For some time I have been looking at results from the pipeline that look like Figure 1. Here the V and I data are plotted on an integer day format. I simply strip off the whole numbers when I plot, and gnuplot fits what is left to the graph. This folds the data on a day by day basis. The star is at RA 303.4174 Dec. 6.9188.
Figure 1. A mag vs time plot for the star at RA 303.4174 Dec
+6.9188. There are 140 data points from 48 frame exposures on 3 different
nights. The integer JD has been removed and the x axis is the fractional
day. The y axis is magnitude. Green is V and red is I magnitude.
There were 140 observations taken of this star on 3 different nights. JD2452458, 2452461, and 2452487. As can be seen from Figure 1, all the V data lines up within the expected error for the three nights. For the I data, two of the evenings line up and the third differs by about 0.3 mag. Why? Is this star variable? I doubt it. There are many stars with plots like this. This makes searching for variable stars with the Welch-Stetson statistic difficult since so many "variables" are flagged. Still, they are only a few percent of all the stars. Most stars with data taken on several nights line up very well. For example, Figure 2. is a star with similar V magnitude. For this star both V and I magnitudes line up for the 3 days within the expected error though the I does not line up as well as the V. Note that there is a difference in y scale from Figure 1.
Figure 2. Data as for Figure 1. for a more common star plot.
Using the pipeline result of all the data taken in July of 2002, we can plot Mag vs Mag Sigma for the V data as Figure 3, and the I data as Figure 4. For these plots, all the flagged data was deleted, as well as all mag measurements over 16 and stars with fewer than 10 measurements. This data is derived using the bigrefcat.dat that Michael Richmond supplied after there were problems fitting stars using the previous version of the refcat. This catalog includes roughly 1.6 million stars with typically 50 comparison stars available per square degree. Looking at Figure 3, the distribution is fairly broad. If we compare it to data taken on a single frame, the distribution is much narrower. Figure 5 is the V camera Mag vs Mag Sigma plot of a 48 field run taken of a dense field to get enough stars to make a good plot. Figure 6 is the I plot for the same data. Something is broadening the plots for data taken over multiple nights. Note that there is something else going on at the bright end of the distributions.
Figure 3. V Mag vs log V Mag sigma for the 747,191 measurements of 32,028
stars from the July 2002 data. Flagged stars were deleted as well as
stars with less than 10 measurements.
Figure 4. I Mag vs log I Mag sigma for the July data.
Figure 5. V Mag vs V Mag sigma for the 46,484 measurement of 1,876 stars
for a single 48 frame run following a star field. Flagged stars were
deleted as well as stars with less than 10 measurements.
Figure 6. I Mag vs I Mag sigma for the data of Figure 5.
We note that V-I for Figure 1 is near 2. This is a pretty red star. For the star of Figure 2, V-I is near 1 and the fit is better for the successive days. This is a general trend but I hesitate to claim that it is significant. I have looked at a lot of examples but have not made a statistical tabulation.
I speculate that the refcat catalog is part of the problem of obtaining precision measurements. Generating I magnitudes from B and V data seems difficult. Further, the redder the star the further the peak of the spectrum is displaced. This might lead to an increased error in projecting I magnitudes from B and V. For data taken on a single 48 frame run, the fields are only slightly offset. This would mean that most calibrations would be made using the same set of reference stars. When on another evening, the measured star is in a different position in the frame a different set of reference stars would be used. If either set contained a few stars with a large error, then the measurements from the two days could differ.
To test this, I generated a new reference catalog. The data for the month of July 2002 was run through the pipeline using the bigrefcat.dat catalog. This consists of about 1.6 million stars with a maximum error of 0.2 mag. From the generated star list, I deleted all the stars that were flagged, and all the measurements with V or I mag over 16. (To get rid of the 99 flagged stars.) Stars with more than 10 observations were then selected. Sigma was computed for the set of observations, and stars were selected where sigma was 0.01 or less for the bootstrapped reference catalog. Note that this rejection process eliminates stars like that of Figure 1. This would seem to result in little comparison data being left for Figure 1. stars.
The raw data was processed again using this new reference catalog. First we processed the data for the single frame using the same data as in Figure 5 and 6. The results are shown as Figure 7 for the V data and Figure 8 for the I data. While there seems little change in the broadening of the distribution, the I data bright star data does seems to straighten out somewhat.
Figure 7. Bootstrapped V Mag vs V Mag sigma for single field data.
Figure 8. Bootstrapped I Mag vs I Mag sigma for single field data.
We next applied the new reference catalog to the entire month of July. This required a two day computation on a 1.3 MHz Athelon. The different reference catalog increased the computation time by nearly a factor of two. The result is shown as Figure 9 for the V data and Figure 10 for the I data. A lively imagination can find some improvement, particularly in the I data. Note the differing number of stars found using the different reference catalogs. This was the result of the fitting process failing on different fields with the two catalogs.
Figure 9. Bootstrapped V Mag vs V Mag sigma for the 689,197 measurements
of 28,360 stars from the July 2002 data. Flagged stars were deleted as
well as stars with less than 10 measurements.
Figure 10. I Mag vs I Mag sigma for the July data.
To test that there was a small improvement, we found the same star in the data that was shown above as Figure 1 and display it here as Figure 11. We note that there is little difference in the V data. The I offset for the one night that differs from the other two has been cut in half. This is a general result for red stars. I examined a number of examples that I found for red stars that varied from night to night. All were improved by about a factor of two. None had the error increase from the use of the bootstrapped reference catalog.
Figure 11. The star of Figure 1. as measured using the bootstrapped
reference catalog.
There are clearly other things going on in this data. The big bump in the Mag vs Mag sigma distribution between mag 8 and 11 for the I data of Figure 4 is probably not real. I suspect that there is more going on here than just a problem reference catalog. The first thing that comes to mind is non-linearity of the data at the brighter magnitudes. This is the next thing to investigate.
It should be noted that this is not claimed to be a way to process the measurements. Any error in measurement is just propagated to the bootstrapped reference catalog. This measurement would seem to point to the need for an improved reference catalog.