Cascade Reconstruction in AMANDA

Transcription

1 Cascade Reconstruction in AMANDA M. Kowalski 1 and I. Taboada 1 DESY-Zeuthen, Platanenalle 6, D Zeuthen, Germany Physics and Astronomy Dept., University of Pennsylvania, Philadelphia PA , USA Abstract. We describe the methods used for the reconstruction of ade-like events in the AMANDA detector. For contained ades, position resolution is in the order of 5 m, energy resolution is.1 -. in log 1 (E) and direction resolution is 3- in zenith-angle. These numbers apply to both AMANDA-B1 and AMANDA-II. The performance of ade vertex and energy reconstruction has been tested with YAG laser experimental data for both AMANDA-B1 and AMANDA-II, and with LED experimental data for AMANDA- II. 1 Introduction High energy neutrino telescopes, such as AMANDA, are typically thought of as µ and ν µ detectors. However, the detection and reconstruction of ades induced by neutrinos is also possible. Cascades may be induced by ν e for both charged-current (CC) and neutral-current (NC) interactions. Both ν µ and ν τ produce single ades via NC interactions and for CC interactions ν τ produce the so called double bang events consisting of a hadronic vertex ade and followed by a ade from τ decay. For energies below 1 TeV, the distance between the two ades is only a few meters and thus they can not be spatially resolved from each other. There are many reasons for studying ades, of which we list a few. The energy resolution for contained ades is better than for muons (Miočinović, 1). When studying extraterrestrial sources of neutrinos the background from atmospheric neutrinos is much lower (φ νµ /φ νe O(1) for E ν > 3 GeV (Lipari, 1993)). And further, for typical astrophysical fluxes the ratio of neutrino flavors, φ νe : φ νµ : φ ντ 1 : :, becomes 1 : 1 : 1, due to neutrino oscillations. In this contribution, we describe the methods available for ade reconstruction in AMANDA. The reconstruction algorithms for ades are related to those used for muon re- Correspondence to: marek.kowalski@desy.de construction (Wiebusch, 1999). In both cases a maximum likelihood method is used, however with different underlying likelihood functions. After describing the ade vertex reconstruction algorithm, we focus on energy reconstruction. Then we briefly describe the method for direction reconstruction. The reconstruction methods described in this paper are used for both AMANDA-B1 and AMANDA-II. We present simulation predictions of the vertex, energy and directional reconstruction performance for both AMANDA- B1 and AMANDA-II. Tests with in-situ light sources have been performed with both AMANDA-B1 and AMANDA-II. All plots of experimental data shown in this paper correspond to AMANDA-II. For a description of the AMANDA detector see (Hill, 1999) and (Wischnewski, 1). Signal characteristics and simulation Due to the sparse instrumentation of AMANDA, many details of the ade development can not be resolved. The main difference between a hadronic and electromagnetic ade in AMANDA is the amount of observable Cherenkov light. Hadronic ades produce on average 8% of the Cherenkov light of an electromagnetic ade with the same energy (Wiebusch, 1995). The amount of light produced by a ade increases, in a very good approximation, linearly with energy (Wiebusch, 1995). The length of a ade grows logarithmically with energy and it is small (L 7.5 m for E=1 TeV) compared to the average string and optical module (OM) spacing in AMANDA. Detector simulation (Hundert, 1998) (Karle, 1999) supposes that ades are point like sources of light. This approximation is justified by noting that an explicit simulation of the longitudinal development has shown that is has a small impact on ade reconstruction. The angular lightoutput is simulated according to (Wiebusch, 1995). Due to the short scattering-length of the surrounding ice, much of the initial angular directionality is washed out. To demonstrate the properties of the various reconstruc-

