Surface Brightness of Faint Extended Objects

A Preface on Surface Brightness

Finding book references for Observing of faint extended objects such as galaxies is complicated by the fact that books generally list the visual magnitude, but a better indicator of whether or not a faint extended object might be seen is Surface Brightness (Sb). Even that is not the best indicator of how easy it will be to see as you will see. But at least read this brief explanation to gain some understanding of how Surface Brightness works.

Visual magnitude of a star has all the light concentrated to a singular point. Not so for extended objects. Extended Objects have varying sizes, some can be very large. Visual magnitude of an extended object would be the magnitude you would see IF you could compress all the light of the object to a size of 1 arcminute area, about the size of M57, the Ring nebula. Surface Brightness of an object and size together gives an indication of how spread out the light is and how faint it will really appear. An object that has a a Sb = 12.0 with a diameter of 10 arcminutes is going to be much easier to see than an object that has a Sb = 12.0, but has a diameter of 25 arcminutes.

The formulas we use to find what limiting magnitude an instrument might reach do not always tell us how well an instrument will perform on all types of objects, especially faint entended objects, which have a whole different set of requirements. While total light gathering (usually measured by limiting magnitude of stars) is important, to differentiate a low surface brightness object from the background sky takes good contrast.

If you have an object that is mag 8.0 visually (in a 1 arcmin area) and you spread the light out over an area of 10x10 arcminutes, or an area of 100 arcmin sq, then the Surface Brightness would drop by a factor of 100x from the visual magnitude. That equates to a drop of 5 magnitudes. Therefore it would have an average Sb of mag 13.0.

Likewise, if an object surface brightness is given as Sb 15.0 and its area is given as 17'x15' or 255 square arcmin, we can figure its visual magnitude for an area of 1 sq arcmin. What magnitude corresponds to 255x brighter? Well its easy enough to get to 250x brighter. 100x is 5 magnitudes and it's 2.51x for each magnitude, so 251x is almost exactly 6 magnitudes. So 255x the area would be close to 6.0 magnitudes difference. Of course, you could never condense the object to a size of 1 arcmin, so it's not as useful to calculate Mv. It's much more useful to have Mmv given and know how to calculate the fainter Sb.

edz

See these threads for discussions of Surface brightness
Does aperture rule in bino land?

Actually no it does not. Dark Skies Rule. Here's Why
An offsite paper by Bill Ferris explaining contrast threshold
Lowering the Threshold

Deep Sky Observing with 70 , 80 and 100mm Binocs

Tonight's objects with 25 x 100 IF Oberwerks

Rain Delayed Observing

An Explanation of Contrast Ratio by Bill Ferris

Surface Brightness (Sb)

Visual magnitude of a deep sky "extended" object is almost always NOT the appropriate measure of how faint the object will appear. Observing faint extended objects such as galaxies is complicated by the fact that books generally list the visual magnitude, but a better indicator of whether or not the object might be seen is Surface Brightness (Sb), and even that can vary due to being brighter towards the middle and fainter towards the edges.

For an object like M101 that has a visual magnitude of mag 7.7, but an area of diameter 26 arcminutes, that light is spread out over 530 square arcminutes. Hence is has a very low Sb = 14.7. That is averaged. As you get out towards the extremities of the object, it is fainter, in towards the center it is generally brighter. So for instance a galaxy with a bright core might be visible, but it would appear much smaller than its full size because you can see the core but not the extension.

M101 has some brightening towards the core, so the core area actually has a little brighter Sb than 14.7, while the extremities are fainter than the average Sb of 14.7. Another example is M33 in Tri, at Sb 14.0 it's fairly easy. This one also has a broad brighter core, so in these cases we generally see just the brighter core area and it's generally brighter than the average Sb that's listed.

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Occasionally, someone comes along and asks, "Why can't I see this galaxy, the book says it is mag 9, that should be easy enough?" The answer lies in the definition of Surface Brightness. Surface brightness will be referred to as Sb.

The criteria we use to determine the limiting magnitude (faintest stars seen) of an instrument do not always give a good indication how well an instrument will perform on all types of objects, especially faint entended objects. These have an entirely different set of requirements. Total light gathering (aperture) is important, but, to differentiate a very low surface brightness object from the background sky takes good contrast. Lower surface brightness objects have very little contrast with the background sky, hence can be very difficult to see.

The magnitude scale works like this. A difference of 5 magnitudes (from mag1 to mag6) is a difference of 100x light, brighter or fainter. Therefore, each magnitude is 100 to the 5 root from the next. That is, one magnitude is approx 2.51x brighter or fainter. So 1 mag difference is 2.51x, a 2 mag difference is 2.51 x 2.51, and so on.

For extended objects, (any object that produces an image larger than the Airy disk of the aperture), the visual magnitude Mv, is given as the magnitude the object would appear if all of the light from the object could be condensed into an area 1 square arcminute. Almost all extended objects have a size much larger than that. For the purposes of figuring Sb, each increase in area of the object by 100 to the 5th root (or 2.51x) will result in a decrease in the apparent brightness of the object by 1 magnitude.

