[Aavso-photometry] Correcting for differences in colour between comparison and program star during differential photometry

[Arne Henden]

On Jan 3, 2008 1:53 PM, Lionel Catalan <lcatalan at lakeheadu.ca> wrote:
> While doing differential photometry, I've noticed that the calculated
> magnitude of some check stars tends to drift slightly upward or downward
> with time as the air mass increases. This effect correlates well with the
> difference in colour (B-V) between the check star and the comparison star.
> Obviously, the program star must be also affected by changes in air mass
> when its colour is not exactly equal to that of the comparison star. I am
> wondering whether there is an accepted procedure to correct for this effect.
> It seems to me that in principle, one should be able to determine the
> parameters necessary for this correction by doing photometry on a standard
> field containing stars of different colours over a range of air masses.
> However, I haven't been able to find such a procedure clearly outlined
> either in the AAVSO ccd photometry manual or other resources available on
> the web. Does such a procedure exist? (please note that I'm not trying to do
> all sky photometry. I'm just trying to improve on my differential photometry
> results).
>
My old book does give the exact equations for differential
photometry, including transformation coefficients and extinction.
In general, you will have two effects: the first order extinction means
that the top of your CCD image will have different airmass and extinction
than the bottom.  For reasonable airmass and typical CCD field sizes
(say, airmass less than 3 and fields 20arcmin square), the effect is
quite small - a couple hundredths of a magnitude max.  However, it
is important under some circumstances and for some programs.

The second effect is appropriately called second order extinction, and
it comes about because the Johnson/Cousins filters are quite wide.
Since extinction is wavelength dependent (less in the red than in the
blue), as you approach the horizon, the redder parts of the filter
bandpass are less affected than the bluer parts, so the effective
bandpass shifts to the red.  Therefore, redder stars will become
brighter compared to their blue neighbors.

Both of these effects will show up as slow changes to the time
series photometry.  You can check to see if such a slow change
is intrinsic to a star or are airmass/extinction effects by plotting
the airmass on the same graph as the light curve, and seeing
if the slow change follows the airmass trend.

To answer your question: yes, I'd like to see everyone eventually
use all of the standard adjustments to their photometry: transformation,
extinction, proper aperture selection, ensemble photometry, etc.
We'll get there in stages, I think - not everyone will be able to
handle the extra complexity, not all CCD systems have the right
features to do the best job (for instance, no filter wheel).  But you
should try to do the best job you can with what you have, and
that takes some tutoring.
Arne