About Surface Brightness
First published in the Bulletin of the Astronomical Society of South Australia
Astronomers use a brightness scale called magnitude to indicate how bright a star appears to the eye. The magnitude scale has been in use since the time of Hipparchus (about 130 BCE). The brightest stars were binned as “magnitude 1” with progressively fainter stars binned down in stages to naked eye limit at “magnitude 6”. After the invention of the telescope stars fainter than naked-eye limit were further scaled down beyond magnitude 6 to as faint as modern telescopes can detect at around magnitude 30! Put simply, a brighter magnitude was a smaller number than a fainter magnitude with a lager number. To make astronomical object listings more complete astronomers also determined magnitudes for non-stellar objects such as nebulae and clusters. When a deep sky object is given a “magnitude” it means that if its light were concentrated to a stellar point it would shine with the same brightness as a star of that same magnitude. This is known as its integrated magnitude. It would then seem reasonable to assume that deep sky objects with brighter magnitudes should consistently be easier to visually detect than those with fainter magnitudes. Yet even a novice soon discovers that many deep sky objects of the same magnitude do not always look the same brightness. Furthermore, sometimes an object of the same magnitude as another may not even be visible while the other still is! What’s happening here?
The discrepancy arises due to the varying sizes of deep sky objects in the sky. For stars, their light is always concentrated into a point so that there is a direct relationship between a star’s brightness and the magnitude scale. But deep sky objects vary in size so their light may be spread more or less over different size areas making them more or less visible for a given magnitude. Their visibility depends therefore on their surface brightness rather than their total brightness or integrated magnitude. You can see surface brightness in action when you aim a torch-light at a surface and move it inward then outwards. While the surface brightness of the circle of light dims as it enlarges and brightens when it contracts, the total amount of light remains constant.
Surface brightness of an object is measured as magnitude per square arc minute. For example the galaxy NGC 55 at magnitude 8 spreads its light over about 180 square arc minutes. This gives it a surface brightness of about magnitude 13 per square arc minute. The planetary nebula NGC 3132 in Vela is also at magnitude 8 but has its light concentrated into a much smaller area about 1.3 square arc minutes. This results in a surface brightness just under magnitude 8 per square arc minute — almost the same as its “stellar” magnitude. This makes NGC 3132 much easier visually detect than NGC 55.
Another example is the “Silver Coin Galaxy” NGC 253 in Sculptor at magnitude 7.6. The Silver Coin is easily picked up with pair of binoculars when near zenith whereas under the same circumstances the enigmatic galaxy Centaurus A at a much brighter magnitude 6.7 is somewhat more difficult. The reason again is surface brightness. NGC 253 has its light concentrated in 160 square arc minutes giving it a surface brightness of magnitude 12.7 per square arc minute, while the light of Centaurus A is thinly spread out over a much larger 550 square arc minutes giving it a surface brightness of magnitude 13.5 per square arc minute. No wonder the Silver Coin is easier to visually detect! Using surface brightness magnitude therefore is a more practical way to estimate the degree of visibility of extended deep sky objects than using integrated magnitude.
NGC 253 The “Silver Coin Galaxy” ( left) at magnitude 7.6 is paradoxically easier to visually
detect than the “brighter” Centaurus A right) at magnitude 6.7
Images: Paul Haese
Most deep sky objects however vary their light distribution across their surfaces and produce variations in visibility for a given surface brightness whereas listed surface brightness magnitudes are the average brightness across the object. Surface brightness is therefore an approximate guide to visibility. For example, galaxies with bright cores will be easier to visually detect than the same size and surface brightness galaxies with a more even light distribution. The Seyfert galaxy M77 in Cetus is a good example. Its 8.9 magnitudes is spread out to a surface brightness of 12.8 magnitude per square arcminute. But it has a bright nucleus that concentrates more of its light making it more star like and more easily visible.
While catalogues also give surface brightness for open star clusters too they are not often that useful. Stars in open clusters vary greatly in distribution, number and brightness of stars and the eye tends to focus on individual stars than the overall light distribution. IC 2602, the bright “Southern Pleiades” for example has a listed surface brightness of magnitude 11.6, hardly an indication of its true visibility! Here IC 2602 has several bright stars ranging from magnitude 2.7 to 5 spread over 7,800 square degrees — plenty of room to dilute its 1.9 magnitudes. Surface brightness is more useful for globular clusters and for open clusters if they are distant and begin to resemble nebulae.
Most planetarium software now include surface brightness magnitudes as well as the integrated magnitudes in their deep sky listings. Other listings such as those in the Bright Star Atlas 2000 (Tirion) provide only integrated magnitudes and object sizes in arc minutes. But these two factors will enable you to calculate surface brightness yourself (see side-box). Serious deep sky observers may use other criteria such as surface brightness per square arc second to determine visibility especially when using large apertures and high magnifications.
Armed with surface brightness listings I have found that with my Meade ETX90 (Maksutov 90mm), I can on a good night from my suburban backyard pick up deep sky objects to as faint as a surface brightness magnitude 13.5 per square arc minute. Of course this appears to fly in the face of the magnitude limit for a 90mm telescope (magnitude 11.0 for stars at my observing site). But then, when you are looking at an extended deep sky object in the eyepiece the eye is recording photons over a larger area of the retina and your amazing brain software is capable of integrating these hits to inform you that “there is something there”.
Calculating Surface Brightness
Get the magnitude and dimensions in arc minutes of the object from a catalogue. Calculate its area in square arc minutes
A=pi*r*r (where r is radius)
A=pi*(a/2*b/2) where a & b are the major and minor axes of the ellipse
A=a*b (where a & b are length and breadth).
Example: Omega Centauri mag 3.7 dimension 36’
A=3.142*17*17 = 907.9
SB= mag+2.5*log10(A) = 11.1
Surface brightness = mag 11.1 /sq arcmin