Transformation Coefficients and M67.
A transformation coefficient generally tells how your instrumental value differs from the true value as a function of star color. This is usually a small correction; important if you need high accuracy but unimportant if your target and comparison stars are similar in color. Hendon, Arne, 26 July 2007.
Frankly, I generally do not apply transformation coefficients to my observations unless there is a specific request for a specific target, self compelling or if I am running alternating filters (usually V & I) doing a time series.
I am also not implying, herein, that M67 is the only or the best option for imaging as a Standards Field for your own computations. There are other suitable FOV’s.
I just finished up my annual computations from three nights of imaging M67 and thought I would share some information that might be of benefit for others. When I say annual, it is true that I try to do this every year, but in this year’s case they are the first for my recent replacement scope.
In past years I have used the chart and data (Arne’s) located at:
Awhile back, Arne uploaded some revised and expanded M67 data to the VSD so that we can obtain a Standard Field Chart of that data from the VSP:
Enter the coordinates: RA 08:51:24 + 11:45:00 and then select Yes, at the bottom of the VSP chart options, Would You Like A Standard Field Chart?
The field is quite crowded with photometry taking these standards as faint as ~ magnitude 16 and contains many duplicated values (which is OK for this purpose).
However, It can be a challenge, therefore, trying to use this Standard Field Chart, because of the crowding, and my first suggestion would be to reduce the number of standards by limiting the magnitude to say 13; but that still leaves a number of duplicates which almost requires that you plate solve your own images or, as an alternative, use Aladin (down load to your desktop) to help you identify specific comps:
I choose to instead use the older chart for identifying the VSP’s standard stars as it is quite visible with its original number system and makes it easy to locate the comps when you are analyzing the data; I of course used the updated BVRI data from Standards Sequence. Once you examine the first links data you will catch on to what I am describing.
Choosing which standard stars to use and how many is, from my perspective, a bit of an art form as much as it is science.
I have made it a habit through the years to zero point on the number 1 star in the original published data and then to subtract all the following instrumental magnitudes from the standard values. If I find differences greater than about .08 I simply do not use that standard star. The twenty stars that I ended up selecting this year had standard deviations of the Standard value vs the zero pointed instrumental value of between .015 & .023, depending upon the selected filter.
The other issue is mixing of color choices (B-V) that go into your selections. In my case the average B-V value was .634 with a median of .582. This average seems to fit well with my typical targets.
Here is the B-V data for each standard star that I choose.
So, as an FYI, I will share with you which specific 20 standard stars I used for my computations, with the first number being the matching star # from following link:
while the second data column is obviously the standard star AUID from the M67 Standards Field.
I am not suggesting that you use these specific standards or this many or few; Just a starting point for your own research if you choose to image M67 for TC computations.
For those of you who are curious or would like to compare your own TC’s (and please keep in mind that they will vary a lot from system to system) here are my BVRI computed values:
Tbv = 1.008
Tvr = 1.091
Tri = 0.965
Tv = -0.005
Tr = -0.049
If you compute TC’s for two or more filters the formula’s can be found in the Sarty paper:
Here is my data for the two cases where I may just use two filters:
V & I filter: Tvi = 1.020
B & I filter: Tb = 0.003
Computing the Transformation Coefficients
I just read this morning in anther forum post, that Arne wrote they have a volunteer writing a program for computing your transformation coefficients as other progress towards making the process more user friendly. That is great news for many observers:
In the meantime, however, I really like the Pricilla Benson paper as it lays out the whole process of how to generate your own transformation coefficients in a simple and straightforward manner and has enabled a lot of us to generate our own spread sheets for both the creation of the transformation coefficients as well as their application to observations.
There are other reference pdf’s that the AAVSO has available on this topic and here is another one:
Arne’s suggestions, to me, some years back, were, when following the Benson paper or any of the others, with similar suggestions, would be to:
1) Instead of plotting (R-r) vs (R-I) for Tr to instead plot (R-r) Vs (V-I)
2) Instead of plotting ((V-v) vs (V-R) for Tv to instead plot (V-v) vs (V-I)
V-cI has more change with star color and so results in a better transformation; V-Ic is also more sensitive to interstellar extinction; using Rc-Ic means you use Rc, a bandpass that has H alpha in it; which is a very prominent line that can be in emission or absorption causing an error in transformation, especially with novae, where H alpha emission can dominate the continuum in the Rc bandpass. Arne
I have continued to follow this advice.
I hope some of this information may prove to be useful for your own efforts.
Tim Crawford, CTX