2 P arrival per ns d=m 1 t residual in ns P arrival per ns d=1m 6 8 t residual in ns Fig. 1. Probability distribution as a function of time residual, p(d, t residual ), for m (left) and 1 m (right). The histogram is obtained from the photon Monte Carlo simulation (Karle, 1999), while the smooth line is the parametrization. tion algorithm, we use electromagnetic ades simulated uniformly in space and direction around the detector. 3 Vertex reconstruction The position and time of a ade vertex is reconstructed by maximizing a likelihood function which is based on the measured time of arrival of photons at the optical modules time of a hit OM. It is convenient to introduce a new variable, t residual = t i t di c ice, defined as the delay of the hit with respect to the shortest physically possible arrival time. Here t is the time of the vertex, t i is the time of the hit and d i the distance between the vertex and the hit OM. For distances shorter than the effective scattering length, the most probable time residual is very close to zero. For distances considerably larger than the effective scattering length the most probable time residual is quite large. This is shown in fig. 1 for two different distances (d i = and 1 m). The effective scattering length of the ice that surround AMANDA is of the order of 5 m. The normalized probability for observing a time residual t, was parametrized as a function of distance by (Pandel, 1996). An equivalent parametrization is also used for muon reconstruction in AMANDA (Wiebusch, 1999), p(d, t) = τ (d/λ t (d/λ 1) e (t/τ+cice/x+d/x), (1) Γ(d/λ) where the parameter X can be interpreted as an absorption length, λ as a scattering length and τ as a scattering time. The values of these parameters, are obtained by fitting equation (1) to a full photon Monte Carlo simulation (Karle, 1999) and they are, λ = 7 m, τ = 98 ns, X = 5 m. Equation (1) neglects the dependence on the direction of the ade and orientation of the OM (see (Kowalski, 1999) for further discussion of this approximation). The parametrization (1), as well as the underlying Monte-Carlo simulation of the distribution of residual times is shown in figure 1 for two different distances. We note that the parametrization (1) needs to be corrected in order to take into account the effects of Photo- Multiplier and electronic jitter. This is solved the same way as for the case of muon reconstruction (Wiebusch, 1999). With the parametrization of the probability for observation of a time-residual as a function of distance, and supposing that each photo-electron can be resolved, a likelihood function can be constructed, L = all hits i=1 p(d, t residual ), L = log(l) N hits N free. () Here we have defined the function L, in analogy to a reduced χ, as the function to be be minimized, N free =, is the number of degrees of freedom. Since we make the assumption that each photo-electron is resolved, we call this likelihood function the 1-pe time likelihood. Alternatively, it is possible to construct a likelihood for the case where more than single photo-electrons contribute to a hit. This method is particular suitable for electrical cable signal transmission, used in the OMs of AMANDA-B1, since the pulses widen considerably after passing through km of cable. Assuming that the number of contributing photoelectrons in a hit, n, can be measured, one can construct the probability distribution of time delays as a function of distance, ( ) n 1 p n (d, t) = np(d, t) p(d, t )dt. (3) t Here, the integral represents the probability, that n 1 photo-electrons arrive with a time delay larger than t. In analogy to the 1-pe time likelihood a multi-photo-electron (mpe) time-likelihood can be constructed, (see equation ()). With AMANDA we use peak sensing ADCs to measure the number of photo-electrons of a hit. Cascade reconstruction works better if seeded by an estimate of the vertex location. Such an estimate can be obtained with the center of gravity method. The mean of the OM location of all hits is used as the approximate vertex position, r = r i, where each hit is weighting by the amplitude of the pulse, ADC γ, with γ typically being or 1. The disadvantage of such a simple method are obvious, the center of gravity can not represent correctly ades outside of the detector, but it works sufficiently well as a seed for the more complex likelihood methods. Figure shows the result of the vertex reconstruction for 1 TeV ades using the mpe-time likelihood method. The reconstructed y coordinate of the vertex behaves similar to the reconstructed x coordinate and is therefore not shown. The resolution for ades inside the AMANDA-II detector is about 5 m for the x and y coordinate, and slightly better for the z-coordinate. The better resolution of the z coordinate is due to the smaller OM spacing in the vertical direction. The vertex resolution for ades inside the AMANDA-B1 detector is approximately the same if the fiducial volume is adjusted to a cylinder of 6 m in radius and ± m in height. In general, the mpe-likelihood method produces slightly better position resolution than the 1pe-likelihood method.

