Data collected during the year 2006 by the first 9 strings of IceCube can be used to measure the energy spectrum of the atmospheric muon neutrino flux. Atmospheric neutrinos, an important scientific output by itself (for instance, to understand the high-energy hadronic interaction models), are also fundamental in order to check the performance of the detector and to estimate the background for the extraterrestrial high-energy neutrinos searches. A full reconstruction of the neutrino-induced muon tracks provides both directional and energy information. The reconstructed energy- correlated parameter, the photon density emitted by the muon along its track, can be used to calculate the energy spectrum, which is reconstructed by using unfolding techniques. We will discuss the unfolding procedure to be applied to data from the 9-string configuration of IceCube Muon Energy Reconstruction and Atmospheric Neutrino Unfolding with the IceCube Neutrino Telescope Juan-de-Dios Zornoza and Dmitry Chirkin on behalf of the IceCube Collaboration XXX International Cosmic Ray Conference, July 2007, Mérida, Mexico Acknowledgments: J.D. Zornoza acknowledges the support of the Marie Curie OIF program. Motivation The atmospheric neutrino spectrum is one of the basic measurements of neutrino telescopes: Fundamental for understanding background in other analysis, in particular point-like source searches Intrinsic interest for the study of atmospheric neutrino studies The aim of this analysis is to set up the basis for the reconstruction of the energy spectrum of atmospheric neutrinos using unfolding techniques. Unfolding techniques are needed for neutrino spectrum reconstruction because of the combination of two features of this problem: The energy resolution is limited, since the energy loss of the muon is stochastic (and moreover only part of the muon energy is observable, which is turn is only part of the neutrino energy). Second, the spectrum falls very quickly with the neutrino energy. Therefore, the low-energy events for which the energy is overestimated "bury" the regions at higher energies. Spectrum Unfolding Data - Monte Carlo comparison The comparison between data and Monte Carlo simulation allows us to check that the detector simulation is under control. This comparison has be to be done at a level at which the blindness policy of the experiment is respected. Analysis procedure The main steps of the analysis are the following: Cleaning of the bad OMs (based on abnormal noise rates) Feature extraction (determination of the times and charges of the pulses) Energy reconstruction with the RIME algorithm Track reconstruction in a two-step procedure (prefit based on the + likelihood maximization fit) Conclusions IceCube is a neutrino detector being built at the South Pole (22 out of 80 strings already installed and smoothly working) A method for reconstructing the muon energy based on the estimation of the photon density emission along the track has been developed The energy resolution using this estimator is better than other estimations based on the number of channels or the total charge The application of the Single Value Decomposition Method using this photon density is proposed for the unfolding of the 9-string configuration of the IceCube detector The preliminary results (no coincident muon background included) are promising in terms of stability and convergence Likelihood function The full log likelihood function contains terms which depend on the muon energy and describe the probabilities to observe more or less or no hits in each sensor. The number of photons vs. distance to the track is constructed by merging 2 approximations: for the near and far (diffuse) regions. This is fitted/verified with data. The reconstructed parameter is number of photons per unit length of the muon track times the effective PMT area. The probability (likelihood) that an event is described by a particular track hypothesis is Muon energy reconstruction Log likelihood may be rewritten to emphasize the energy term: hit positional/timing likelihood energy density term Photon density parameter In ice muon energy loss is dE/dx=a+bE with a=0.26 GeV / mwe b= / mwe (1 mwe = 1/0.917 m of ice) The number of Cherenkov photons generated by a bare muon is When convolved with ice and sensor glass transmission curves, this is about Cherenkov photons per meter of muon track. From Geant-based simulations each cascade left by a muon generates as much light as a bare muon with the length of track of 4.37 m E / GeV for electromagnetic cascades 3.50 m E / GeV for hadronic cascades For a typical muon the average is ~ 4.22 meters E/GeV A typical cascade emits 4.22x32440 = photons/GeV For a muon track the “photon density parameter” is Area x Nc [m] = [m -1 ] ( x E/[GeV]) x 81 cm 2 Average quantum efficiency ~ 17% PMT area = cm 2  81 cm 2 effective area Energy resolution number of channels total charge reconstructed photon density When comparing the energy of the muon at the point of the closest approach to the COG (center of gravity, weighted with charge) of hits, we see that the best correlation is obtained with the reconstructed photon density IceCube IceCube will be the first neutrino detector with an effective volume of 1 km 3, which is the “natural” size for this kind of detectors, given the low flux expected. Like AMANDA, it will be located in the South Pole, with 80 strings containing 4800 PMTs. The first 22 strings have been already installed and it will be finished by The analysis presented here uses data obtained with the first 9 strings of the detector. number of channels total charge reconstructed photon density 7 Tev32 TeV150 TeV680 TeV3.2 PeV14 PeV stringarity holds and rms is 30% in log 10 (E) from 25 TeV to 25 PeV number of channels total harge reconstructed photon density Unfolding performance We have checked the robustness of the unfolded results as function of the spectral index used when creating the smearing matrix and the initial assumption made for the solution of the system. As a spectral index of gamma=-2 is far from gamma=-3.7, the dependence on the uncertainty of the smearing matrix is small. We used rather different shapes for the initial assumption on the solution and could show that the algorithm converges towards the expected solution. Input for the algorithm: distribution of estimator for one year (obtained by Poison randomization of a larger MC sample) Unfolded spectrum (blue) compared with the real one (black). This result is preliminary, since no coincident muons are included. References: [1] A. Achterberg et al., submitted to PRD (2007), arXiv: v1 [2] A. Hoecker and V. Kartvelishvili, Nucl. Instr. & Meth. A372, (1996)