# Transforming Rc band data

Affiliation
American Association of Variable Star Observers (AAVSO)
Sun, 05/19/2013 - 19:07

I've been formatting my photometry spreadsheets to fully transform my differential B,V,Rc,Ic photometry onto the standard system. Using Gordon Sarty's useful paper, I was able to do this for B,V and Ic. I'm a little unsure about how to handle the Rc data. Some years ago, Arne recommended determining Tr vs. V-Ic instead of V-Rc. So when I calculated my Tr coefficient, I did it vs. V-Ic. In Gordon's paper, he shows examples of R mags transformed using Tvr or Tri, but not Tvi. How do I transform my Rc data using Tvi? Do I still need Tvr to first calculate the standard color or can I use Tvi for the Rc data? Thanks, Bob

Affiliation
American Association of Variable Star Observers (AAVSO)
>So when I calculated my Tr…

>So when I calculated my Tr coefficient, I did it vs. V-Ic

If you calculated a Tr coefficient using (V-I), then that coefficient is labeled "Tr_vi".  It can be used as follows:

Rs = rs + (Rc-rc) + Tr_vi * ((Vs-Is)-(Vc-Ic))

Where

'Rs' is the reference magnitude of the target (in R band)

'rs' is instrument magnitude of the target (in R band)

'Rc' is reference magnitude of comp star (in R band)

'rc' is instrument magnitude of comp star (in R band)

'Vs' is reference magnitude of target star (in V band)

'Is' is reference magnitude of target star (in I band)

'Vc' is reference magnitude of comp star (in V band)

'Ic' is reference magnitude of comp star (in I band)

Affiliation
Variable Stars South (VSS)
High order polynomial functions may be needed

Robert,

Have at look at Caldwell J.A.R. et al, SAAO (South African Astronomical Observatory) Circulars, No. 15, 1993.

The authors tabulate the coefficients for high order polynomial functions to transform photometric colours. An important point is that the functions differ for dwarfs and giants.

If my simple school maths are correct, I think your equation assumes that the functions describing such transforms are linear.

Roy

Affiliation
American Association of Variable Star Observers (AAVSO)

>I think your equation assumes that the functions describing such transforms are linear.

It is not my equation.  At least, I did not come up with it.  However, it is what is used by "Transform Applier" (TA), developed by George Silvis and a part of VPhot.  But since they use that equation, then I use it too, so as to generate results that conform to what others are producing.  Honestly, I have never seen anyone use transformation coefficients outside of linear transformations, at least not on AAVSO website.  That said, TA and other transform tools will invoke the functions inside a loop to iterate until the delta from the previous value to the current value is below some epsilon.  So a more complete pseudocode is as follows:

while (iter < max_iter)

{

orginal_Rs = Rs

Rs = rs + (Rc-rc) + Tr_vi * ((Vs-Is)-(Vc-Ic))

delta = fabs(orginal_Rs - Rs)

if (delta < epsilon) { break; }

iter++;

}

Affiliation
Variable Stars South (VSS)
Yes, I the usual plots for…

Yes, I the usual plots for determination of transformation coefficients are themselves linear. You wrote:

"How do I transform my Rc data using Tvi? Do I still need Tvr to first calculate the standard color or can I use Tvi for the Rc data?"

If I read this correctly, you wish to calculate Rc using Tr_vi, and V-I. If this calculation is to be accurate, my reasoning was that V-Rc and V-I should be related linearly. They are, for V-Rc values from just less than zero to about 0.8 (V-I values of just less than zero to about 1.5). However, the slope is different for V-Rc values from 0.8 to just less than 1.0 (V-I values from about 1.5 to 2).

Maybe my reasoning is not correct, or the V-Rc / V-I relationship is not important for what you wish to do. In either case I don't want take up your time needlessly.

Roy