3 σ=5. m 5 xtrue xreco ztrue xreco-xtrue σ=.6 m Yreco 1 1 Xreco zreco - - zreco-ztrue Fig.. Left: reconstructed versus generated vertex coordinates for 1 TeV ades as obtained for the mpe-likelihood method. The dotted lines indicate the borders of A MANDA -II. Right: Distribution of the difference between reconstructed and generated vertex coordinates, obtained for ades inside a fiducial volume roughly of the same dimensions as A MANDA -II (a cylinder of 1 m radius and ± m height) and fitted with a Gaussian. The y coordinate behaves as the x coordinate and is therefore not shown Zreco Fig. 3. Reconstructed coordinates of a YAG-laser light source in A MANDA -II. The full line is the experimental data and the dashed line is a Monte Carlo simulation of the corresponding light source. The vertical bar indicates the true position (which is known with 1 m accuracy). The 1-pe time likelihood-method has been used for reconstruction. for the expected number of photo-electrons as a function of distance (Askebjer, 1995) The reconstruction performance, as obtained from Monte Carlo simulation can be verified with the help of in-situ light sources. A Nd:YAG laser at the surface operating at 53 nm can be used to inject light pulses into optical fibers connected to nylon diffuser balls located at.3-.5 m from almost every OM in the detector. The position of the OMs, and hence the diffuser balls, is known with approximately 1 m accuracy (Andre s, ). The light output of a diffuser ball is assumed to be isotropic. The result of the reconstruction for a single diffuser ball is shown in figure 3. The agreement between experiment and the Monte Carlo simulation is reasonably good. The distributions are narrower than seen in fig., where the difference arises due to different optical ice properties at 53 nm compared to Cherenkov light (OM sensitivity peaks at nm) (Woschnagg, 1999). E d/λattn e, () d p where λattn = λeff scatt λabs /3 is the attenuation length. At Cherenkov wavelengths the attenuation length is 9 m. We have also used the fact, that the intensity scales linearly with the ade energy. I is a normalization constant which, in principle, is also dependent on the angle between the direction of the ade and vector joining the ade vertex with the OM and in the OM orientation. The probability for observing a hit from a ade can now be expressed as µ I Phit = 1 Pnohit 1 e µ. (5) We fit this expression to Monte Carlo simulations, averaging over angle and OM orientation. For the free parameter we obtain, I = 1. GeV 1. Finally, one adds the probability for observing a noise hit, Energy reconstruction + Pnoise Phit Pnoise. Phit = 1 Pnohit = Phit Energy reconstruction is also based on a maximum likelihood method, where the likelihood is given by the probability of observing a certain hit-pattern. We first derive a simple function for parametrization of the hit probability. For a point-source, and distance larger than the effective scattering length, d >> λeff scatt, there is a simple expression The functional dependence of equation () is illustrated in figure. A likelihood function can be constructed as Y Y L= Phit (E, d) Pnohit (E, d). (7) all hit OMs all un-hit OMs (6)

4 P hit log 1 (E/GeV) distance / m Fig.. Hit probability from equation (6) as a function of the ade energy and distance log 1 E reco Maximizing L provides the most likely value of the energy. In principle, one can use this likelihood also to reconstruct the vertex, however the resulting vertex resolution is considerably worse than the one obtained from a time likelihood reconstruction. The energy reconstruction is therefore seeded by the output of a vertex reconstruction. Figure 5 shows the performance of the energy reconstruction for ades of four different generated energies (.1, 1, 1 and 1 TeV). The vertex is restricted to lie inside a fiducial volume, a cylinder of radius 1 m and height ± m. The energy resolution is about.1-. on a logarithmic energy scale, with systematic shifts of similar magnitude. The energy reconstruction works best at intermediate energies of 1-1 TeV. For 1 TeV energies, a saturation of the reconstructed energies becomes visible. It can be explained by noting, that at these energies the event radius begins to outgrow the dimensions of the detector. As can be seen from figure, 1 TeV ades at the center of the detector will illuminate practically the entire AMANDA-II detector. Without the restriction that the vertex lies within the fiducial volume, the energy resolution mainly broadens due to events with miss-reconstructed vertex. With simple quality cuts applied (Taboada, 1) (Kowalski, 1999), one obtains comparable energy resolution even for ades outside the fiducial detector volume. The energy resolution of ades in the AMANDA-B1 detector worsens by about 3%. Also