Dr. Aaron Titus | Department of Physics, High Point University
PHY1050      Astronomy of Stars, Galaxies, and the Cosmos
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apparent brightness

Apparent brightness is how bright a star appears. There are two factors that determine how bright a star appears: (1) its energy output per second (i.e. luminosity) and (2) distance.

Imagine that I turn on a 100 watt light bulb and hold it in front of you. If I move the light bulb further from you, it will appear dimmer. Likewise, if I replace it with a 60 watt light bulb, it will appear dimmer. Thus, simply thinking conceptually about light bulbs, you can understand that both energy output and distance affect the apparent brightness of a star.

Apparent brightness is measured as energy of light received per unit area per second. For example, you could have a detector that is a square 1 cm by 1 cm with photosensitive material. By calibrating the detector, you could measure energy of light incident on the detector per second.

Astronomers use the magnitude scale to compare apparent brightness of stars. This scale dates to antiquity (Hipparchus, second century B.C.). The apparent magnitude of Vega is 0. Stars brighter than Vega have a negative apparent magnitude. Stars dimmer than Vega have a positive apparent magnitude.

The larger, or more positive, the apparent magnitude of a star, the dimmer it is. The smaller, or more negative, the apparent magnitude, the brigher it is.

For the reason just stated above, I like to think of the apparent magnitude scale as a "dimness" scale since large apparent magnitude indicates that a star is dim.

Apparent magnitude (which does not have units) is related to apparent brightness (measured as energy received per unit area per unit time), in the following way.

An addition of 1 in apparent magnitude is a decrease in apparent brightness by a factor of 2.512. A subtraction of 1 in apparent magnitude is an increase in apparent brightness by a factor of 2.512.

The previous sentence is a mathematical statement. It's difficult to understand if math is not your thing, so reread it and reread it until it's etched in your memory.

Let's illustrate this with a few examples.

Example 1

Rigel Kentaurus has an apparent magnitude of 0. Spica has an apparent magnitude of about 1. Since the apparent magnitude of Spica is larger than Rigel Kentaurus, then it is dimmer.

The difference in magnitude is the magnitude of Spica minus the magnitude of Rigel Kentaurus.

But a difference in magnitude of 1 is a factor of 2.512 in brightness. Because Spica is dimmer than Rigel Kentaurus, then

or we can say

In words, both of these equations simply say that Spica is 2.512 times dimmer than Rigel Kentaurus, or Rigel Kentaurus is 2.512 times brighter than Spica.

Example 2

If the difference in magnitude between stars is something like 2, then the brightness differs by a factor of 2.512 to the 2 power, or 2.512 x 2.512.

In other words, the difference between magnitudes corresponds to the number of factors of 2.512 that is the ratio of the brightness of the stars.

The table below should help you understand this more clearly. Suppose that Star A is a hypothetical star of brightness -1. If Star B had a brightness of zero, then Star A would be 2.512 times brighter than Star B.

If Star B had a brightness of 1, then the difference in magnitude is 1-(-1)=2, and Star A would be 2.5122 times brighter than Star B.

You can use the same reasoning to calculate the ratio of brightness for any two stars. The Table below should help.

If the
magnitude of
Star A is
And if the
magnitude of
Star B is
Then the difference
in magnitude is
And the
power of 2.512 is
And the ratio
of brightness is
So Star A is
brighter than
Star B by a
factor of ...
-1 0 1 1 2.5121=2.5 2.5
-1 1 2 2 2.5122=6.3 6.3
-1 2 3 3 2.5123=16 16
-1 3 4 4 2.5124=40 40
-1 4 5 5 2.5125=100 100






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