[Aavso-photometry] Aavso-photometry Digest, Vol 52, Issue 8

[Jeff Hopkins]

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

At 18:32 -0700 03/08/2008, Brad Walter wrote:
>  I think there is confusion between differential vs. absolute photometry and
>absolute magnitude.
>
>Absolute magnitude (often shorthanded as M or Mag) is the magnitude of a
>star at 10 parsecs.
>
>Absolute photometry is a photometric magnitude converted to a standard
>system. Differential magnitude is simply the magnitude difference between
>measured values of a comparison star and a target star.
>(instrumentalTarget-instrumentalComp), normally with both stars in the same
>FOV of your CCD so that the images of the two stars are at the same airmass.
>If you have the magnitude of the comp star determined in a standard system
>(transformed), you can convert your differential magnitude into an absolute
>magnitude by adding the transformed magnitude of the comp star to the
>differential magnitude. This gives you a magnitude determined by absolute
>photometry. However, if you only do the process in this simplest form, you
>will have inaccuracy in your measurement. First you have introduced
>inaccuracy due to any color difference between the stars. To eliminate that
>error, you should correct your measurements for second order extinction.
>First order extinction is taken care of because your comp(s) and target are
>in the same FOV (and for amateurs this almost always assures they are << 1
>degree apart) so they have the same airmass. The second inaccuracy is that
>the differential magnitude hasn't been transformed. To improve accuracy you
>would apply the transformation coefficients you established for your
>telescope-filter-camera combination, after extinction correction, to your
>comp and target magnitudes. Then calculate Target - comp and then add the
>"standardized" magnitude you have for the comp in the filter you are using
>(e.g. V). Adding back the "standardized" magnitude of the comp star adds in
>the Zero Point. If you don't have a standardized magnitude for your comp
>star then you have to measure the zero point for your evening by measuring
>several standard stars (say 10) near the meridian. Correct those
>measurements for extinction and transform them. Then average the differences
>you get between your transformed values for the standard stars and their
>standard values to give you your zero points. Then Target-Comp + Comp + zero
>point (where the Target and Comp magnitudes have been transformed) gives you
>a magnitude for your target star using absolute photometry. It does not give
>you the absolute magnitude of the star.

-- 
Jeff Hopkins
HPO SOFT
Counting Photons
http://www.hposoft.com/Astro/astro.html
Hopkins Phoenix Observatory
7812 West Clayton Drive
Phoenix, Arizona 85033-2439 U.S.A.
(623)849-5889
(623) 247-1190 (Fax)
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