Let's use an example of a DSO listed as visual mag 9. If the object size is 2.5'x2.5' then it has an area of 6.25 sq arcmin. The light would be spread over an area 6.25x greater than the compressed area used to determine the Mv value. It would actually appear 2.5x2.5, or 6.25x fainter than the visual magnitude. From above, we know a light difference of 6.25x is equal to 2 magnitudes, so the Sb of this object would be Sb = 9 + 2 = Sb mag 11.0. BUT what if the object size is 10'x10', then it has an area of 100 sq arcmin. The light would be spread over an area 100x greater than the compressed area used to determine the visual magnitude measurement. It would actually appear 100x fainter than the visual magnitude. A light difference of 100x is equal to 5 magnitudes, so the Sb of this object would be Sb = 9 + 5 = Sb mag 14.0.

The second concept that must be considered is brightness gradients. Look at the photos of almost any galaxy or globular cluster. Often the central core is much brighter than the outer fringes. Our 10x10 example object might appear with the central 50 sq arcmin at Sb 13.0 and the outer edges 50 sq arcmin at Sb 15.0, for an "average" of Sb 14.0. What we would see is the brighter central area. We may not see the outer fringes at all.

Some example galaxies as observed in 25x100:

Using 25x100 binoculars, I have observed several faint extended galaxies that have little to no brightening of the core (meaning the core was not significantly brighter than the spiral extensions). Many of the faintest Surface Brightness galaxies are face-on. Under mag 5.4-5.7 skies, in approximate order of difficulty, some I was able to see were:

M 33 in Tri has a visual magnitude (Mv) of mag 5.7 but it has Sb = 14.0. Its size is a very large 62'x39'. The area of this galaxy makes its Sb about 9x fainter than its Mv value. But it's actually fairly easy to see! Why? because it has a broad brighter core and wispy faint extensions, so we only see the brighter core.

NGC 3628 in Leo near M65/M66, at Sb 13.5 was pretty easy, more edge-on than face-on, it measures 4'x15' and has a bright core.

M 95 in Leo is 7'x5' and has Mv about 9.6. About fout magnitude fainter its Sb 13.6 was not as easy, but a small 3' core is brighter, so makes the center easier to see..

M 101 in UMa is Mv 7.7, but has Sb 14.6 and it is not very easy. Its size is 27'x26', but it shows only about 15' dia. with a slight brightening to the core. This means the 15 arcmin diam. that we see is brighter and the outer fringes are much fainter than Sb 14.6.

M 74 in Psc at Sb 14.4 is difficult, weakly brighter center, size is 10'x10', so visual magnitude is Mv=9.0, but this is no indication of how difficult this is to see.

NGC 6946 in Cyg (near Cepheus) has Mv 8.9, but it's size 11'x10', and the fact it has no brighter core at all makes it a very even lit and difficult to see Sb 13.8.

IC 342 in Cam at Sb 15.0, with little brightening in the core, broad face-on wispy galaxy, difficult even in the best conditions. It's 18'x17' means it's Mv is labeled about 6.25m brighter than its Sb. Whereas Sb=15.0, Mv = 8.75.

For me, IC342 has been one of the most difficult galaxies in all the sky for my small instruments. It has a surface brightness of mag 15.0. As a comparison M74 has a surface brightness of mag 14.4. NGC 2403 has a surface brightness of 13.9, about the same as M33, easier than M74 and much easier than IC 342.

What can you roughly predict from this. In NELM mag 5.4 skies, with 100mm objectives I can gather enough light that I can see faint extended objects with surface brightness 8.0 to 9.0 magnitudes fainter than NELM. Using this instrument under this sky I gather enough light to get enough contrast to see about 9.0 mag fainter than sky. That is the limit of contrast detection I can get.

Either a smaller aperture or a brighter sky may not allow that limit. So, as far as NELM goes, if mine were let's say 4.9, a half magnitude brighter, it would be likely I would lose sight of probably all but NGC 3628.

So, What happens to faint Low Surface Brightness Objects as we vary aperture and magnification?

OK, let's try increasing magnification to darken sky background and increase contrast. This works great on stars since it doesn't decrease the brightness of the stars but it does decrease the brightness of the background sky, which is an extended object, so you get to see fainter stars. However, with an extended object such as a faint face-on galaxy, the problem you will have with trying to darken a bright background sky by increasing magnification is that you have a very narrow range where that will produce a darker sky and yet still provide a large enough exit pupil or enough brightness to the eye to keep the image bright enough for the eye to see the very faint object.

If you increase magnification in hopes of darkening the sky background, you reduce exit pupil and you will also darken the extended light of the galaxy. If you increase the aperture too much without increasing magnification, you increase exit pupil and you will brighten the entire image, both object and sky background, and you may get a washed out image. However if you increase aperture AND increase magnification, maintaining constant exit pupil, you may improve the contrast detection of the faint extended object because you have gathered more light. Of course this will only work when sky is dark enough to permit at least reaching the lower magnitude limit of contrast detection.

So then, 'under brighter local light pollution, magnification increases in importance relative to aperture' would always be true for viewing stellar targets and is usually true also for very bright extended objects but is may not help at all for very faint, extended, low surface brightness objects.

On the other hand 'under darker skies, there is more gain from increasing aperture relative to magnification' is probably always true, at least up to the limit of the eye pupil. Exceptions to this would be very small extended objects that require increased magnification to increase image scale or to reach ODM, optimum detection magnification. (see Binoc Web Links - Mel Bartels).

How are you supposed to know what works? I guess the answer to that is go out and observe as many objects as you can in all kinds of conditions with as many different instruments as you can get your hands on. You'll find out what works.

edz