[Aavso-photometry] V filter only - transforms possible?

[arne]

Michael Koppelman wrote:
> Yeah you are best off using your system in a manner which emphasizes its 
> strengths and minimizes its weaknesses. There is tons you can do with 
> untransformed differential photometry.
> 
> But let me hasten to add, you can play with this stuff, for fun, and do 
> whatever the hell you want. You will learn stuff if you try to transform 
> single bandpass observations. But like Dr. Newberry said, you won't be 
> improving them.
> 
My intent is to concentrate on observing techniques in 2009, in an effort
to get observers producing even higher scientific quality data.

I think there are three levels of calibration involved here:

1) V filter, untransformed
2) V filter, approximately transformed
3) two or more filters, properly transformed

The third possibility is always what you would *like* to have, but is
not always available.  You may not have a filter wheel, appropriate
filters, or may be running a time series in a single filter, or the
object may be too faint at B for your telescope.  So the
question is whether #2, where you approximately transform, is better
or worse than not transforming at all.  My working hypothesis is that
an approximate transform *is* better.  Note: *all* transformation
processing is approximate: you have an error associated with your
determination of the transformation coefficient; you have errors
in the photometry of your B and V measures, used to calculate the
instrumental color indices; you may or may not be including second
order extinction; etc.  What we are talking about here is all
relative.

An approximate transform is entirely appropriate if the variable does
not substantially change its color during its variability.  This includes
the small-amplitude red variables (SARVs) that John Percy works with;
cataclysmic variables during outburst; many non-radial pulsators, etc.
For stars that change brightness quickly, such as flickering CVs,
using non-simultaneous B and V measures can give *very* erroneous
colors, if the star fades/brightens between exposures.  Mean colors
are often the only solution.

For other variables, approximate transforms are appropriate to remove
most of the offsets between observers, especially if the transformation
error is included in the reported error.  The light curves improve;
many of the analysis projects, such as determining times of minimum
or maximum from light curves formed from observations from many
observers, have a lower light curve scatter and have improved results.
The point is that you are making a reasoned guess as to the correct
color of the object; it is not a random process.

Say that you are imaging a Mira variable, with (B-V) = 1.80 (this is
the approximate minimum magnitude color for RU Ari, for example). Your
comparison stars have (B-V) = 0.70 (also the case for RU Ari).  Then
the differential color between the comparison and target is 1.1 magnitudes.
If your V-band transformation coefficient (Tv) is +0.05 (not uncommon),
then applying transformation will adjust the reported magnitude by +0.055mag.
If the next observer has Tv = -0.05, then his/her magnitude would be
adjusted by -0.055mag.  Not applying any transformation means that the
light curve will have about 0.11mag scatter, just due to the difference
between the two instrumental systems.  Lack of transformation
is one of the major reasons why CCD photometry appears to have
so much scatter on the AAVSO program stars.

Now if the true (B-V) was 1.70 rather than 1.80, the error in using the
wrong color is 0.005magnitudes.  You've done most of the correction by
using approximate colors; the remainder is like a second-order correction.
The scatter in the light curve for these two observers caused by using
the wrong (B-V) color index is 0.01mag.

What have you gained?  First, the light curve appearance has been improved;
all of the observers have been corrected to first order.  You can see this
on all of the PEP light curves - multiple observers, but tight curves;
they use just the V filter and transform using mean colors.  Second,
for those stars that *do* change color through their cycle, if you apply
the mean color appropriate for the phase of the observation, most of
the systematic differences caused by the lack of transformation disappear.
Again, the light curve is improved.  It requires more information before
processing your data.

What have you lost?  If the color index you use is not appropriate for
the particular observation, you can end up correcting in the wrong way.
An example is a CV, which has (B-V) = 0.0 during outburst, but has
(B-V) = 0.60 during quiescence.  If you use 0.0 for the quiescent magnitude
transformation, you can make a substantial error as a result.  Approximate
transformation takes a highly precise differential measure and creates
an approximate result, but one that can be used to compare between
different observers.  Transformation is always approximate, whether or
not you think you have a better estimate (from multifilter photometry) for
the color of both target and comparison.

I recommend determining your transformation coefficient, and applying
approximate transformation if you do not have the ability to take
two-filter data.  In the "Notes" field, include (1) the transformation
coefficient you used, and (2) the color index you assumed for the variable.
These two pieces of information give the researcher the option of removing
your transformation and applying a different correction method if they
want to.  The "Mag Error" field should also change when transforming,
but that should be the subject of another email.
Arne