EDIT: See the highlighted word “fainter” in the last para. I got it precisely backwards!
The Millennium Star Atlas is a magnificent work. Over a million stars, down to apparent magnitude 11, boasting accurate brightnesses, positions and other information off the Hipparchos satellite. Its also, unfortunately, out of print. But I have a copy…
One of the features of the atlas is that all stars on the atlas, that is, all stars apparent magnitude 11 or brighter, within 200 ly of the sun are marked with their distances, in ly. As it turns out, there are over 10,000 stars in the atlas so marked. Of course, there are many more stars than that within 200 ly, but many appear too faint to be included in the atlas. For example, Proxima Centauri, the nearest star to our sun is NOT included in the maps, although only 4.2 ly away it is a faint red dwarf of m = 11.13, so it doesn’t quite make the grade. In fact, of the 75 stellar objects within 5 parsecs (1 pc = 3.26 ly) of the Sun less than half are bright enough to show up on the atlas. Most are red or brown dwarfs, and some are as faint as m = 24.07. For comparison, our own sun appears to us at a dazzling m = -26.71. The full moon is about m = -12. The brightest star in the night sky is Sirius, at m = -1.43. Proxima orbits Alpha Centauri A, a star intrinsically about as bright as Sol, which appears to us as m = 0.01.
Of course, many of the plotted stars in the atlas are much brighter, and fall within the Atlas’ magnitude limits even though they are very far away. Like all star atlases with a strict magnitude cut-off, Millenium favors bright stars far away more than it does faint stars close up. Even to the naked eye, which can see all stars m = 6 or brighter, no red dwarfs are visible in the night sky even though they make up about 3/4 of all stars.
The apparent magnitude m of a star tells us how bright it appears from Earth. If we want to know how bright a star “really” is, we need to know its distance. This is called the Absolute Magnitude, M, which is how bright the star would appear if it could be magically moved to a standard distance of 10 pc, or 32.6 ly.
For the stars listed above, the Absolute Magnitudes M are
Proxima M = 15.56,
Sol M = 4.84,
Sirius M = 1.45,
Alpha Centauri A M = 4.38.
The magnitude-distance relation astronomers use is log (base 10) of distance in ly = 0.2(m-M) + 1.513435
The quantity (m-M) is called the distance modulus. It is useful in many different calculations.
Using this relation we can calculate that a star just barely within the m = 11 limit of the atlas 200 ly away must have an Absolute Magnitude M of about 7. Stars intrinsically fainter than this would just not make the grade unless they were correspondingly closer.
The ten thousand stars in the Atlas marked with their distances are roughly comparable in brightness to Sol, and form a complete list of those stars that lie within 200 ly. These are stars of SETI potential, Although this topic is being hotly debated now, I consider stars intrinsically fainter than M = 7 are not potential SETI targets. I, personally, do not think the faint red dwarfs are good places to look for intelligent life, although many authorities on the subject do not share that opinion. A sphere of 200 ly radius containing 10,000 potential candidates is our neighborhood. The galactic disk is about is about 2000 ly thick in this vicinity (Sol is located very close to the midline of the disk,) so this neighborhood is a very tiny volume of the entire galaxy. The boundary of the sphere does not even come close to poking above or below the galactic plane.
NOTE: The magnitude system astronomers use was inherited from the Ancient Greeks. It is cumbersome, but has some advantages, its intervals are based on ratios rather than differences, so it matches the behavior of the human eye, or photographic emulsions. It is a power law. Each magnitude is about 2.512 times brighter than the previous one, so that a 6th magnitude star is exactly 100 times FAINTER than a first magnitude star. Another way of saying this is the log of the light intensity ratio = 0.4 times the magnitude difference. The bigger the magnitude, the fainter the object. The 0.0 point of the magnitude scale has been arbitrarily set equal to the brightness of the star Alpha Lyrae, Vega, that is m = 0.0. Vega is not variable, so it can be used as a standard candle to calibrate photometric measurements.