[Aavso-photometry] Red star transformations

[arne]

Michel Bonnardeau wrote:
> I wonder if it is worth transforming photometry measurements for red stars.
> The problem comes from the large color difference with the comparison star
> (which should not be red itself as most red stars are variable). Any
> error/uncertainty on the transformation coefficients translates into a huge
> error in the transformed magnitudes.
> 
> More precisely, the transformed I magnitude is computed from the measured
> v,i magnitudes as:
> I = i + TiTvi*[(v-i)-(Vc-Ic)]
> where Vc and Ic are the magnitudes of the comparison star and TiTvi the
> transformation coefficient.
> The term [(v-i)-(Vc-Ic)] is very large for a red star, so any error on TiTvi
> translates into a large error on I.
> 
> I have the problem with KU Her (Alert 351) for which I measure v-i=3.466 and
> the comparison 119 has Vc-Ic=0.878. I have a standard deviation on TiTvi of
> 0.073. This gives a wooping error on I...
> 
Intrinsically red stars are always a problem - look at the spectrum of
a Mira variable, and you will see all kinds of molecular bands and
very little continuum.  This means transformation depends on how those
sharp irregularities fall in the bandpass of your filter.

An additional problem is the large value of (V-Ic).  If you use Landolt
standards to calculate your coefficients, then you will find *very* few
that are this red, which means you are assuming the coefficient remains
linear outside of the range for which it was determined.  This is not
always the case, and for Ic in particular, you will often find nonlinear
terms.  I'm not going to get into that here.

The first point is whether transformation helps.  Say your coefficient
has a value of 0.100.  Then if the color difference between your two
stars is 2.588, as for the KU Her example here, by transforming you
will change your instrumental value by 0.1*2.588 or about 0.26 magnitudes.
So comparing your transformed values to someone else who may not be
transforming, you could easily see a zeropoint shift of many tenths of
a magnitude.  That is one reason why CCD measures of a long period variable
often show a similar scatter to that from visual observers, even though
the internal photometry is far more precise.  So point number 1: transformation
helps, especially for wide color ranges or for where your filter does not
match the standard system very well.

The second point is the standard deviation of your coefficient.  From
Sonoita, our calculation of transformation coefficients is only done
on good nights, and the typical scatter in the determination of, say,
the coefficient for (V-Ic), is on the order of 0.013.  So your error
of 0.073 is quite large, and is probably of the same order in size as
the coefficient itself.  I think you should look a little closer in
your coefficient determination to see if you can improve the result.
Otherwise, I agree that transformation for you is a problem since
you don't know your coefficient precisely enough for transformation
to help.
ARne