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Calculating Apparent Magnitude

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scopegal
Calculating Apparent Magnitude

I have a few questions concerning the formulation of apparent magnitude for RR Lyrae variables.  I was examining the well known formula:

Mapparent = -2.5 * log(Flux / Flux of comparison star)

and my questions are, #1:  is the flux the instrumental magnitude?   #2:  Is the flux of the comparison star its instrumental magnitude?  #3:  given that two comparison stars are used to do the photometric process-the check and reference star-is the "comparison star" measurement an average of the instrumental magnitude of both of these or just the reference or check star?

Thank you so much for any help or direction that you can give.

-Melanie

spp
spp's picture
instrumental magnitudes and fluxes

Melanie,

For the equation you quote, I don’t understand what “Mapparent” means.  I’m used to seeing this equation written slightly differently.

mag1 - mag2  =  -2.5 log ( flux1 / flux2 )

Look at the text in the box on page 47 of the AAVSO CCD Photometry Guide.  Here mag1 and mag2 are the instrumental magnitudes for the target and the comp.  The equation converts the ratio of the fluxes to a difference in magnitude.

The instrumental magnitudes themselves are somewhat artificial since their values depends on an arbitrary choice of zero point.  We are doing differential photometry.  What we really want to know is how the ratio of the fluxes of the target and comp are expressed as a difference in magnitude on the standard magnitude scale.

We already know the standard magnitude of the comp star, and we measure the fluxes of target and comp when we process our image.  Using that equation we (actually our software) convert the flux ratio into a difference in magnitude.  Then it’s an easy step to calculating the magnitude of the target.

So what is the flux?

In our CCD photometry the flux is the rate at which photons from the star strike (and knock loose an electron) in the pixels which are eventually included in the measuring aperture.  

If we have done our image calibrations correctly, and the photometry software has removed the signal coming from the sky background, we can then sum the ADU’s (or electrons if we apply the gain) in all the pixels included in the measuring aperture.  This is the total signal coming from the star.  When this signal is divided by the exposure time in seconds, we have the flux.  In this case the flux is  ADU’s (or electrons) per measuring aperture per second. 

These fluxes for the target and comp will give a valid flux ratio as long as we use the same size measuring aperture  on stars in the same image.

I hope this answers your first two questions.

Q 3.  The comp star and reference star are the same thing.  The magnitude measurement of the target star vs the comp star is independent of the check star.  

The check star is also measured vs the comp star.  This is the standard method used to see if the comp star itself is varying during the observing run.  The magnitude difference between the comp and check stars should remain constant unless one of these stars is varying.

Phil

scopegal
RE:

Great, thank you Phil,

I have a follow up question,  how do I determine from MaximDL software what the difference is between the instrumental magnitude and the flux?

In MaximDL, I can complete the photometric measurement and it generates a report of the instrumental magnitude of my target star along with info like date, coordinates, etc.  How do I compute flux from instrumental magnitude?  Or is this already done and I am just not looking in the right place in the report?

Thanks again!

spp
spp's picture
more fluxes and instrumental magnitudes

I don't use MaximDL, so I can't be much help to you with that.  Maybe a MaximDL user can join the discussion. 

You don't need to compute (or even know) the fluxes involved.  The goal is to know the standard magnitude of the variable by knowing the *difference* in the instrumental magnitudes of the variable and the comp.

In the photometry software which I have used, the calculations of flux, and flux ratios, are done automatically and "out of sight" so to speak.  The photometry tool calculates an instrumental magnitude for the target and the comp (using the ratio of the fluxes) as a step toward measuring their difference in magnitude.  Since the standard magnitude of the comp is known, the standard magnitude of the variable star is just:

V = Δv + Cpublished

where V is the standard magnitude of the variable, Δv is the difference in instrumental magnitudes, and  Cpublished is the standard magnitude of the comp star.   Except for just a basic understanding of how the process of calculating the magnitudes is done in software we really have no "need to know" the fluxes involved.

Phil

scopegal
Oh my goodness, thank you so

Oh my goodness, thank you so much Phil!!!   You have solved a lot of problems for us by showing that formula, that is one that we had to find and it was causing us trouble as you can imagine!

Oh and the correct standard magnitude is the value in MaximDL that comes up just labeled "Magnitude" in their CSV report.  After we worked through the formula you gave above for V and delta-v we were able to verify the numbers we were seeing in that software's report.

Again THANK YOU!

-Melanie and Dave

spp
spp's picture
AAVSO resouces for new CCD variable star observers

https://www.aavso.org/ccd-photometry-guide

https://www.aavso.org/carolyn-hurless-online-institute-continuing-educat...

https://www.aavso.org/aavso-ccd-school-videos

The CCD Photometry Guide is the place to start.  It is written wth beginners in mind, and the basics are all there.  If you read that first it should keep you from going up some blind alleys.

The one month long CHOICE courses are the fastest way to get up to speed, but they require a fair amount of time and attention and may be a challange for people with jobs or young families.

Arne Henden no longer teaches his one week CCD School sad, but you can stream videos of his lectures and learn from the master at your own rate.

Phil

 

 

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