Data reduction methodology for V-I colors

[Richard Miles <rmiles.btee@btinternet.com>]

Tom et al.,

Am following TASS developments with interest.  It's a fascinating project.

One of the uses that I have found for the data is in helping to identify the
color indices of potential comparison stars for asteroid absolute
photometry: choosing comp stars which are fairly close in color to that of
the asteroid helps to minimize systematic bias in absolute photometry.

However, it occurred to me that TASS may not be making optimal use of some
of the data, in particular those pertaining to V-I color index.  The
thinking goes like this.  (Someone correct me if I have not got the
methodology right) :

The photometric reductions in V and I are performed separately.
The last step (step 8) of the data reduction pipeline is to calibrate the
magnitude of each star.
Each frame in each color is reduced against a subset of Tycho stars and a
zero-point for each frame is determined.

N.B. I have skated over the full details of how the reduction is achieved in
that I want to draw attention to the most pertinent aspects that I am
concerned about: the rest of the details can be found in "The TASS Mark IV
Engineering Run" note of 14th March 2004 at:
http://stupendous.rit.edu/tass/showtell/st0010.html

Now here's my concern.  To calculate V-I for each star and frame, the value
of I must be subtracted from the value of V.  However, each of these have a
contribution to their uncertainty contributed by the two independent
zero-point values determined for each of the frames.
Surely there is a much better methodology for arriving at a more accurate
V-I color index whereby the reduction (for V-I only) is carried out by
always working in terms of the differential instrumental magnitudes, v-i.
Qualitatively, changes in sky transparency have a significant effect on V
and I zero-points whereas the equivalent v-i values are relatively immune to
such changes if each pair of images are made simultaneously.  Therefore, why
not add an additional step in the pipeline to derive V-I for each star by
working entirely in color index space?

Personally, I would try using the V-I data for the Hipparcos stars in each
frame to arrive at a calibration of the v-i data.
I know about all of the concerns re. the provenance of the Hipparcos V-I
data (non-homogeneous dataset, etc.) but some cross-checks could be put in
to verify the data that are actually used in the calibration step.

I took a quick look at some Mark IV data to see if my concern might be
valid.
In particular I looked at 9 stars having 9.7<V<12.7, and 8.8<I<11.2 each
having between 76-257 measures.
The calculated mean error for the V data for each star ranged from
0.006-0.062 mag.
The actual standard deviation is of course significantly larger than the
formal error on each frame and for the V data the mean standard deviation
for the 9 stars ranged from 0.050-0.160 mag.  In the I band the
corresponding range was 0.036-0.177 mag.
Now coming to the V-I values, the mean standard deviation ranged from
0.046-0.152 mag.
If the V and I data are independent variables then on average the standard
deviation of each can be added in quadrature to arrive at an expected
standard deviation for the quantity V-I.  Doing this for the 9 stars and
comparing the result with the actual mean standard deviation in V-I for each
star showed that the actual uncertainty varied from 62-101% of the
theoretical, assuming the quantities are independent.  The observed range
appears to show that the two quantities do occasionally appear to be
independent of each other.

This result does appear to bear out my concern in that I am sure that more
precise values for V-I are achievable via a different data reduction
methdology.  I suggest that an alternative calibration route be examined for
deriving V-I color indices, one which is likely to benefit from the fact
that the V and I images are taken simultaneously.  At present no calibration
advantage is being derived from the contemporaneous nature of the image
pairs (or am I mistaken about this?)
It might even be possible to arrive at a more accurate estimate of the I
magnitudes themselves via this approach than by basing this on Tycho Vt and
Bt data as used at present.

Richard Miles
Golden Hill Observatory (MPC Code J77)