In various threads, we are told that magnitude is not meaningful for extended objects like galaxies or nebulae because the light is spread over the surface area in contrast to stars, which have essentially zero size.
That is absolutely untrue. On the contrary, magnitude remains the single best predictor of visibility. However, surface brightness also plays a critical role. To a very crude first approximation, you can think of it like this. In order to see an object, first of all the total brightness (magnitude) needs to be sufficiently bright. And in addition, the surface brightness needs to be sufficiently bright.
Total brightness (magnitude) relates primarily to aperture. Given two objects of identical surface brightness but different total brightness, you will need a bigger telescope to see the object that is fainter in terms of total brightness.
Surface brightness relates primarily to sky conditions. Given two objects of identical total brightness but different surface brightness, the one with brighter surface brightness will almost always be easier to see even under dark skies. But that advantage is magnified in the presence of artificial light pollution. And if the sky is sufficiently bright and the surface brightness sufficiently dim, you won't be able to see the object no matter how bright its total brightness is.
The classic example is the Milky Way. Its total brightness is quite a bit brighter than Venus. Yet it is invisible from most urban areas because its surface brightness is so much lower than the skyglow from artificial light sources.
For example, M101, the Pinwheel Galaxy, which I've not been able to see from my Bortle 5 yard but can see (dimly) from a Bortle 4 spot 8 miles away. Stellarium rates M101's surface brightness as 14.82 mag/arcmin^2 (magnitude 7.86). So maybe 15 is a limit for my 150 mm Newtonian. (Note that a bigger number refers to a higher magnitude, which is dimmer.)
M101 is tremendously bright in terms of total brightness, so aperture plays little role here. It is only a little bit easier to see through my 8-inch Dob than through my 70-mm refractor. A good rule of thumb is that an object that is 3 magnitudes dimmer than the skyglow will be visible.
Skyglow is usually expressed in magnitude per square arcsecond, which is equal to magnitude per square arcminute plus 8.9. So M101's nominal surface brightness in magnitude per square arcsecond is 22.9. That means that it should be visible in skies of 19.9 mpss or better. That corresponds to good suburban/bad rural in my part of the world.
This is an exceedingly crude guideline; there are numerous exceptions.
By contrast, M51 Whirlpool Galaxy rates 12.56 (magnitude 8.1). I can just see it at Bortle 5 while M81, Bode's Galaxy rates 13.13 (magnitude 6.94) but I can see it (plus its companion M82) better than M51.
There are two different things going on here. First of all, total brightness and surface brightness are not completely independent, as my initial introduction suggested. In this case the very large difference in total brightness outweighs the smaller difference in surface brightness.
More to the point, M81's nominally dim surface brightness is misleading. This galaxy's extended disk is indeed quite hard to see even under excellent conditions, but it has a very bright core, and the core is what catches your eye and makes the galaxy easier to see than the numbers suggest.
This subject is discussed at length in my Urban/Suburban Messier Guide. Note my suburban sites are somewhere between Bortle 5 and 6, yet I could see all the Messier objects with my 70-mm refractor. That illustrates what might be the most important factor of all: experience. With sufficent practice, I predict that you will have no trouble seeing any of the Messier objects from your yard.
Edited by Tony Flanders, 29 May 2020 - 07:25 AM.