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.

Where's the Problem?

I still can't figure out what's wrong.  I think I must have made a mistake on some of the more basic magnitude equations.  My CCD transformations are definitely right, so the problem must be deeper.  The spreadsheets I make to do these equations are a little confusing.  I probably told the computer to look in the wrong box for a number.  Now I just have to find that number.

What is Wrong!

I've been going through my data and I can't figure out what I'm doing wrong.  The most likely answer was that I did my CCD transformation equations (the ones where I accounted for differing equipment) wrong, but I keep going over and over that and it's not working.  Historically, the U band pictures I've gotten haven't always been the best, but I've never had trouble with the B band.  Most likely, the problem is with the B band, because I need the information from that for the CCD equations for the U band.  If the B is wrong then the U is definitely wrong.  But where did I go wrong!?

Sort of Right?

So the equations J.D. gave me to correct for the different equipment have almost worked.  On green pictures (V band), red pictures (R band), and infrared pictures (I band), they work perfectly.  But the blue pictures (B band) and the ultraviolet pictures (U band) they're completely off.  I need to know why, or any temperature measurements I take in the future could be unusable.  I'm going to have to spend a few hours going over it again and again until I figure it out.

Still not Working

So my numbers are still off, by a lot.  I haven't been able to figure it out, but J.D. thinks that it might be that we used different equipment than the people who took the original measurements.  Our equipment might be just a little more or less sensitive in some color bands.  He's given me some equations to figure out which should correct for that.

Inaccuracies in My Measurements

I've been taking measurements, and the numbers I'm getting are wierd.  I'm taking magnitudes for stars whose magnitudes are already known, and the numbers I'm getting don't line up with the data we already have.  I've got another set of data to work with, so hopefully the numbers I get for that set will be right.  If not, there must be something wrong.

What I've Been Doing

Lately, I've been practicing taking the magnitude of stars in different color bands.  I'll be taking the temperatures of stars later, but for now, I need to get good at finding the magnitudes.  I'll be able to do this because the color a star glows is determined by its temperature.  So by finding its color, I can find its temperature.