From:" "John Learned at the Universityof Hawaii"

11-NOV-1996 15:46:53.46


Subj: upgoing muon analysis description and output available now

out of data.... new data coming soon 12/96

Dear Moophiles:

I have ported (at last... after a big fight with the ALPHA which did not like my code from VMS) and updated for SK a program for upgoing muon track analysis. It is located in my area here at UH, The program is twopoint.f (yes folks, FORTRAN with all those shouting caps), and you can find a (probably too lengthy) description in that /post area, called twopoint.html. This text tells you how the program works, and a gives a tour of typical output, which can be found in the same area as twopoint.prt (an ASCII file, with run information, data summary and old fashioned line printer output towards the bottom for the plots). Also in the same area are the figures ( in postscript (check out, though a bit large).

What does this program do?

1) It reads data files from not only SK, but also IMB, Baksan, Kamioka, KGF and CWI experiments (all the upcoming muon data I could find). You can plot it all, though it will take a while. (Actually I have not tried anything but SK and IMB since porting, so probably work will be needed to process the others).

2) Has lots of controls for selecting the event sample by such things as minimum path length in the detector, dE/dx, time window, etc.

3) Makes a data list of the events for peruseal, and plots lots of things to allow you to see that things make sense (local coordinates, times, and such).

4) Makes sky maps and projections in local, equatorial, galactic, and ecliptic coordinates.

5) Does a background calculation via bootstrap statistics, namely by making false data sets from scrambling the local directions of events with the times of these events. It also introduces some wiggling of the coordinates (important for small data sets). Then it makes a sky plot with the event directions replaced by gaussian functions. A background subtracted plot is made and scaled to SD units, assuming the numbers in the bins to be Poisson distributed (yes, I know they are not... this is a long discussion, which I am sure we will have much to say about in the future).

6) It also makes a two point correlation analysis of the data. The idea is that if there are a few weak point sources or slightly clumped sources (and we know there are not very strong ones in past data sets of comparable magnitude, so far), they may show up first by a tendancy for the data to be more clustered than randomly. This can be revealed by looking at the distribution of pairwise angular distances of the muon track directions (in celestial coordinates). The distribution is easy to calculate, but the exepected distribution is not, because the detectors do not see the whole sky, and that part they do see is not observed uniformly. So we need a calculation, which is done, as above, by scrambling the data set: shuffling the local coordinate pairs with their arrival times and thus making false data sets (bootstrap statistics, as this techniques is formally known). One divides the data by mean background results and subtracts one, and voila, the twopoint correlation function. For our purposes, the integrated 2pt function is better, since it looks at the probability inside some angular region. (If do you see something, then the diffrential 2pt function will tell you where the correlation is originating).

Anyway, this is what I have working now. It needs work, but you can see some preliminary results. Of course the 79 events we have from SK so far are not very interesting. If anybody does look at this and has comments I would be appreciative.