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Accidental Astrophysics: The Devil's In the Magnitudes, Part II  

Mercury, July/August 1998 Table of Contents

As a child I recall all those evenings spent outside and away from my house and its lights. At bedtime I would wander back, all the time noticing how lights at the house and barn would grow in intensity, their anti-darkness pouring over and enveloping the stars.

Light intensity, you see, is a strong function of distance. The closer you are to a source, the brighter, or more intense, that source appears. Nature has even codified this effect for us as the inverse-square law of light: The intensity of incident light-the amount of energy received by your eye or other detector per unit area per unit time-decreases as the square of the distance between you and the emitting source. Floating out around Jupiter (just imagine, okay?), you'd notice the Sun to be only 1/25 as bright as it appears from Earth; the mighty Jovian world is just a little more than five times farther from the Sun than Earth.

And any source of light, be it a porch light or a star 10000 lightyears away, is constrained by this dilution effect. Now, this makes things a little dicey when you start comparing stars. The star second to the Sun in brilliance is Sirius. It is simply impossible to ignore. And while Sirius is larger than Sol, the primary reason behind its brightness in our evening skies is that it's close to us.

Okay, different distances lead to different perceived brightnesses, but there is more. Stars have different intrinsic brightnesses. A 100 watt light on my porch dumps out the same energy per time as a 100 watt bulb on my neighbor's porch a kilometer away-her's just appears dimmer because it's farther away. But stars are not like identical bulbs: Their varied masses and evolutionary states result in a variety of intrinsic brightnesses.

Recall the magnitude system, passed down to us through a hundred generations of sky watchers, as a means of quantifying stellar brightness ("Accidental Astrophysics," May/June, p. 9). Bright stars have small, even negative, magnitudes; faint ones, larger. This system, as I have described it thus far, has a severe limitation, however. Magnitudes as we've discussed them are based on how bright the stars appear to us. Sirius has a magnitude of 1.46, Rigel, in neighboring Orion, shines at +0.14, but the mighty Sun dominates the sky with a magnitude of 26.72. With this limited information, we correctly conclude that the Sun is apparently the brightest of the three stars. Here's the problem, though: The Sun's intrinsic brightness is by far the lowest of the three! It is brightest to us because it is so near, but compared to Sirius and Rigel, it is truly dimmest.

What are we to do then to extricate ourselves from this confusing situation? Think of your favorite police drama, the setting a line-up room. Before a white wall stand six rough-looking chaps; a police officer tells them to stand with their backs to the wall. Why does the officer want them at the same distance from you? What, for goodness sakes, has this to do with stars? Having them at the same distance from you permits you to see differences between the individuals: The effect of distance, which might make a shorter person standing close to you appear taller, is removed. And this is what we do with stars. We put them in a line up, all at the same distance from us. Now we compare the stars based on their intrinsic brightnesses.

Apparent magnitude is how bright a star or quasar appears to us-what we measure on a CCD image or photographic plate or estimate with our eyes. As a measure of intrinsic brightness, we use absolute magnitude: As in the police line-up, we imagine moving stars or other objects 10 parsecs away ("back against the wall, #4!") and then measuring their brightness. The absolute magnitude is, therefore, the apparent magnitude of an object at a distance of 10 parsecs. Recall my examples Sirius, Rigel, and the Sun? Well, even though Rigel appears less bright than Sirius, its absolute magnitude is actually 6.8, while that of Sirius is only +1.4. And Rigel is more than 800 lightyears away! It is incredible. The Sun, however, is a meager star. Its apparent magnitude is an impressive 26.72, yet its absolute magnitude is only +4.8. Viewing Sol from that comparison distance of 10 pc, you'd see a star only slightly brighter than most of its neighbors stars.

Apparent magnitude is a relatively straightforward quantity to obtain. Getting an absolute magnitude is a battle, one that I'll discuss in future columns. But what we have so far is wonderful! Let's say we have a star's apparent magnitude, and, through strenuous means, we've obtained its absolute magnitude as well. What's the difference between these two numbers? Yes, it is a magnitude difference, but that difference is due to the distance between us and the star. Distance, yes! Magnitudes have led us to a means of determining distances in outer space.

JAMES C. WHITE II is the editor of Mercury and an associate professor in the Physics and Astronomy Department at Middle Tennessee State University. He admits that his old brightness scale of "dim," "bright, " and "it hurts," is too coarse for good astronomical research.


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