Presentation given at the analysis phone call (August 27 2009).

The 6-parameter ice model describes scattering and absorption properties of ice at the location of the AMANDA-II detector, as functions of depth and wavelength. In order to describe the layering structure of ice the unfolding method was used that employed a hybrid of bulk-ice fitting code and photonics. From this "full-circle test" it appears that the description of absorption could be as much as a factor of ~2 off in the near or far regime (indicating a problem with the unfolding technique?).

Here an attempt is made to perform both in a single step of an iterative procedure. Also, instead of fitting timing distributions, absolute photon counts between data and simulation are compared, and timing distributions are pretty much only looked at. This is clearly an oversimplified procedure that may need modifications (taking into account timing distributions) to ultimately succeed in fitting the data.

Runs 111738-111744 of "request B" contain data with each of DOMs 1-60 of string 63 of IC40 flashing in a sequence. For each of the flashing DOMs 200-300 flasher events were recorded. All 6 horizontal LEDs were switched on with maximum brightness and length, creating a pattern of light around string 63 that one may argue should be rather symmetric. As seen in the 2 figures below it is not completely symmetric.

The estimate of the mean charge from the above figures has a relative uncertainty of ~10-20% in most of the ice, increasing to ~30% in the dust layer:

This number includes uncertainties in the flasher orientation, string misalignment and range variations. It is however much smaller than the difference between data and simulation based on nominal aha ice model:

The variation due to angular sensitivity using hole ice (red line) compared to that without (pink line), or even AMANDA OM angular sensitivity (yellow line) is also much smaller than the discrepancy observed.

For the following analysis the sum of charges collected at the same DOM position on strings 64, 55, 54, 62, 70, and 71 was compared to a similar sum calculated with ppc simulation. Each of the charges is well below the saturation charge (of ~7500 at gain of 10⁷) so no saturation correction was performed (which seems ok given the large dispersion of charges at each given DOM position on the 6 strings nearest to string 63).

For each flasher position the ratio of data/simulation (of sum of charges in 6 DOMs on 6 strings nearest to string 63 at the same position as the flasher) was calculated. The absorption coefficient a400 in the layer of the flasher was then replaced with a400_new=(a400_old-amin)*exp(log(ratio)/4)+amin where amin=-0.0359449. The log(ratio) for layers in between was then extrapolated linearly. To get the scattering coefficient the relation s400=(a400+0.025)/1.5 was used. This relation appears to the the basis for extrapolation within the aha model:

The value of amin was chosen as a ratio of 2.6/71 of fit in Figure 18 of the ice paper linked above. With amin=0 it was not possible to achieve a good fit to the flasher data in the bottom of the detector using the iterative procedure described above. A linear relationship s400=a400 was also tried, but that lead to too many direct photons in most of the ice layers.

Sets 0-6 start with bulk ice description with a400=0.044 and s400=0.046 (set 0), and go through the sequence of a400(depth) coefficients shown below:

It was then noticed that time distributions in set 6 exhibit too many early photons in the clearer ice. The relation between scattering and absorption was then modified to s400=sqrt{[(a400+0.025)/1.5]^2+0.0002}, which is how set 7 and set 8 were obtained. In the above plot model coefficients of the aha ice (red) are compared to those of set 6 (green) and 8 (blue).

It appears that the peaks are somewhat shifted toward shallower depths, also have more structure, both appear to be in the right direction (compare with a plot here). The linear relationship between scattering and absorption is preserved in most of the ice, thus selecting the most consistent with previous measurements direction (see Figure 9, page 11 of the ice paper).

Although there is some discrepancy in the description of the tails of the time distributions, the front of the timing distribution and the total charge agree much better than in the same comparison shown above for the simulation based on the nominal aha model:

Below is the result of running the single muon background simulation (mmc+ppc) for sets 6 and 8:

<--- model of set 6 --->
Efficiency: x 1.0 no rate adjustment	hole ice	data: black ppc: blue
Efficiency: x 1.0 no rate adjustment	no hole ice	data: black ppc: blue
<--- model of set 8 --->
Efficiency: x 1.0 no rate adjustment	hole ice	data: black ppc: blue
Efficiency: x 1.0 no rate adjustment	no hole ice	data: black ppc: blue

Note that although the iterative method chosen here to fit the ice model is not very sensitive to the "hole ice"/"nohole ice" angular sensitivity model chosen (as can be seen in the in the "strings like 64" columns of the flasher plot pages), the "hole ice" model was used during the fit procedure.

The flasher data taken in October of 2008 can be used to demonstrate that the description of ice based on the nominal aha model is inconsistent with the observation. A much improved description of both flasher and muon data appears possible, and the preliminary results are encouraging.