V magnitude: the magnitude of V from the B-V transform or from the V-I transform

Hi Tim,

This is a good question, of course. Transformation error is part of your total error budget, which might include things like your measurement errors for comp and target in the various filters, the error in your transformation coefficients, calibration errors, etc.  In your case, it looks like the difference between the two transforms is smaller than the measurement error, so which transformed magnitude you choose is not that important.  If I felt like the extra work, I might average the two values before reporting, and then indicate in the notes section what I did.

Now, more detail   Transformation works best when the object being transformed is a black body, smoothly changing at every wavelength.  In the real world, stars have emission and absorption features, and the stars you used to determine your transformation coefficients might have looked somewhat different.  In addition, your (B-V) transform might have coefficients with smaller error than your (V-Ic) coefficients, or may be defined over a smaller or larger color range (transforming stars outside of the color range of your standards is risky).  For a very red star, B might be difficult to obtain with long exposures, while Ic takes seconds, so you might be using V and (V-Ic) and not observing at B at all.

In your case, the NSV 18582 transformation is nearly identical between the two color indices, and probably irrelevant which one you choose to report, especially since the transformation error is smaller than the measurement error for your target star.  It is listed in VSX has K0 spectral type.  TW Hya has a 0.01mag difference between transformations, with spectral type K7.  A 0.01mag transformation difference is probably not important, and might represent a difference in the uncertainty of your B-band observations in comparison with your I-band observations of the target and comp star, and/or a difference in the transformation coefficient errors.

For very red stars like Mira variables, transformation gets difficult because of the large deviation of the spectrum from a black body.  You have lots of molecular features in the red wavelengths like Ic and fewer in the blue wavelengths like B.  This is one of the reasons that (B-V) for a Mira might be a number like 2, while (V-Ic) could be 5.  So any transformation has a lot of uncertainty.  Likewise, transforming emission-line stars like novae, which make the spectrum decidedly non-blackbody, will yield some pretty weird results.

Just do the best that you can!

Arne