Tuesday, May 22, 2012

Taking Star Magnitudes

I figure some of you are interested in how to take the magnitude of a star, so I'll explain it here. 

The magnitude of a star is essentially its brightness in a specific wavelength range, or band.  When the system for deciding on the brightness of stars was made up, when there were no sophisticated light-measuring tools, people had to eyeball it.  They came up with a ranking system of magnitudes, where the brightest star is a 1, and dimmer stars are labled 2, 3, 4....  The system has become more sophisticated and accurate, but it has still kept this numbering system.

To find the magnitude of a star in a specific band you need 2 stars, one that you want to find the magnitude (target) of and one nearby whose magnitude you already know (comparison or standard).  We do this because the atmosphere causes the brightness of a star to appear to fluctate (aka twinkle), but stars nearby each other tend to twinkle at about the same times.  So if one gets brighter, so does the other and vice versa.  Then you use a telescope to take a picture of the stars.  You can get a lot of information from this, but we only need two things: the net counts and the exposure time. 

The net counts represents the number of photons from the star which hit your telescope, and the exposure time is how long your telescope stares at the star.  Then, you need to find the counts per second (aka flux).  Divide the counts by the exposure time to get the flux.

Once you have all of this, you can find the magnitude of the star using this equation:

m1-m2=-2.5*log(f1/f2)

Where:
m1 is the magnitude of star 1 (doesn't matter which, just be consistent)
m2 is the magnitude of star 2
f1 is the flux of star 1
f2 is the flux of star 2

You can re-arrange this equation by moving the magnitude of the standard star to the other side.  Then you have everything  you need to find the magnitude of your target.

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