Visual magnitude, or apparent magnitude, is a good indicator of the visibility of an object when it is point or near point, such as a star or a very small galaxy less than one arc minute away.
For large objects, such as galaxies and nebulae, consideration should be given to surface brightness. For example, if a galaxy has a visual magnitude of 12, it means that we are receiving the same amount of light from that galaxy that a star of magnitude 12 would emit. A star is generally seen as a point source in the Most observations, while a galaxy can span several arc minutes, see more than a hundred. Thus, a large galaxy (seen from the earth) can be more difficult to perceive against the background of the night sky than a star of the same magnitude, especially the arms of this one which have a low luminosity. This difficulty is even more important in a sky of light pollution.
The surface brightness of an extended object is measured in magnitude per minute of arc squared (mag / arcmin2). It is more precise than the visual magnitude for this type of object. Some planetariums have this value (in mag / arcmin2), whose Stellarium. You can also consult the link following for a second reference. For example, the Triangle galaxy M33 has a visual magnitude of 5,72 and its surface brightness is 14,1 (according to data from Stellarium). The difference is really huge for this large galaxy seen from earth (68,7 x 41,6 arc minutes, more than 2,5 times larger than the Moon seen from earth). It is the surface brightness that should be retained for large objects with a continuous light spectrum (galaxies, star clusters and reflection nebulae) by ensuring that it is equal to or less than the limit magnitude estimated in astrophoto. according to the light pollution zone of the observation site.
We can also calculate the surface brightness of a deep sky object (in mag / arcmin2) using the following formula:
S = m + 2,5 * Log A
S = Surface gloss in mag / arcmin2
m = Visual magnitude or apparent magnitude
A = The area of the deep sky object in arc minutes2
For example, here is the calculation for the Triangle galaxy M33 mentioned above. The baseline data varies a bit from planetarium to planetarium. So here is the basic data from the software Skysafari (which does not provide information on the surface brightness of the deep sky object):
m = 5,79
A = the dimension of M33 is 62,1 per 36,7 arc minutes. So the surface of the object is 2279,07 arc minutes2
S = 5,79 + 2,5 * Log 2279,07
To find the Log of 2279,07, use a scientific calculator. The result is 3,3578.
S = 5,79 + 2,5 * 3,3578
S = 14,2 mag / arcmin2
The surface gloss shown in the Stellarium software is similar (14,1 mag / arcmin2) to that calculated from SkySafari software data above (14,2 mag / arcmin2). The other reference above (the second reference) indicates a surface gloss of 14,2 mag / arcmin2. Therefore, the surface gloss is roughly the same for the above three evaluation methods. There is therefore no longer any difficulty in knowing the surface gloss in mag / arcmin2 of a deep sky object. You only have to use one of the three references above.
Richard Beauregard
Sky Astro - CCD
Revised 2021/11/03
References :
https://fr.wikipedia.org/wiki/Brillance_de_surface
http://www.astrosurf.com/bsalque/cpselect1.txt : Shows the surface brightness of several deep sky objects.