In the May issue of Sky & Telescope, Fred Schaaf kindly mentions my “mostly astronomical” blog, so there may be some new astronomically-minded readers and I’d better provide something astronomical.
An idea is suggested by something Fred said in his February column, about Sirius: it is “a star so bright that you’d need to combine the light of the second, third, and fourth brightest stars of mid-northern latitudes – spring’s Arcturus, summer’s Vega, and winter’s Capella – to match its brilliance.”
What Fred is talking about is the actual quantity of visible light that comes to us from these stars. You’d have to pour the photons from Arcturus, Vega, and Capella into one bucket to match the bucket of light from Sirius.
This is not the same as “magnitude,” the term we customarily use to describe stars’ brightnesses. The magnitude scale is something we’re stuck with for historical reasons. It is logarithmic, like the Richter scale for earthquakes, but whereas the Richter scale goes up by jumps of 10 – a 4.0 earthquake is 10 times stronger than a 3.0 earthquake – the magnitude scale goes up by powers of about 2.5 (There’s a full explanation of this in our glossary book, Albedo to Zodiac.)
So there has to be a formula, a rather complicated one, to find what a difference of magnitude means in terms of actual luminosity, that is, quantity of light.
The magnitude of Sirius is -1.44, that of Arcturus is -0.05. So the difference of magnitude between them is 1.39. That works out to a difference in luminosity of 3.6. Sirius sends us 3.6 times as much light as Arcturus. Inversely, Arcturus sends us 0.278 as much light as Sirius – a bit more than a quarter.
Here is a diagram of the 24 brightest stars as square buckets of light. The two figures after each name are the star’s magnitude and its corresponding luminosity compared with Sirius. The area of the square is proportional to the luminosity, the amount of light reaching us from the star.
(The exact figures for the magnitudes may differ slightly in different catalogs. Astronomers are always re-measuring these things. I’ve colored the stars according to their spectral types, to make the diagram prettier. Actual star colors are much paler.)
Now, it appears that my information differs somewhat from Fred’s. It would take more than those three greatest stars of the northern hemisphere to equal the light of southerly Sirius. Their buckets add up to little more than three-quarters of Sirius’s.
To make a Sirius you might have to throw in a Rigel and a few “smaller” stars as well!