Updated Graphs

I have run the code again using a log plot for the histogram seen below:

There appears to be a change in gradient around the -650 and 650 points. I took these values as the new threshold for the umbra/penumbra.

This gives thresholds which look like this:

Plotting just the umbra i produced the following plots of Area Vs. Time and Flux Vs. Time

The values of flux obtained seem to be consistent with those in the literature (~10^22 Maxwells)