The apparent magnitude of an astronomical object is generally given as an integrated value - if a galaxy is quoted as having a magnitude of 12.5, it means we see the same total amount of light from the galaxy as we would from a star with magnitude 12.5. However, while the star is a point source, the galaxy may extend over several arcseconds or arcminutes. Therefore, the galaxy will be harder to see than the star. Quoting an object's surface brightness gives an indication of how easily observable it is.
Calculating surface brightness
Surface brightnesses are usually quoted in magnitudes per square arcsecond. Because the magnitude is logarithmic, calculating surface brightness cannot be done by simple division of magnitude by area. Instead, for a source with magnitude M extending over an area of A arcseconds, the surface brightness S is given by:
S = M + 2.5 log A
Surface brightness does not decrease with increasing object distance. For an object emitting a given amount of light, if it was twice as far away, half the amount of light would reach us, but it would also have only half the angular extent, resulting in the same surface brightness.
The concept of surfacebrightness is crucial for urban and suburban observing, and indeed, for deep-sky observing of all kinds.
The surfacebrightness of an object does not decrease with distance; like the total light output, it is an inherent property of the object, not dependent on the observer.
I have derived the peak surfacebrightness of these objects from his data for the brightness of the central arcminute.
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