I received the following excellent question from a reader today, and thought the question and answer made for nice blogging:
What are the factors that contribute to the brightness or dimness of stars? Is there a particular combination of these factors that makes Sirius the brightest?
This is a very good question. There are three main factors that contribute to the brightnesses of a star as seen from Earth: the temperature of the star, the diameter of the star, and its distance from the Earth. The temperature and diameter of the star depend mostly on the star's mass and where it is in its life cycle. For example, every star with as much matter as the sun will be just as hot and just as large as the sun for most of its life, but when it starts to run out of nuclear fuel, the star will swell up into a giant and cool off until it glows red (a so-called "red giant" star). Stars with more matter than the sun tend to have larger diameters and hotter temperatures, while stars less massive than the sun are smaller and cooler.
But, as I said, a star's distance is also important. The further away a star is, the fainter it appears. Sirius is not the closest star to the sun -- there are many closer stars, most of which are very low mass "red dwarf" stars, which are too faint to see without a telescope. But Sirius is about twice the mass of the sun, so it emits much more light (about 23 times more than the sun). So, even though Sirius is twice as far away as the sun's closest neighbor and near-twin, Alpha Centauri, Sirius appears four times brighter than Alpha Centauri in the sky. But Sirius is far from the hottest or most massive star in the Milky Way galaxy, so it is a combination of its higher mass and proximity to Earth that makes Sirius the brightest star in our sky.
To help avoid confusion, astronomers have developed two related but separate measures of how bright a star is. The first, the "apparent magnitude," is how bright a star appears as seen from Earth. The second, or "absolute magnitude," is how bright a star would appear if it were 36 light-years away from Earth. Absolute magnitudes allow us to compare how much energy a star puts out, which is more useful from the standpoint of understanding the physics at work in a star. Of course, we need to know a star's distance to determine the absolute magnitude, which is a trick in and of itself.