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Surface Brightness
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The concept of surface brightness is crucial for urban and suburban observing, and indeed, for deep-sky observing of all kinds. It is often a little hard for novice astronomers to grasp.

Let's start by imagining three terrestrial light sources: an incandescent light bulb with clear glass, a light bulb with frosted glass, and a fluorescent light, all three with identical light output. For the moment, let us ignore the fact that light is composed of different colors, so that the reddish light from an incandescent bulb appears quite different from the greenish light of a fluorescent light bulb.

If you consider the three light sources in terms of their illuminating power, all are identical, because they have the same total brightness. But if you look directly at the light sources, you are more likely to be aware of the surface brightness, or brightness per unit area. The bulb with clear glass allows you to see the glowing tungsten filament, which is painfully bright to look at even in a sunlit room. The bulb with frosted glass has the same filament, but you cannot see it directly; instead, the frosted glass spreads the light over the entire surface of the bulb, a much larger area. It is still painful to look directly at the bulb at night, when your eyes are somewhat dark-adapted, but in sunlight, the bulb appears bright but not painfully so. The fluorescent bulb spreads the same light over an even bigger area, making it appear only modestly bright even at night, and making it barely visible when it is in direct sunlight.

Now consider what happens when we move farther from these light bulbs. The total light output of the bulb, of course, remains the same. Astronomers call this an object's luminosity, inherent brightness, or absolute magnitude. The illuminating power of the bulb, however, decreases with the square of the distance. Astronomers call this an object's apparent brightness, apparent magnitude, integrated brightness, or simply its magnitude.

The surface brightness 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. When an object is twice as far away, it appears one quarter as bright; however, it also appears to be half as big, or one quarter the area, so the surface brightness, or brightness per unit area, remains the same.

A great deal of confusion ensues from the fact that amateur astronomers habitually fail to specify whether they mean integrated brightness or surface brightness when they say that an object is bright or faint. Consider, for instance, M33, the Triangulum Galaxy. At magnitude 5.7, it is fifth in integrated brightness of any galaxy in the sky, after our own Milky Way, the two Magellanic Clouds, and M31, the Andromeda Galaxy. Nonetheless, M33 is referred to as a faint galaxy, because its light is spread out over a huge area -- nearly a square degree -- giving it one of the lowest surface brightnesses of any Messier object. On the other hand, the planetary nebula M76 has one of the highest surface brightnesses of any nebulous Messier object, but it is often called faint because of its low integrated brightness. (For mathematicians, the term integrated brightness refers to the integral of the surface brightness over the object's area, which in the case of M76, is tiny.)

To make matters worse, amateur astronomers frequently use the term brightness to mean both integrated brightness and surface brightness in the same paragraph, and also often use it to denote the subjective impression of brightness, which depends both on surface brightness and on integrated brightness. Thus, the galaxy M33 and the globular cluster M13 have almost identical integrated brightness, but M13 appears much brighter both to the naked eye and through any optical instrument because its light is concentrated in a smaller area, i.e. because it has a higher surface brightness. But M13 also appears much brighter than the globular M28, which has almost identical surface brightness, because M13 is much bigger, and so has higher integrated brightness.

There are many different measures of surface brightness, such as candelas or lamberts. In this web site, I always express surface brightness as magnitudes per square arcsecond, a popular unit among professional astronomers. If one says that an object's surface brightness is 20 magnitudes per square arcsecond, that means that if you divide the object into squares measuring one arcsecond on a side, each square will (on average) emit as much light as a magnitude 20 star. As with stellar magnitudes, the higher the number, the lower the surface brightness.

Surface brightness is also a useful way to express natural and artificial sky glow. The following table gives a crude estimate of sky glow in magnitudes per square arcsecond for various different sites on a moonless night with good transparency:

17.0 poor urban skies
18.0 good urban skies, poor suburban skies
19.0 fairly good suburban skies
20.0 very good suburban skies
21.0 typical rural skies
22.0 ideal dark-sky site

For another data point, sky glow is about 18.0 magnitudes per square arcsecond at full Moon at an otherwise dark site with very clear air, and about 20.5 at the same site at half Moon (first or third quarter phase). Thus, at normal suburban sites, when the Moon is less than half full, its contribution to skyglow is small.

