University of Wisconsin-Madison

First Year Performance Paper - Section 4.1

4.1 Muon track reconstruction

A maximum likelihood algorithm for one-string track reconstruction employing the full waveform unfolding method of Section 3.5 was used to reconstruct the In-Ice data. The likelihood function was built using an approximation to the photon arrival time distribution for multi-layered ice first introduced for the AMANDA reconstruction in [36], and refined in [37]. The approximation can be used for ice with variable properties (i.e., depth-dependent scattering and absorption) if scattering and absorption coefficients are averaged between the photon emission and reception points in ice [37].

Waveforms of an air-shower seen by all sixteen DOMs in the 4-station IceTop array. The timing of the signal in DOMs at different locations is used to determine the shower arrival direction.
Waveforms of an air-shower seen by all sixteen DOMs in the 4-station IceTop array. The timing of the signal in DOMs at different locations is used to determine the shower arrival direction.

The scattering and absorption values used are based on in situ measurements with AMANDA [38]. This measurement was extrapolated to deeper ice using ice core data collected at Vostok station and Dome Fuji locations in Antarctica, scaled to the location of AMANDA using an age vs. depth relation [39]. Figure 15 shows the resulting scattering coefficient as a function of depth. The scattering depth profile was further confirmed between 1300 and 2100 m at much higher resolution with data collected by a dust measuring device (dust logger) used during the IceCube string deployment [30].

The effective scattering coefficientfor light at 400nm, the sensitivity maximum for IceCube DOMs, as a function of depth in the ice (from Ref. [38]).
The effective scattering coefficientfor light at 400nm, the sensitivity maximum for IceCube DOMs, as a function of depth in the ice (from Ref. [38]).

For muon tracks, reconstructed parameters are the zenith angle, distance of the closest approach to the string, depth and time of closest approach to the string, and an estimate of the average photon density along the muon track. The latter is correlated with the average muon energy. Reconstruction of the azimuthal angle is not possible with a single string because of the cylindrical symmetry about the string.

The track-fitting algorithm was tested on a simulated data sample of downgoing muons and was found to reconstruct it rather well (given that only one string was used [40]). Figure 16 compares the true zenith angle with the reconstructed zenith angle of simulated events. The RMS resolution of the muon tracks with an event hit multiplicity of 8 or more is 9.7°. The resolution improves rapidly as the multiplicity increases, reaching 1.5° for multiplicity of more than 30 hits. This is similar to the one-string IceCube prototype analysis results [23].

Zenith angle difference distribution of reconstructed and simulated tracks.
Zenith angle difference distribution of reconstructed and simulated tracks.
Figure 17 compares the hit multiplicity distribution for 8 hours of data and a similar amount of simulated data. The zenith angle distribution of the reconstructed tracks in data is compared to the simulated data in Fig. 18. The simulated data used in Figs. 16-18 were produced with a standard AMANDA simulation, which does not account for detailed differences in trigger logic, ice conditions and sensors of the deeper IceCube String-21. As the IceCube simulation matures, the apparent discrepancy observed in Fig. 18 is expected to become smaller.

Hit multiplicity distribution of muon events in data and simulation.
Hit multiplicity distribution of muon events in data and simulation.