[Aavso-photometry] Differential vs. absolute magnitudes Aavso-photometry Digest, Vol 52, Issue 8

[Brad Walter]

Agreed. My answer was sloppy. You can't accurately get to the standard
system unless you transform, even using differential photometry, and you
have to transform the individual extinction adjusted raw magnitudes. If you
simply add the standardized magnitude for the comp star to the differential
magnitude of the untransformed star magnitudes, you get close if the colors
aren't too different, but you have not completely corrected to the standard
system. The first order extinction term and zero point term are lumped
together when you do this but it can't take care of color differences
between the Comp and Target stars. Of course, if you are calibrating your
comp(s) to a standard system by taking measurements of standard stars, then
you are doing all-sky photometry to do the calibration and you must
extinction correct and transform to avoid gross inaccuracy.

  

> -----Original Message-----
> From: Jeff Hopkins [mailto:phxjeff at hposoft.com] 
> Sent: Saturday, March 08, 2008 9:44 PM
> To: Brad Walter; aavso-photometry at mira.aavso.org
> Subject: Re: [Aavso-photometry] Aavso-photometry Digest, Vol 
> 52, Issue 8
> 
> Hi Brad,
> 
> Well.... almost.
> 
> As you correctly state absolute magnitude is the magnitude of 
> the star at a standard distance of 10 parsecs or 32.6 light 
> years. What I failed to mention is there are two magnitudes 
> for stars that are normally used, the absolute and the 
> apparent magnitude. The apparent magnitude of a star is its 
> magnitude as seen from Earth, but outside the Earth's 
> atmosphere. What we see on the surface has been attenuated by 
> the atmosphere. The least attenuation is at the zenith and 
> the most near the horizon. At the zenith the amount of 
> atmosphere is considered one air mass. The air mass increases 
> somewhat exponentially the closer you get to the horizon. 
> This is known as atmospheric extinction and it is different 
> at different wavelengths (greater at shorter wavelengths).  
> The apparent magnitude is also known as the standard 
> magnitude, but because variable stars vary, it gets a bit 
> fuzzy when referring to them. Star catalogs usually use the 
> variable's maximum brightness as the reference magnitude.
> 
> Here on Earth we measure a star's brightness and produce a 
> number representative of that. Typically for a CCD 
> measurement of the star-sky the total pixel ADU count may be 
> something like 300,000.  We then calculate a raw magnitude by 
> taking the log (base 10) of that number and multiplying it by 
> -2.5. For 300,000 ADUs that would be a raw magnitude of 
> -13.6928. Now we can do that for both the comparison star and 
> program star and take the difference to produce a 
> differential magnitude. This is what most CCD software does.
> 
> This differential magnitude has a problem right away and the 
> more different the stars colors (color index ... B-V) the 
> bigger the problem. This is where knowing your transformation 
> coefficients comes in. Ideally you do not work with the 
> differential magnitude at this point. Work with both star's 
> raw magnitudes. Transform them and yes account for the 
> extinction for best accuracy.
> 
> Now zero point are system dependent and not dependent on the 
> star or atmosphere. This is why they cancel when you take the 
> difference between the comparison and program stars (after 
> transforming and accounting for extinction). Zero points 
> account for the system's sensitivity. If you have a gain 
> factor at different settings you will have different zero 
> points, but it is best to always use the same gain for the 
> comparison and program star measurements. Also a 6" 
> telescope will produce a much lower raw magnitude than a 16" 
> telescope for the same star and air mass. The zero point 
> adjusts for that. Again, when you take the difference the 
> zero points cancel. The zero points only matter if you are 
> doing all-sky photometry.
> 
> Now to get the apparent or standard magnitude of the program 
> star you add or subtract (depending on how you determined the 
> differential
> magnitude) the standard (from a catalog) magnitude of the 
> comparison star to produce the apparent magnitude of the program star.
> 
> Make sense?
> 
> Jeff
>