Creating a Star Scale of Magnitude

So astronomers have learned to be very careful when classifying stars according to apparent brightness. Classifying stars according to their magnitude seemed a good idea to Hipparchus (in the second century B.C.E.) when he came up with a 6-degree scale, ranging from 1, the brightest stars, to 6, those just barely visible. Unfortunately, this somewhat cumbersome and awkward system (higher magnitudes are fainter, and the brightest objects have negative magnitudes) has persisted to this day.
Hipparchus’ scale has been expanded and refined over the years. The intervals between magnitudes have been regularized, so that a difference of 1 in magnitude corresponds to a difference of about 2.5 in brightness. Thus, a magnitude 1 star is 2.5 ×2.5 ×2.5 ×2.5 ×2.5=100 times brighter than a magnitude 6 star. Because we are no longer limited to viewing the sky with our eyes, and larger apertures collect more light, magnitudes greater than (that is, fainter than) 6 appear on the scale. Objects brighter than the brightest stars may also be included, their magnitudes expressed as negative numbers. Thus the full moon has a magnitude of –12.5 and the sun, –26.8. In order to make more useful comparisons between stars at varying distances, astronomers differentiate between apparent magnitude and absolute magnitude, defining the latter, by convention, as an object’s apparent magnitude when it is at a distance of 10 parsecs from the observer. This convention cancels out distance as a factor in brightness and is therefore an intrinsic property of the star.

Luminosity Versus Apparent Brightness

Ask an astronomer this question, and she will respond that the flashlight, a few feet from your eyes, is apparently brighter than the distant headlights, but that the headlights are more luminous. Luminosity is the total energy radiated by a star each second. Luminosity is a quality intrinsic to the star; brightness may or may not be intrinsic. Absolute brightness is another name for luminosity, but apparent brightness is the fraction of energy emitted by a star that eventually strikes some surface or detection device (including our eyes). Apparent brightness varies with distance. The farther away an object is, the lower its apparent brightness.
Simply put, a very luminous star that is very far away from the earth can appear much fainter than a less luminous star that is much closer to the earth. Thus, although the Sun is the brightest star in the sky, it is not by any means the most luminous.

Do Stars Move?

The ancients believed that the stars were embedded in a distant spherical bowl and moved in unison, never changing their relative positions. We know now, of course, that the daily motion of the stars is due to the earth’s rotation. Yet the stars move, too; however, their great distance from us makes that movement difficult to perceive, except over long periods of time. A jet high in the sky, for example, can appear to be moving rather slowly, yet we know that it has to be moving fast just to stay aloft and its apparent slowness is a result of its distance. Astronomers think of stellar movement in three dimensions:

• The transverse component of motion is perpendicular to our line of sight—that is, movement
• across the sky. This motion can be measured directly.
• The radial component is stellar movement toward or away from us. This motion must be measured from a star’s spectrum.
• The actual motion of a star is calculated by combining the transverse and radial components.

The transverse component can be measured by carefully comparing photographs of a given piece of the sky taken at different times and measuring the angle of displacement of one star relative to background stars (in arcseconds).
This stellar movement is called proper motion. A star’s distance can be used to translate the angular proper motion thus measured into a transverse velocity in km/s. In our analogy: If you knew how far away that airplane in the sky was, you could turn its apparently slow movement into a true velocity.
Determining the radial component of a star’s motion involves an entirely different process. By studying the spectrum of the target star (which shows the light emitted and absorbed by a star at particular frequencies), astronomers can calculate the star’s approaching or receding velocity. Certain elements and molecules show up in a star’s spectrum as absorption lines (see Chapter 7). The frequencies of particular absorption lines are known if the source is at rest, but if the star is moving toward or away from us, the lines will get shifted. A fast-moving star will have its lines shifted more than a slow-moving one. This phenomenon, more familiar with sound waves, is known as the Doppler effect.
How fast do stars move? And what is the fixed background against which the movement can be measured? For a car, it’s easy enough to say that it’s moving at 45 miles per hour relative to the road. But there are no freeways in space. Stellar speeds can be given relative to the earth, relative to the sun, or relative to the center of the Milky Way. Astronomers always have to specify which reference frame they are using when they give a velocity. Stars in our neighborhood typically move at tens of kilometers per second relative to the sun.