Calculation of apparent magnitude from apparent brightness

[AstroT]

I am a bit confused. The apparent magnitude of a star is given as m = -2.5*log10(F) where F is the apparent brightness of the star. In some textbook F is given as

F = (sum of E_xy) / (texp * A),

where E_xy is the number of counts in a given region around a star, texp is the exposure time and A is the telescope area.

Does that mean that AstroImageJ, for a given user-defined aperture for a given star, sums and obtains a total E_xy, then devides that number with (texp * A) (both quantities extracted from the FITS header) for each image? Assuming this is what is happening, what bothers me, is that once you do the above calculation, you end up with a number with unit: counts per time per area. Then we take the logarithm of a quantity with dimension which is not permissible. What am I missing here? What is the train of correct thoughts? Quite confusing.

[karenacollins]

AIJ is calculating apparent magnitudes of target ('T' labeled) stars from the apparent magnitudes of comparison ('C' labeled) stars that you look up from catalogs (e.g. SIMBAD) and enter into either Multi-Aperture or the Ref Star Panel. In other words, it is calculating the difference in apparent magnitude compared to the comp stars based on the difference in flux from the comp stars. This avoids needing to know anything about the telescope, detector, observing conditions, etc.

As a note, the catalog comp star apparent magnitudes should be in the same filter that is used for the observation.

Karen

[AstroT]

Thank you Karen. I think I got the idea behind differential photometry: ratios in fluxes give differences in magnitudes. But many textbooks introduce magnitude as m = -2.5*log10(F). Is F the summed ADUs (multiplied by the gain; I forgot that detail in my previous email) divided by (texp*A)? Then the unit of F would be electrons per second per squaremeter. However, is it permissible to take the logarithm of a dimensioned quantity? Taking the log. of a ratio of two F's provides a dimensionless quantity and then all is good.

[karenacollins]

I expect that the textbooks are referring to some ideal measurement of flux F. I think there are many things other than texp and telescope area that are related to the measurement, such has how much dust is on your telescope's mirrors and other optical path surfaces, any filters you are using, the quantum efficiency of your detector across all wavelengths, the airmass you are observing through, and probably many other things that don't come to mind right away. This is why we adopted the differential approach.

That said, I have limited experience observing for purposes of measuring apparent magnitude. We have many other experienced users on the message board, so I invite others to chime in to clarify or correct any of my assertions above, and/or elucidate how apparent magnitudes are measured in other tools.

Karen