As long as TASS has been operating, the data has been analyzed by making plots of mag sigma vs magnitude. The data has been noisier than expected. Many things have been investigated to try to pin down the source of the noise. TASS Batavia does not operate in an ideal location. The lights of Chicago are to the East, there is an Interstate Interchange to the south, the telescopes are located in a suburban residense where neighbors turn lights on and off at random times during the night, and there are many other things which might affect the quality of the data. The telescope mounts are not as rigid as they could be and are mounted on the roof of a suburban house which is not as rigid as might be desired. The weather is not controlled as it would be on a mountain top. There is often haze which reduces the signal.
With all this, sometimes blocks of data were seen to have lower than normal sigma. Until recently many things have been tried to select a better data set in an unbiased fashion. In general, as large as possible data set has been used when making magnitude vs sigma plots.
Recently MWR visited the TASS, Batavia site. While here there was discussed on the mail lists a star of some interest. Looking at the TASS data, MWR found of order 50 measurements. This was exciting since it covered several years of history before the star became a topic of discussion. Upon examination, the TASS data was found to be quite noisy, and thus useless. There were found to be two stars quite close to the star of interest which bled into the star in varying amounts. This is mostly a function of the focal length of the lens and the pixel size. Other factors could be the rigidity of the mount and the precision of tracking the sky. This led one of us (TFD) to consider investigating the star density. It is noted that the sigma vs magnitude plots for TASS always seem to be noiser than plots from similar experiments that use even shorter focal length camera lenses.
With the completion of 5 years of running, there is a large data set available for analysis. This data has been "collected" so that all the measurements of a star are together in one place. The data has been further sorted by telescope and by one degree bins. For the telescope TOM2 which this note uses for discussion, these bins cover Declination values +21.9 to +54.1 degrees.
In the least dense bin, which covered 180 degrees < RA < 181 degrees, the dataset provided a measured star density of 16261 measurements of 2317 stars or 71.9 stars per square degree and an average of 7.02 measurements per star. In the most densely populated bin, which ran 311 degrees < RA < 312 degrees, it provided 471341 measurements of 22091 stars or 686.1 stars per square degree and an average of 21.3 measurements per star.
The "most dense" bin at RA = 311 degrees is plotted first.
In Figure_1, all the measurements in this range are plotted. The procedure is to collect all the measurement of the same star together. Then the mean and standard deviation from the mean (= "sigma") of the V and I filter measurements are computed for each star. A list is then made which contains one line for each star including a star number, the number of measurements made of the star, the V filter mean value and the V sigma, the I filter mean value and the I sigma. Plotting the V mean value and the V sigma for bin 311 produced Figure 1. The data is very noisy containing a lot of high sigma measurements. This is obviously not due to variations in the brightness of the stars but is likely some measurement artifact.
The data for Figure 1. contains a number of stars which are measured only a few times. By sorting, a second list is extracted which contains only stars measured 10 or more times. This is plotted as Figure 2 below.
Applying the Welch-Stetson statistic to the data of Figure 2 , there is found a very large number of hits greater than 1, which is should indicate variability with a high degree of confidence. This is plotted in Figure 3 below.
It would be convenient to use tools like the WS statistic in searches for interesting stars. Here it would appear to be worthless. As hinted in the introduction, crowding is possibly the source of the difficulty in using ws. To investigate this, the least crowded field, RA 180-181, is plotted as Figure 4 below. below.
There are not enough stars to make the comparison obvious, so it is plotted as the green field on top of the red field of Figure 2 as Figure 5 below.
Now the comparison is obvious, the sparse field has less scatter than the dense field.
For a better comparison, 9 sparse fields spread out between RA of 168 and 195 degrees are summed together for a total of 22111 stars compared to the 22091 of Figure 1. The collected sparse field is plotted below as Figure_6.
Again for comparison, the collected sparse field (green) is plotted on top of the dense field as Figure 7.
This suggests that the data might be made "cleaner" and thus more useful if stars that might be contaminated by the light from nearby stars are removed from the data set. This reduces the amount of data available, but does not bias the measuement since stars are proposed to be removed in their entirety. No adjustments are made to the measured magnitude values. If a star is found to be close to another star, all the measurements of both stars are removed from the data set.
For the data set of Figure 1, all stars within 8 pixels of another star are removed. All measurements remain the same, so there is a red point under every green point in Figure 8.
A large number of red points can be observed that are several sigma above the mean value at that magnitude. These would tend to fool star finding programs into a false positive indication.