The Pennsylvania State University

The Graduate School

Department of Astronomy and Astrophysics

A SEARCH FOR TEV NEUTRINO EMISSION WITH ICECUBE

COINCIDENT WITH SWIFT BAT FLARES FROM BLAZARS

A Dissertation in

Astronomy and Astrophysics

by

Steven Michael Movit

c 2011 Steven Michael Movit

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

December 2011 The dissertation of Steven Michael Movit was reviewed and approved1 by the following:

Douglas Cowen Professor of Physics, Astronomy and Astrophysics Dissertation Adviser Chair of Committee

Eric Feigelson Professor of Astronomy and Astrophysics

Stephane Coutu Professor of Physics, Astronomy and Astrophysics

Tyce DeYoung Assistant Professor of Physics

Steinn Sigurdsson Head of the Department of Astronomy and Astrophysics Graduate Program

1 Signatures are on file in the Graduate School. iii Abstract

One of the most important unsolved questions in astrophysics is the source of the ultra-high energy ( >TeV scale) cosmic rays (UHECR) that are seen here on Earth by detectors such as Auger. One potential source for these UHECR is black hole engines in active galaxies. It is known that active galaxies have jets of relativistic charged particles that follow their rotational axes, however the composition of these jets is still unknown, and hadrons must be present in the cosmic accelerators. Neutrino detections coincident with photon flaring from AGN would provide strong evidence for hadrons in blazar jets. If no hadrons are present, gamma-ray production in AGN jets would be driven by electron synchrotron-self Compton processes. In an attempt to test the hadronic hypothesis for blazar jets, we developed a catalog of significant hard x-ray photon excesses from blazars using the Swift BAT mon- itoring catalog and a new wavelet approach adapted from the statistics literature. This approach was applied for the first time to an astronomical time series. We processed the Swift monitoring data from April 2008 until May 2009, to correspond with the 40 string season of IceCube, a neutrino detector located at the South Pole. Previous analyses have produced a neutrino data set known as the Point Source selection, which was a starting point for our timing and spatial coincidence analysis. This sample of IceCube events contains only muon neutrino charged-current events which were reconstructed with a very high degree of confidence. We strongly reduced noise contamination of the final sample through simple cuts on the photon flares and some new techniques in the wavelet denoising involving testing overlapping time series. While no on-source neutrinos were found, this analysis remains an excellent prescription for future studies, and we have set upper bounds on neutrino flux from each of the four AGN from which X-ray flares were 7 6 2 seen, ranging from 3.23 10− to 3.82 10− GeV/cm /sec. · · iv Table of Contents

List of Tables ...... vi

List of Figures ...... viii

Acknowledgements ...... xiv

Preface ...... xv

Chapter 1. Introduction ...... 1 1.1 Overview ...... 2 1.2 A Brief Description of BL Lac Objects ...... 2 1.3 Neutrino Production and Interaction ...... 5 1.4 Feasibility Calculation and Summary ...... 8

Chapter 2. Instrumentation ...... 12 2.1 SwiftBAT-X-rayInstrumentation ...... 12 2.2 IceCube: Neutrino Instrumentation ...... 15 2.3 DetectorConfiguration...... 18 2.4 Previous Time-Dependent Searches for Point Source Neutrinos . . . 18

Chapter 3. Statistical Technique ...... 23 3.1 TheoryandExample...... 23 3.2 Wavelets and Astronomical Data ...... 37 3.3 Sensitivityplots...... 39

Chapter 4. Verification of Methods using Swift BAT Data ...... 51 4.1 BlankPointings...... 51 4.2 Mrk421Datafrom2006...... 61 4.3 OtherTestsandSummary...... 62

Chapter 5. Results: Catalog ...... 65 5.1 SourceCharacteristics ...... 73 5.2 Flare results and characteristics ...... 75

Chapter 6. Neutrino Analysis ...... 86

Chapter 7. Unblinded Results, Summary and Conclusions ...... 94 7.1 FinalResults ...... 94 7.2 Conclusions and Future Possibilities ...... 99

Appendix. Source Code ...... 101 v

Bibliography ...... 118 vi List of Tables

2.1 Adapted from Tramacere, et al, 2009 - this shows the very bright and active nature of Mrk 421 during the spring and summer of 2006. Asterisks indicate events which the workers declared would have “triggered” the BAT...... 14

3.1 For three different Gaussians with σ not divisible by two, 250 realizations with white noise were created, and the passing rate with and without tiling was recorded, with a significant improvement due to tiling . . . . 45

