for the ratio of a circle's circumference to its diameter |
| d | Distance, often measured in meters |
| b | Brightness, often measured in Watts per meter squared W/m2 |
Notice that in order to calculate luminosity with this method, brightness must be known. Even though the brightness of an object is based on perception of the object's distance, it still is a measurement that can be calculated. For example, light bulbs are measured in watts (W). A 40 watt (40W) light bulb generates 40 joules of energy every second. A 120W light bulb would generate 120 joules of energy every second.
The same equation for luminosity can be manipulated to calculate brightness (b). For example:
Brightness has units of watts over meters2 (distance), so the brightness of an object will decrease as distance increases. When two variables do the opposite of each other in a proportional way, it is known as an inverse relationship (brightness decreases while distance increases and vice versa). Therefore, the brightness of an object portrays an inverse relationship, specifically an inverse square law. Brightness is one example of an inverse square law, and it states that the brightness of a star will decrease inversely proportional to the distance away from Earth or wherever the observer is located. For instance, if a telescope orbiting Earth was observing Sirius and then was moved twice as far away from Sirius, the brightness of Sirius that it observed would decrease by a factor of 4, since 22 equals 4. This is even true if Sirius were to somehow move 5 times further away from Earth. Because 52 equals 25, the brightness of Sirius would decrease by a facor of 25.
Another way scientists can measure the luminosity of a star is by using a ratio of the sun's luminosity.
{eq}\ \displaystyle \frac{L}{Lsun} \ = ( \displaystyle \frac{d}{dsun} )^2 \ \displaystyle \frac{b}{bsun} \ {/eq}
The following explains each ratio in the above equation:
| {eq}\ \displaystyle \frac{L}{Lsun} \ {/eq} | The ratio of a star's luminosity to the Sun's luminosity |
| {eq}( \displaystyle \frac{d}{dsun} )^2 {/eq} | The ratio of the star's distance form Earth to the Sun's distance from Earth |
| {eq}\ \displaystyle \frac{b}{bsun} \ {/eq} | The ratio of the star's apparent brightness to the Sun's apparent brightness |
Another way to describe the brightness of a star is called apparent brightness. Apparent brightness of a star is known as apparent magnitude and is the measurement of the star's brightness when observed from Earth. Over 2,000 years ago, a Greek astronomer named Hipparchus observed the stars and developed a system based on the apparent brightness of them. His system places stars into different groups or magnitude classes. For example, Hipparchus placed the brightest stars he saw into the first magnitude class and the next brightest stars into the second magnitude class. He continued this classification until he was able to categorize all the stars he observed into six magnitude classes.
However, this magnitude class system is flawed today, since Hipparchus' classifications were based on the unaided eye. To modernize the system, astronomers were able to use technology to quantify the magnitude rather than place it in a class. For example, first magnitude class stars are around 2.512 times brighter than second magnitude class stars. Additionally, second magnitude class stars are 2.512 x 2.512 times brighter than third magnitude class stars. This trend continues up until the sixth magnitude class, which is 100 times less bright than class 1. However, scientists today have discovered many celestial bodies that fall outside of the original 6 classes. Some very bright objects, such as the Sun, have a negative number while very dim stars have magnitudes greater than 6.
Since the Sun is a very bright object in Earth's sky, the Sun has an apparent brightness or magnitude of -26.7. Below are examples of other celestial bodies and their apparent brightness as measured by the magnitude scale:
| Celestial Object | Apparent Magnitude |
|---|---|
| Sun | -26.7 |
| Sirius | -4.4 |
| Rigel | 0.12 |
Absolute brightness or absolute magnitude is the measurement of a star's brightness if it was 10 parsecs from Earth. A parsec is 3.26 light years away, so 10 parsecs is 32.6 light years away. If the Sun were to be observed 32.6 light years away, its absolute brightness would be 4.83. Notice the number is much larger than its apparent brightness of -26.7. Remember, the smaller the number, the brighter the object, and the larger the number, the dimmer the object. The table below shows the absolute magnitude of the same 3 objects:
| Celestial Object | Absolute Magnitude |
|---|---|
| Sun | 4.83 |
| Sirius | 1.4 |
| Rigel | -8.1 |
Since absolute magnitude places the star at the same distance from the observer, the true brightness or luminosity of different stars can be compared. Since Rigel has the lowest absolute magnitude, it has the greatest luminosity as compared to Sirius and Earth's Sun.
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Throughout the galaxy, billions of celestial bodies like stars can be observed. Suns or stars of other solar systems can use nuclear fusion to generate energy. The core of the Earth's Sun is under such intense pressure that a nuclear reaction occurs. The nuclei of hydrogen atoms combine to form helium. When this nuclear reaction occurs, energy and heat is released from the core and up to the surface. This release of energy can be measured in forms of brightness or also in luminosity. Brightness has units of watts, which is the amount of joules of energy released per second. The brightness of an object decreases inversely proportional to the square of the distance the object is away from the observer. This type of relationship is known as an inverse square law. For example, if a star were to move two times further away from Earth, its brightness would decrease by 4 times.
In order for scientists to more accurately measure a celestial body's actual brightness, they calculate luminosity. Luminosity does not depend on the star's distance from Earth and is the intrinsic or actual amount of brightness. Another way scientists can compare stars is by their apparent brightness and absolute brightness. Apparent brightness was first determined thousands of years ago, but the classification system was modernized to now futher quantify a star's brightness. The lower the number, the brighter the star. However, apparent brightness is still dependent on distance. Therefore, absolute brightness is the brightness of a star from a set distance (10 parsecs). If a star was to move closer or further from Earth, its absolute brightness would not change. Absolute brightness provides scientists a better way to compare and contrast the amount of light from a star.
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Some stars appear brighter than others just because they are closer to Earth rather than have greater energy. True brightness, or luminosity, is the actual amount of energy a star outputs, regardless of the distance it is observed from.
There are over a hundred billion stars in the Milky Way and billions of galaxies in the universe. However, so far the star with the highest observed luminosity is R136a1.
Luminosity is not the same as brightness. Brightness is the amount of watts per square meters. Brightness is based on the object's distance from the observer and can therefore change. Luminosity is the actual brightness of an object and does not change based on the observer's distance from the object.
In order to calculate luminosity, the mathematical constant "pi" (3.14) is used. The distance of the object from Earth in square meters is multiplied by the object's brightness in watts per square meters. That is then multiplied by 3.14 and then again by 4 to calculate luminosity.
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