Visual Magnitude, Surface Brightness and Skyglow

The brightness of individual stars and larger objects such as star clusters and galaxies can be measured in terms of visual magnitude or surface brightness (SB).

Although commonly regarded as a point of light, a star will appear as an airy disk due to diffraction. Most stars will only appear about 1 arcsecond in diameter or smaller.

As surface brightness is measured in magnitudes per square arcsecond and taking a star roughly of this apparent size, it will have a surface brightness about equal to its visual magnitude.

The surface brightness of a star's airy disk diminishes with fainter visual magnitude and the apparent radius of the airy disk shrinks as its edge surface brightness falls below the eye's threshold of light detection. That is why brighter stars appear bigger, fainter stars smaller.

If the magnitude and hence surface brightness of a star is significantly fainter than the skyglow, the star becomes undetectable. Stars considered naked eye (with visual magnitude < 6) begin to disappear under increasing light pollution or skyglow. In the city, you would be lucky to see magnitude 4 stars using the naked eye. If your scope can detect stars to magnitude 14 under dark skies, you might only get to magnitude 12 under bright skies.

For larger objects such as galaxies the visual magnitude is a measure of the total amount of light given off by the object as if it were a star. If this light is spread evenly over the surface of the object its surface brightness can be measured as so many magnitudes per square arc second. If a galaxy has a surface brightness of 22 magnitudes per square arcsecond, then each square arcsecond of its surface emits the same amount of light as a star of visual magnitude 22.

Skyglow can also be measured in terms of surface brightness (SB). A sky quality meter will give a value in terms of so many magnitudes per square arcsecond.

Diagram above is from my Unihedron Sky Quality Meter - SQM-L.

Some skyglow estimates for various locations:

17.0 poor city skies

18.0 better city skies

19.0 fair suburban skies

20.0 good suburban skies

21.0 typical rural skies

22.0 ideal dark-­sky site

An object will adds its own light to the skyglow but if it is very faint, it will blend into the skyglow and become invisible.

In darker skies, a larger telescope will pick up fainter objects than a smaller scope. However in bright skies, a larger scope will magnify the skyglow as well as the object being looked at. So the gain, if any,  will be substantially less.

Even at an ideal dark site, where there are no man-made contributions to skyglow, the sky still has a natural glow. Hence, the limit of 22. That is why there is a limit to the magnitude an Earth-based telescope can detect.

According to Tony Flanders, an object becomes undetectable when it is about 3 magnitudes fainter than the skyglow. Under a city skyglow of 17.0, Omega Centauri (SB 20.1) fades away. Under fair suburban skies, with a skyglow of 19.2, M83 (SB 22.0) becomes invisible.

For more on the above, download the pdf file below.