Brian Skiff of the Lowell Observatory in Arizona has studied sky glow extensively. Jerry Lodriguss has collected some of Brian's comments at his web site .

Just as with my example of a fluorescent light bulb in daylight, an astronomical object is difficult to detect when its surface brightness is significantly lower than the background skyglow. In such a case, the object will always appear somewhat brighter than the background, because its own light will be added to the skyglow. But if the combined light is only a few percent brighter than the background, it will not be detectable.

My own case of seeing M97, with surface brightness around 21.0, under urban skies with a surface brightness around 18.0 indicates that an object is detectable (barely) when its surface brightness is three magnitudes fainter than the sky glow. For another data point, in a private E-mail to me, Brian Skiff reports seeing objects roughly down to surface brightness 24.0 under 22.0 skies. In that case, presumably, only part of the problem is due to lack of contrast against the sky; the other part is due simply to faintness. There is some minimum surface brightness below which objects appear invisible to the human eye even against a perfectly dark background.

My guess is that the limit of detectability is reached when an object is about three magnitudes fainter than the skyglow, and then only when the object is reasonably large and has fairly sharp edges, like M97. It is much harder to detect an object which fades out gradually towards the edges, like M33. The human eye is good at detecting edges and boundaries, not subtle gradations. In any case, all other things being equal, the lower an object's surface brightness, the more it will be harmed by light pollution.

Tables of astronomical objects often list object's average surface brightness, but this statistic is flawed in a number of ways. No object has uniform surface brightness; the average gives little idea how the surface brightness is distributed across the object. Also, the average surface brightness depends critically on the object's size, but few astronomical objects have clearly defined boundaries. For galaxies and star clusters in particular, the size is more of a manmade convention than an intrinsic property. M31, the Andromeda Galaxy, is usually consider to be about 1 degree wide and 3 degrees long, but traces of the galaxy can be detected far beyond those boundaries. M31's size could defensibly be stated as 1.5 by 5 degrees, which would reduce the average surface brightness statistic by a full magnitude without any change to the object itself. Finally, for urban and suburban observers in particular, the surface brightness of most object's outer reaches is irrelevant, because only the central part will be visible.

Brian Rachford, for somewhat different purposes, has suggested that a better guide to an object's visibility is the brightness of the central section. He has computed this from publicly available data for many galaxies and globular clusters, as explained at his web site. I have derived the peak surface brightness of these objects from his data for the brightness of the central arcminute. I have found this to be an excellent guide to an object's visibility under light pollution, assuming sufficiently large aperture to render the object visible at all. Note that I could have derived considerably higher brightnesses (about 0.5 mag on average) by using his figures for the central 30 arcseconds, and without a doubt, I could have derived higher values still by using a smaller circle, especially in the case of the numerous galaxies, like M31 and our own Milky Way, which have extremely bright and compact nuclei. Technically, my figure actually gives the surface brightness of the brightest arcminute circle, not the true peak surface brightness.

I have also made some wild guesses about the peak surface brightness of the four planetary nebulae among the Messier objects. Two of those (M57 and M97) are very nearly uniform in brightness, so that the average surface brightness is close to the peak surface brightness. The other two (M27 and M76) have small, fairly uniform bright sections embedded inside a large more diffuse glow. For those objects, I estimated the size of the bright section and used that to compute the peak surface brightness, assuming that the bright section contains almost all of the total brightness. My results are listed below.

ObjectMagSizePBrt
M277.43.7x2.318.4
M578.81.2x1.017.6
M7610.11.3x0.718.6
M979.93.3x3.321.1

It is interesting to note that this gives M97 the lowest peak surface brightness of any Messier object, by a fair margin, but M97 is in fact easier to see under moderate light pollution than galaxies with much higher peak surface brightness. I believe that this is because M97, at over 3 arcminutes, is much bigger than the bright section of most galaxies, and it also has a very well-defined edge.