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Old 17-02-2019, 01:16 AM
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ngcles
The Observologist

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Join Date: Dec 2006
Location: Billimari, NSW Central West
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Converting magnitudes per square arc minute to magnitudes per square arc second

Hi All,

This is the second addendum to my post above but I have placed it in a separate post for clarity. Read the first addendum at the bottom of my first comment first:

The conversion of surface brightness per arc minute to surface brightness magnitude per arc second so they are in the same units is more straightforward than you might think. There are 3600 square arc seconds per square arc minute. 2.5 * log (3600) = 8.8907.

So to convert (as a quite accurate approximation ) from one to the other, simply add 8.9 to any magnitude provided in arc minutes to get square arc seconds. This would provide an average S.B magnitude for M104 (The Sombrero Galaxy) of 20.5 magnitudes per arc second -- about 4.5 magnitudes higher than a perfect (in space) background of 25.0. Quite a contrast! For NGC 45 -- 23.6 quite a low contrast. How can the eye detect such faint light.

Well, you have to remember the brightness of one is superimposed over (on top of) the other. In theory even in a sunlit sky the very low surface brightness NGC 45 is still 1.4 magnitudes brighter than the daytime sky -- because its light is superimposed upon and added to the skies' luminance. But, the eye at such high brightness levels cannot detect the difference -- so it can't be detected. In modern parlance -- the sensor is flooded.

The same problem to a much lesser extent applies at night in the difference between a suburban sky and a rural one or better a premium site. The darker the native background + the larger the telescope (assuming good contrast elements in the 'scope), means it is easier for the eye to detect smaller differences between a very low surface brightness object and the native sky it is superimposed upon.

I hope that is some help for the reader.

Best,

L.
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