Log 10

Justin Vandenbroucke

justinv@hep.stanford.edu

Stanford University

2/8/03

 

This file contains log entries summarizing the results of various small subprojects of the AUTEC study.  Each entry begins with a date, a title, and the names of any relevant programs (Labview .vi files or Matlab .m files – if an extension is not given, they are assumed to be .m files).

 

2/8/03

Quiet livetime

quietLivetime.m

      The plot below gives the left-hand tail of our threshold livetime distribution.  These are the quietest periods, and only these values are used to calculate our limit.  Note that there are only 4 discrete thresholds present (the thresholding algorithm steps in multiples of 0.004).  For each threshold the total livetime (summed over all minutes with that threshold) is given.  The total amount of quiet (threshold < 0.025) livetime is about 1/3 of our total livetime.

Figure 1

2/8/03

Flux limits for interactions and neutrinos

calcLimit3.m

      The first plot below gives the cross section used (an extrapolated power law from Gandhi et al) for our neutrino flux limit.

      The second plot gives integrated flux limits, both for interactions (per unit volume per unit time per steradian) and for neutrinos, assuming all interactions are neutrinos.  The difference between the two is that the neutrino limit incorporates the nucleon density of water (6e29 m-3) and the cross section (as shown in the first plot).

      The third plot gives differential flux limits, also for both interactions and neutrinos.

      The limits are calculated as follows: N(E) = X(E) * F(E), where N is the number of events detected, X is our exposure, and F is the flux (all quantities integral).  Exposure is calculated first for each threshold independently: it is the acceptance at that threshold times the livetime at that threshold.  X is then our total exposure, the sum over all four thresholds.  For generic interactions acceptance is in m3 sr, and for neutrinos it is this value multiplied by nucleon density and cross section.  This multiplication is done before inverting and differentiating the integral flux to determine the differential flux.

      The integral flux is simply F(E) = N(E) / X(E).  The differential flux, dF/dlog(E/eV), is then calculated by numerically differentiating F(E) with respect to log(E/eV).  Note that F is nearly equal dF/dlog(E/eV).

      The fourth plot gives N(E), determined by a table of upper limits at 95% confidence for a Poisson process with 0, 1, or 2 events observed in a small time.  The two events we have seen are at nearly equal energies on this log scale.

Figure 2

 

Figure 3

 

Figure 4

 

Figure 5

 

2/8/03

Limited bathymetry

allBathymetry.m

      The two figures below give rough bathymetry from the 62 phone coordinates that we have.  Depth contours are linearly interpolated from hydrophone depths.

      The first figure gives literal depths (direct depths from the surface, not ellipsoid heights, which are also availble).

      The second figure gives sea-floor heights normal to the SAUND plane, where the SAUND plane is defined to be the least-squares plane fit to our 7 hydrophones (inclined at 1 degree from the horizontal).  In this figure it is apparent that the floor curves up around our phones, cutting off our effective volume.  However the data are insufficient to determine the entire shape of our effective volume.  It would be best to have these data out to at least 10-20 km from our central phone.  It would also be best to have sufficient resolution to determine if any hills in the sea floor are blocking our effective volume.

Figure 6

 

 

Figure 7

2/8/03

Limitations of our triangulation

variableT.m

variableC.m

      Our triangulation method (intersecting hyperboloids) assumes no error in phone coordinates, signal times of arrival, or sound speed.  It also assumes spatially constant sound speed.  The first plot shows the effect of timing uncertainty on our depth determination.  The depth is determined with various offsets (up to 1 ms, quite a large offset) added to the first time of arrival.  We see that the depth determination is not sensitive to this uncertainty.

      The second plot shows the sound velocity profile (SVP) for the date of our light bulb drop, July 30 2001.  These SVP’s should be available for many days from an FTP site but I’m waiting to hear from an AUTEC employee about obtaining them.

We have been assuming a sound speed of 1516 m/s, constant throughout depth and over seasons, but our depth determination turns out to be quite sensitive to sound speed.  Assuming the second plot (with sound speeds ranging from 1480 to 1550 m/s)  is the appropriate curve for one of our candidate neutrinos, we plot in the third figure the reconstructed depth as a function of a particular (constant over depth) sound speed in this range.  The depth uncertainty turns out to be 100 m.  However we can iterate this procedure again: we can focus on sound speeds that occur in this 100 m depth range, a much narrower range of speeds (1491 to 1494 m/s).  Applying this range of speeds gives a range of depths of only 4 m. 

This is a particularly good case because the event is near the sea floor: for events near the sea surface the entire SVP must be considered.  But this is okay for us because we are primarily interested in events near the floor.

If we have SVP’s for many days throughout the year, hopefully we can apply this method successfully and continue to use one effective speed for each triangulation.  It should be possible to determine this from the reconstructed-depth profile once we obtain the SVP’s.  It would be much more difficult to consider the sound speed varying over depth for each triangulation, as the soultion would not be trivial and w have to calculate hundreds of thousands of triangulations for our current data set.

Figure 8

 

Figure 9

 

Figure 10

 

Figure 11