[Aavso-photometry] Color Index for Transform

[arne]

Massimiliano Martignoni wrote:
> Dear Friends,
> recently I started CCD photometry of variable stars using B V R I filters.
> I find the transformations coefficients (T) for each filter using the 
> AAVSO (Cohen) procedure, after I apply (T) to my instrumental magnitudes 
> using the well-known formula: M = m+T(CI).
> First and second order extintion are not important for my question and 
> are here omitted from the above formula.
> My problem is about the "right" Color Index to use.
> Are correct the following equations?
> 
> M(B)=m(B)+T(B-V)
> M(V)=m(V)+T(B-V)
> M(R)=m(R)+T(R-I)
> M(I)=m(I)+T(R-I)
> 
> Thank you very much in advance for any help!
> Sorry for my poor english...
> 
Hi Massimiliano,
First, congratulations for considering the use of transformation
coefficients.  I transform all of my data, and I will be promoting
transformation to all of the AAVSO observers during the next year.

These equations are simplified versions of the ones normally
used.  The normal equations include a zeropoint term plus
atmospheric extinction.  Normally, when performing differential
photometry, those two missing terms cancel out since two stars
in the same CCD image have the same zeropoint and nearly the same
atmospheric extinction.  So, let's assume that you know what you
are doing and are just choosing a color index for your transformation.

The normal guideline is that the color index you choose needs to
include the wavelength range of your filter.  This is to remove
as many systematics as possible - always interpolate, never
extrapolate.  Your chosen color indices will work; the ones
for B and V are pretty much standard. I prefer to use (V-Ic) as the
color index for Rc and Ic.  (V-Ic) has more change with star color
and so results in a better transformation.  For example, an A0 star
has (V-Ic) = (Rc-Ic) = 0.00.  However, for a G2 star, (B-V) is
about 0.63, while (Rc-Ic) is about 0.33, or half as large.  The
transformation coefficients determined using (V-Ic) are more
accurate since fitting something with wide range + error is
easier than fitting something with smaller range + same error.
(V-Ic) is also more sensitive to interstellar extinction.
Using (Rc-Ic) means you use Rc, a bandpass that has Halpha in it,
a very prominent line that can be in emission or absorption,
causing an error in transformation.  This is very obvious with
novae, where Halpha emission can dominate the continuum
in the Rc bandpass.

That being said, my use of (V-Ic) is a preference, not a rule.
(Rc-Ic) will work.
Arne