Sean Grullon with Gary Hill Maximum likelihood reconstruction of events using waveforms

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill2 Overview Introduction & Motivation Likelihood Formulation waveform-loglikelihood-reco project in IceCube software framework Preliminary Results using IceCube simulated Data Current Development and Future Directions

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill3 Introduction & Motivation All reconstruction algorithms in IceCube are ported from AMANDA. Originally developed for AMANDA’s primary DAQ. –records Time over Threshold (TOT), the leading edge time (LE), and the Peak Amplitude. The Full waveform is not captured Incorporates Leading Edge time & peak amplitude information only. Uses the Pandel function which analytically parameterizes timing PDF in ice. Ice assumed to be homogeneous. Full detail regarding the AMANDA reconstruction algorithms can be found at Nuc. Ins. Meth. A (2004) Focus of talk is on the development of a new reconstruction aglorithm using the full waveform

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill4 IceCube waveforms IceCube’s Analog Transient Waveform Digitizer (ATWD) captures and digitizes full waveform in situ with a ~ 420 ns time window Should prove powerful for high energy & non-contained events. FWHM of Waveform Depends linearly on the distance from the event to the optical module New algorithms need to be developed to take advantage of full waveform information A high priority since deployment has already begun. ATWD Sample # Voltage (mV)

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill5 Example Extracted waveform Event generated by Nitrogen laser located at a depth of 1850 m in AMANDA Array. Pulse Shapes recorded at 3 distances from laser. (45m, 115m, and 167m)

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill6 Likelihood Formulation How can you formulate a likelihood function with the full waveform at your disposal? With the full waveform, we know: –arrival time distribution of the photons –the probability of these arrival times. Given an expected distribution of photons μp(t), what is the probability of observing a waveform f(t)? –p(t) is normalized timing PDF, μ is the total number of expected photons, given either numerically or analytically. – f(t) is your observed waveform

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill7 Probability of f(t) given p(t)? Suppose you bin the photon distributions into k time bins: The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins:

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill8 This product turns into something useful….

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill9 We have our Likelihood Function Take the negative log of it

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill10 Our likelihood function – cont. Likelihood minimized for every optical module

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill11 Where is this applicable? We assumed we knew the photon arrival times precisely, or have a waveform made from the superposition of many photons. If we have a non-delta function time response, this form is still applicable as long as our PDF is slowly varying over the region described by the OM time response. Should be the case for our optical modules, typical pulse widths are narrow relative to the scale of expected photon arrival time distribution.

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill12 IceCube software framework The IceCube software framework is called IceTray. unified object oriented C++ framework for handling online filtering and offline-software for reconstruction, analysis, and simulation. IceTray modules operate on the IceCube data stream. Modules perform specialized tasks such as reconstructions, calibrations, etc. Uses boost C++ libraries for offline data. Data can be saved into a binary format or XML format.

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill13 IceCube data stream

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill14 Waveform loglikelihood reconstruction project This likelihood reconstruction algorithm is currently implemented in IceTray. Currently reconstructing electromagnetic cascades. User has the option of selecting an analytical PDF (Pandel function) or a numerical PDF. The numerical PDF in IceCube is Photonics, a numerical framework that simulates photon propagation in the ice. Uses the SIMPLEX minimizer. Uses calibrated ATWD waveform directly.

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill15 Preliminary Results 2500 cascade events with an energy of 100 TeV generated Generated with a random vertex position and direction. Full IceCube simulation used. ~¼ of the events are not contained in the array (Up to 50 m away) Free parameters of fit are the vertex, the energy, and the time. Results compared to the AMANDA style cascade reconstruction algorithm.

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill16

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill17 Preliminary Results Using Full Simulation: Vertex X RMS: 38.15RMS: Accurate Vertex Reconstruction requires directional fit Results not a final performance indication

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill18 Preliminary Results Using Full Simulation: Vertex Y RMS: 36.32RMS: 48.62

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill19 Preliminary Results Using Full Simulation: Vertex Z RMS: 29.65RMS: 51.23

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill20 Preliminary Results Using Full Simulation: Energy

VLVnT2 November 8 th -11th 2005 Sean Grullon w/ Gary Hill21 Current Development and Future Directions Currently testing new Photon tables with 3-D photon tracking as the PDF for reconstruction Investigate reconstructing the cascade direction. Make the project part of the official IceTray release. Look at some sort of hit cleaning to improve results Improve algorithm performance for non- contained events. Look at other event types Optimize the performance