4.1 34 different blank pointings showed 35 total significant excesses, 29 of them were classified as possible physical excesses. The first two columns of the table give the coordinates of the center of the blank pointing bin, the next column provides the starting MJD for the flare, the fourth and fifth columns note whether or not an excess occured near MJD 53790 or during the IC 40 season, and the final two columns are the category in which we have placed the excesses and the normalized power for the excess. 55 4.2 Categories of excesses and the number of occurrences in the blank point- ings. These categories were subjective and determined by eye. No so- phisticated numerical scheme for identifying the classes was needed since negative excesses and large gaps were the only two categories to be out- right rejected, and these events can be easily identified by eye...... 56 4.3 This table summarizes the results for flares classified as unphysical. The first two columns provide the coordinates for the blank pointing bin, then the next two columns show if the excess occurred near MJD 53790 or during IC 40, and the final column shows the category we have placed theexcessin...... 56

5.1 Sources for the Wavelet-based Catalog ...... 67 5.2 Summary of the findings of the Swift BAT Monitoring wavelet based catalog search. The normalized power, start and end MJD, duration, and comments are included for each flare...... 82

6.1 This table shows the blinded results for the four catalog sources. Mrk 421 and 1ES 1741 did not have any on source neutrinos, so a significance for the result cannot be found. Instead, the probability of detecting at least 1 neutrino in the source bin is given. The significance cannot be calculated for two of the sources, since no on-source counts were seen, so the column reads “NA.” The final column is the probability of seeing at least as many counts as were detected in the signal bin due to pure noise. 93 vii

7.1 Unblinded results: The probability of seeing at least one neutrino given the null hypothesis is calculated; no significances are found because no on-source neutrinos were seen. After the source name, the first column is the RA coordinate in degrees for the source, the second column is the declination of the source in degrees, the third column is the ratio between the source bin and the rest of the declination band, the fourth column is the number of counts in the entire declination band surrounding the source, the fifth column is the product of A and the number of dec. band counts which is the expected number of neutrinos in the source bin, the sixth column is the number of neutrinos seen in the source bin during the flares, the seventh column is the number of on-source neutrinos seen, and the eighth column is the probability of seeing at least one background neutrino in the signal bin during the flare time given the effectivebackground...... 96 7.2 Upper bound on neutrino flux in the source bins based on figures from Abbasi & Collaboration (2011) ...... 98 viii List of Figures

1.1 The AGN zoo by type and radio luminosity. The lower the type number, the more luminous the source class. Blazars are viewed head-on and thus display special properties such as relativistic beaming. Most of the sources explored in this study are blazars, however there are examples of radio loud quasars and one LINER galaxy, which stands for Low- ionization Nuclear Emission Region. Adapted from Tadhunter, 2008. . 4 1.2 Taken from Dumm (2011), this figure shows the effective area for neu- trino detection in the muon channel for astrophysical neutrino sources 2 with E− spectra in various declination bands. This information coupled with the theory from Kappes et al. (2007) allows for a calculation of an expected flux from a flare of a given length from a given AGN at a given energy. Each colored trace corresponds to the effective neutrino detec- tion area for a given declination band on the sky, as a function of energy, forthe40-stringIceCubedetector...... 10

2.1 Schematic representation of the BAT detector - the coded mask casts a shadow on the detector so that the direction of incoming photons can be determined with a Fourier signal processing algorithm. Source: Krimm (2004) ...... 14 2.2 The last DOM deployed on the 86th string of IceCube...... 16 2.3 Schematic of the inner workings of a DOM. The DOM is a glass pressure sphere housing a photomultplier tube and on-board electronics to digitize the signals from the PMT and send them to the DAQ system on the surfaceviaEthernetcables...... 17 2.7 Taken from Abbasi & Collaboration (2011), this figure illustrates the position of all 86 deployed strings of IceCube. The 2006-2007 season ran with 22 deployed strings and was known as IC22, represented by black circles. The blue circles represent the 40 string detector (IC40) which ran from 2007-2008, and the white circles represent the full detector as currentlydeployed ...... 20 2.4 Drawing of a DOM’s positioning on a string. The orientation of the DOM is important because the DOM contains LED’s that are used for calibration and emit in the ultraviolet to mimic Cherenkov radiation. . 21 2.5 Schematic diagram of the entire IceCube array, including the IceTop surface tanks and the low-energy extension known as DeepCore. . . . . 22 2.6 Taken from Kestel (2004), this figure illustrates the timing of short pulses sent from the GPS clock in the IceCube Laboratory on the surface down to DOM’s hundreds of meters deep in the ice cap to keep the internal DOMtimeaccurate...... 22 ix

