PNe9 - Running (old) statistics on simulated theoretical PNe positional data

Armed with the PNe coordinates from the PNe8alpha methods, we try to do statistics on this data, which DOES have a correlation between PNe and light, in it (since we generated it that way!)
For this we used the PNe coordinates from alpha_2.5 = 23 x 10^-9, and subsampled the catalog according to the number of PNe found by Feldmeier/Okamura, as described on this page.

The statistics applied are similiar to this page: PNe7. We used 4 histograms:
2 PNe - place box between every pair of PNe that are close enough to fit in the box
1 PNe - place a box centered on every PN
Random - place random boxes, 2 runs
       placing as many random boxes as there are PNe - Random(1)
       placing as many random boxes as there are 2 PNe pairs - Random(2)
None - place random boxes but make sure they have 0 PNe in there, 2 runs:
       placing as many Zero boxes as there are PNe - Random(1)
       placing as many Zero boxes as there are 2 PNe pairs - Random(2)

Error bars were plotted from the Monte Carlo-ing of ## trials. Error bars on 1 and 2 PNe came from the respective Random and None runs with the same number of boxes.

Error bars on DELTA plots are from the sigma/quartiles from the calculated DELTAs  over all runs.

       We do not (in this iteration) Monte Carlo the PN catalog, that is, we (should?/could?) subsample that catalog randomly to get better error estimates


THESE ERROR BARS ARE NOT TOTAL ERROR - they reflect a "minimum" or "partial" error in the data as they only deal with errors associated with our box selections around the images and NOT with PNe selections (or anything else)


     
NOTE: for the Delta 2 - R_2 graph, the value of the data point at a half-box width of 1.45" (1px)
                has been manually set to the value of the next point. It originally was ~ -200. This
                was due to the difficulty in finding 2 PNe boxes with a box width of 3 pixels.
     


     
     


     
NOTE: for the Delta 2 - R_2 graph, the value of the data points at half-box widths of 1.45" (1px),
                4.35" (3px) and 7.25" (5px) have been manually set to the value of the point at 10.15" (7px).
                They originally were >1000. This was due to the difficulty in finding 2 PNe boxes with box
                widths so small
     


     
     







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