A. Event Selection
Because of the correlation between in-ice muon energy and NPEs, event selection is based on NPE, with the threshold NPE values dependent on linefit zenith angle.
Energy and NPE relation
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1) 
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1) Event from the Monte Carlo simulation of the IC-9 detector in a plane of NPE and charged lepton energy measured at 880 meters from the IceCube center. Events passing within 880m of the center of IceCube are considered in the plots and more distant events do not contribute to the data sample. The distribution in the left plot is for muons. The plot for taus on the right illustrates the suppression of energy loss compared to that of muons and the contributions from tau-decays. The charged lepton energy distribution is assumed to follow E^-1 in these plots for illustrative purposes. |
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2) 
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2) The same as left plots in Fig. 1) but now event distribution is that of GZK induced muon and atmospheric muon. Normalized to 125 livetime. |
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3) 
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3) The left plot is the same as the left plot above Fig.2) but now also from different flavors at 880m from the center of the IceCube all weighed with a GZK model. Normalized to 125 livetime. Note that the major part of neutrino events emit the largest NPE when they made CC/NC interaction near the detector unlike the other radiative energy loss proccesses as for muon and taus. |
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Of course there is some directional dependence in this relation because with IC-9 has narrow x-y geometry compared to z direction. |
Experimental Sample and MC Simulation Distribution Comparisons
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4) 
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4) Event distributions of data as a function of NPE (left) and zenith
angle in the center of IceCube coordinate (right). Black dots with error bars denote the
IC-9 high energy event sample in 4.0 \leq log NPE
\leq 5.0. Red histograms are from the Monte Carlo simulation of the
empirical atmospheric muon bundle model that gives good agreement
with experimental data. |
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4-1) 
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4-1)
The same as above but now also a signal model (GZK1 in the flux plot here) is compared. Black line is that of GZK1 signal and red line is background.
Colored markes indicate singal events from different flavors and channels (black lines are the sum of all flavors).
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4-2) 
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4-2)
The same as above but now also with different signal model (GZK1, GZK2, ZB, TD in the flux plot here), that of muon flavor only is compared (for practical reason). The red hist is background and blue circle is the same blue circle from GZK1 model above in 4-1). colors are blue: (GZK1) the GZK neutrinos m=4 Zmax = 4, green: (ZB) the Z-burst, pink: (TD) the Top Down (SUSY), light blue: (GZK2) the GZK neutrinos (by Sigl) m=5 Zmax=2 gamma=2 Emax=10ZeV |
Signal and Background MC Simulation Event Distributions
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5) 
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5) Event number distributions in the plane of NPE and cosine of zenith angle obtained by Monte Carlo simulations are shown to illustrate the distribution differences for an expected signal and background. Plotted on the left is that for GZK neutrino-induced events and the background atmospheric muon bundle model is shown on the right. Projections of the atmospheric muon bundle distribution onto each axes are represented by red histograms in above figure 4). |
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6) 
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6)
Event selection is defined by the right-hand side part of the lines on the plane of NPE and zenith angle as shown or the eqs. below.
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Event Rates
7)
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7) With the cut defined above, the numbers of expected IceCube EHE signal events induced from the GZK models, the Top Down model, the Z-Burst model, and from the background atmospheric muon models with 2 sets of empirical parameters. The predictions are normalized to a livetime of 125 days. Signal event numbers are from neutrino fluxes of all flavor sum assuming that nu_mu to nu_tau ratio is 1:1. Errors are statistical errors only. The cut retains, for instance, 26 % of 'GZK 1' signal events which passed the 80-DOM filtering condition, while only 3.2x10^-6 % of Atmospheric Muon BG is held. |
B. Results
The event selection is applied to the full IC-9 high energy event sample in 2006 of 125 days of effective livetime and it resulted zero signal candidate event over 0.00097 expected background in it.
Based on this null result, the upperlimit at 90% confidence level to the all flavor EHE neutrinos from the first year 9-string IceCube are obtained as shown below.
The relations between in-ice muon energy to surface neutrino energy for example and other flavors are shown
here.
Sensitivity
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Effective Area
Corresponding neutrino effective area is shown below as function of neutrino energy at surface.
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Effective Area Flavor Dependence (average over full solid angle) 
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Effective Area Zenith Angle Dependence (all flavor is added) 
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Effective Area Comparison with the other analysis
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Shown is the neutrino effective area from Christin Wiedemann's AMANDA-II 2003 UHE analysis with our IC-9 muon neutrino effective area superimposed (star marks). Note that to be compared with IC9 star mark is the black dash line from Christin (I plotted only A_eff for nu_mu): We have almost the same effective area up to logE/GeV leq 8 and at the higher energy IC-9 has a factor of 2 or so larger area, which is probablly due to larger fiducial volume of the IceCube. |
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The line up to 10^8 is effective area from Kotoyo's IC-9 2006. We see the effeciency turn over at around 2 x 10^7 GeV. |