High-Energy AMANDA Reconstruction

Jodi Lamoureux (LBNL)
&
Chris Spitzer (UCB)

Friday - April 13, 2001

ABSTRACT:

We evaluate the timing residuals for a high-multiplicity AMANDA event. The distribution of residuals shows for the first time, that the leading edge times in these high multiplicity (large pulse-height) events can be used for tracking. There is no obvious distinguishing power between the track and point-source hypotheses. Improvements in particle-ID depend on better dynamic range or very long lever-arms which do not seem likely before IceCube.

VISUALIZATION OF AMANDA EVENTS:

Chris and I developed algorithms and visualization tools for light transport in South Pole ice and AMANDA detection. The model starts with a basic cerenkov cone or point source transport equation and then modifies it for scattering and detector effects. The scattering model depends on depth in the South Pole ice. Light is absorbed as it travels, so attenuation affects can be seen in the timing. The AMANDA data-acquisition measures the arrival time of the first photon. Long pulse shapes absorb later photons into the pulse, or are removed explicitly by the analysis. The arrival time of the first photon is on average earlier for a multi-pe pulse, than for a single-pe pulse. All of these effects can be observed in the light model.

The scattering model is based on a simulation from Kurt Woschnagg. The depth dependence comes from Kurt's measurements (and publication) using AMANDA calibration sources. The geometry of light propagation is identical to what is in recoos (Ole Streicher, Christopher Wiebusch, et. al.) which we were familiar with when when we started this project.

The following is a series of movies showing the mean arrival time of light including different transport models.

movie of cerenkov cone.
movie of cerenkov cone + scattering
movie of cerenkov cone + scattering + npe
movie of cerenkov cone + scattering + npe + depth
movie of cerenkov cone + scattering + npe + depth dependence+ attenuation
movie of cerenkov cone + scattering + npe + depth dependence + attenuation + AMANDA data
screen shot jpg: eview screen shot with residuals.

The purpose of this exercise is to see that the residuals for a well fit track are clustered around zero. The track above is a good example of this. Below is the residuals plot.

The y-axis shows the difference between the mean expected arrival time and the measured time of each hit. The x-axis shows the path-length over which the photon traveled. This version of eview is available from the eview web page. Each hit is colored by the measured ADC. In general, 1 pe pulses should be further from the track than multi-pe pulses as is the case in this event. In addition, the scatter for 1 pe pulses should be wider than for the multi-pe pulses. The two lines are labeled backwards. The inner set indicate the 2-pe RMS and the outer set indicate the 1-pe RMS. A high-side tail is expected especially for large photon paths. This track was fit using recoos. Recoos uses 1-pe likelihoods and may be the reason the hits cluster around the lower line.

HIGH-MULTIPLICITY AMANDA EVENT:

Residuals can be used to visually evaluate the quality of a fit produced by any algorithm. On an event-by-event basis, they give some indication of the quality of the fit at a glance. They are also a tool that is useful in developing and debugging numerical algorithms. We have used these tools to evaluate a few high-multiplicity events in AMANDA. Below is a movie of the first event with 152 hit PMTs after cleaning.

movie of a high-multiplicity event.

The track was fit by hand, by adjusting the track parameters until the residuals looked good. Looking string by string at the time profiles (a feature now available in eview) we would tweak the fit toward or away from each string until the residuals started to clump near zero. This chi-by-eye method is not a proof that the residuals are the best that can be found by a numerical algorithm, only that at least one reasonable fit exists. Below are two eview screen-shots showing the final residuals for a track and a point-source.

eview screen shot of high-multiplicity AMANDA event with fitted TRACK including residuals window.

eview screen shot of high-multiplicity AMANDA event with fitted POINT SOURCE including residuals window.

CONCLUSIONS:

This method of measuring fit quality can not distinguish between a track and a point-source in the highest multiplicity horizontal AMANDA events. It is possible that more information may remedy this situation, but the current residual is composed of the combined effect of depth-dependent scattering and absorption as well as AMANDA digitization effects and multi-photon statistics. Since this is most of the available information, it is not clear what additional analysis variables can be constructed to improve the situation.

Some of the techniques used in the atmospheric muon analysis, such as the Phit/no-hit variables that take into account the probability that a PMT did not fire, are obviously not terribly effective here. All the hits that are close to the track fired unless the PMTs were dead. Most of the other cuts attempt to distinguish up from down or the smoothness of the hits along the track. Since half the detector fired in this event, these cuts are not really relevant. All they can do is map out the density of the photo-tubes.

Improvements in the >10 pe dynamic range could result in a tighter residuals distribution with better distinguishing power. My understanding of the current peak-ADC and TOT calibration makes improvement seem unlikely. Wave-form recording applied to B-10 is likely to saturate in this kind of event since the signals are quite broad when they arrive at the surface electronics. The distribution of residuals is already very broad where the ADCs are calibrated (photon paths>100 meters). The clustering of the residuals is most evident among the uncalibrated >10 pe hits.

A bigger detector could take advantage of the added lever-arm to separate tracks and showers. I don't know if AMANDA-II is big enough. The lever arm can be extended by looking at smaller zenith angles. From simulated high-energy muons events, I found that these could also be fit reasonably well with a point source hypotheses. Plots of this were shown at the Irvine AMANDA collaboration meeting, Sept. 2000.

The good news in all of this is that the leading-edge times for very high amplitude pulses are close enough to the expected time for ~50 pe to approximately locate the vertex and general direction. If the light model is sensitive enough, a measure of the energy may be pursued through adjusting the number of pe until the residuals tighten. This is the most sensitive energy reconstruction that I can concoct. It will certainly be more sensitive than looking at the radius of the <10pe hits which are very broadly distributed.

In these events, we need to find better methods for the first guess and iteration into the final answer. The method employed in recoos is to multiply all 152 probabilities and then tweak the track slightly and multiply again. Unless the first guess is very close to the final answer, the probabilities do not smoothly direct the track to its minimum. In fact, the recoos track for this event found 3 direct-B hits and did not converge on anything close to the right track direction. We have not discovered a replacement for the line-fit, or any improvements to it at this time. We are aware that others in the collaboration are working on this and feel it is of utmost importance.

Here's the event in case you want to fit it better. theEventFit.f2k