the energy saturation is about half an order magnitude lower. This is simply due to the fact, that AMANDA-B1 is smaller. Again we can use in-situ light sources for verifying the performance of the reconstruction. LEDs working at 37 nm represent a Cherenkov light emitting point-source fairly well. While the absolute intensity can only be estimated very Fig. 5. Distribution of reconstructed energies for monoenergetically simulated ades of energies,.1, 1, 1 and 1 TeV. The vertex is restricted to lie inside a fiducial volume, a cylinder of radius 1 m and height ± m. vaguely, the relative intensities for a given LED can be estimated by counting the relative number of photo-electrons observed by the surrounding OMs. In order to reduce the systematic error of a non-linear ADC response, one uses OMs which are read out optically so that photo-electrons are likely to be resolved. Furthermore OMs at an intermediate distance from the LED are chosen so that the hit multiplicity is low (around 1) but hit rates are still significantly above the noise rate. Figure 6 shows the distribution of reconstructed energies for an ultra-violet LED operated at two intensities, I 1 and I. With the method explained above, we estimate the relative intensities to, I /I 1 =. ±.. This estimate of the relative intensity is consistent with the ratio of reconstructed energies. The resolution of the corresponding LED energies is better than for ades of similar energies, since the spatial resolution of the LED due to its fixed location is better. Note that here the energy scale is linear. 5 Direction reconstruction For reconstruction of the direction of the ade a likelihood function similar to equation (7) is used (Taboada, 1) (Kowalski, 1999), µ g(cos ψ)i E d e d/λattn, (8)

5 1 15 I1: µ=9 GeV σ=8 GeV 1) (Kowalski, 1999). The performance of the vertex-position and energy reconstruction has been verified with in-situ light-sources References I: µ=939 GeV σ=18 GeV E reco /GeV Fig. 6. Distribution of reconstructed energies for two runs of different intensity of an ultra-violet LED. where g(cos ψ) is a function of the ψ, the angle between the ade direction and the vector joining the ade vertex and the OM. This function can be fitted to Monte Carlo simulations using Legendre polynomials. Zenith angle resolution obtained with this method is 3. There are no calibration light sources with Cherenkov-like angular light output available, and thus this procedure hasn t been tested with data. Andrés E. et al., Astropart. Phys. 13 (), 1 Askebjer P. et al., Science 67 (1995), 117. Hill G. et al. Proc. of Int. Cosmic Ray Conf., Salt Lake City (1999), HE 6.3. Hundertmark S., PhD Thesis, Humboldt Univ., Berlin (1998). Karle A., Proc. of Workshop Simulation and Analysis of large Neutrino Telescopes. DESY-PROC , DESY-Zeuthen (1998), 17. Kowalski M., Diploma Thesis. Humboldt Univ., Berlin (1999). Lipari P., Astropart. Phys. 1 (1993), Miočinović P., PhD Thesis. Univ. of California at Berkeley., Berkeley (1). Pandel D., Diploma Thesis. Humboldt Univ., Berlin (1996). Taboada I., Kowalski M. et al., Proc. of Int. Cosmic Ray Conf., Hamburg (1), Wiebusch C., Proc. of Workshop Simulation and Analysis of large Neutrino Telescopes. DESY-PROC , DESY-Zeuthen (1998), 3. Wiebusch C., PhD Thesis. RWTH, Aachen (1995). Wischnewski R. et al., Proc. of Int. Cosmic Ray Conf., Hamburg (1), 115. Woschnagg K., Proc. of Int. Cosmic Ray Conf., Salt Lake City (1999), HE Conclusions The reconstruction capabilities of AMANDA for detection of ade-like events were presented. Using the timing information of the hits, the vertex resolution is about 5 m for the x and y coordinate and slightly better for the z coordinate. Using the information of whether a certain OM registered a hit or not, the energy-resolution is.1-. on a logarithmic scale. The method works best in the intermediate energy region, where the flux of atmospheric neutrinos drops to that of an hypothetical astrophysical neutrino flux of observable strength. Due to the low background of ades from atmospheric neutrinos (charged current ν e as well as neutral current ν µ interactions), this crossing point is at energies around 1 TeV (Wischnewski, 1) and therefore, depending on the spectrum of astrophysical neutrinos, an order of magnitude lower than in the case of ν µ. The presented method of energy reconstruction works up to energies of about 1 TeV. Above that energy, saturation of the reconstructed energy sets in, as the typical event size outgrows the size of the detector. Reconstruction of the direction has been mentioned only briefly, as it represents work in progress. Current methods have a resolution of the zenith-angle of 3. While this is certainly too large for a point-source analysis, it helps to reduce the background of atmospheric muons (Taboada,