3.1 The Haar wavelet, the first conceived and simplest of all. In physical terms, the wavelet sums all the points in each of two adjoining bins and finds the difference between them. Ψ represents the relative height of the wavelet function; the function is normalized by an extra factor of 1 for √2 each level of additional detail...... 25 3.2 Figure reproduced from Modi et al. (2004) This figure demonstrates the dyadic nature of the wavelet transform and the way that the levels rep- resent different scales in the time series...... 27 3.3 This sample input time series with measurement errors demonstrates how the multi-resolution decomposition is performed when combined with Figures3.4and3.5below...... 28 3.4 The result of the multiresolution decomposition of the time series in Figure 3.3. The vertical black lines represent the detail coefficients. Each X-axis point represents a different spatial scale from left to right in the original time series. The relative sizes of each coefficient within a level of detail are important, but the comparison of coefficient magnitudes is not possible from this plot because the scale is different for each level. All coefficients are subject to the same universal threshold, at the proper scaleforthelevel...... 29 3.5 Shown in this figure is the inverse transform of the thresholded time series. The structure at y=0.75 was not significant with respect to the universal threshold of 0.6 that was applied, so those points now have a y-valueofzero...... 30 3.6 Input sine wave for denoising, error bars=0.05; the thickness of the trace is due to the error bars on each point of the densely sampled curve. A sine wave was chosen because the shape of the curve is familiar to the reader and the effect of the denoising is obvious in Figure 3.8 ...... 33 3.7 In this figure, the red and blue lines are the positive and negative thresh- olds for each level. Coefficients that extend beyond the threshold lines are statistically distinct from white noise. Those that fall in between the colored lines are zeroed out since they are deemed to be noise coefficients. The y-scale varies for each level of decomposition, but the relative heights of each coefficient in a given level can be compared on the same scale. . 34 3.8 The red trace is the output of the inverse transform of the denoised time series from Figure 3.7. The error bars=0.05, and the thickness of the gray trace is due to the error bars. The errors are accounted for in the denoising technique, and the shape of the reconstructed series differs from the sine curve because the insignificant wavelet coefficients have beenzeroedout...... 35 3.9 Input time series for the Maximum Coefficient Magnitude plot, this is a square wave across 80 samples, shifted 238 samples from the center of thetimeseriestosample750...... 41 x

3.10 This Maximum Coefficient Magnitude plot shows the oscillation of the sensitivity of the algorithm as a function of the position of the input signal in the sample time window. A clear oscillatory pattern is shown in this plot, and there is a clear minimum as well as a maximum, demonstrating the importance of the tiling to try and increase the sensitivity of the algorithm. The x-axis contains the horizontal shift away from the center of the sample window, and the y-axis represents the absolute value of the three largest coefficients in the multiresolution decomposition. Triangles represent the largest coefficient in a given decomposition, asterisks the second largest, and circles the third largest. Even though these coeffi- cients are obtained from square wave input data, the oscillatory pattern intheMCM’sisangular...... 42 3.11 Ideal sensitivity plot, where the input signals are placed at the high- est MCM location in the sample window. This ideal sensitivity is not achievable in the data as the ideal placement for the start and end times of the underlying flares is not known. All data points had a constant measurementerrorforthisplot...... 46 3.12 Sensitivity plot for the simulated measured Monte Carlo data. The sensi- tivity plots for the three different signal profiles: square wave, Gaussian, and “sharkfin” all follow the same curve. This allows us to state that we can determine the sensitivity of the algorithm to signals of arbitrary shape and extent in time. The black trace represents a Gaussian sig- nal with σwidth = 0.879, the blue and purple traces are sharkfins with a width=50 and 25, respectively, and red and green are square waves with width=8and4,respectively ...... 47 3.13 Sigmoid curve fit to sensitivity plot data - The black trace represents a Gaussian signal with σwidth = 0.879, the blue and purple traces are sharkfins with a width=50 and 25, respectively, and red and green are square waves with width=8 and 4, respectively. These are the same data showninFigure3.12withthesameaxes...... 48 3.14 Three Gaussians integrated to find the normalized power: the first is an ordinary Gaussian with σ = 1 and an amplitude of 0.4. The second Gaussian is identical to the first except 0.2 is added to all the y-values. The third Gaussian is the same as the first Gaussian except the y-values are all divided by two and then are added to 0.2. The normalized powers for the Gaussians are respectively 40,960 , 102,320, and 122,800. These results show that the normalized power is not standardized, meaning that the baseline is not subtracted off of the time series. However, the baseline for all of the positive detections in our catalog is close enough to zero that this should not be a significant effect on our catalog, as the absolute value of the flux measurements affects the normalized power, not the absolute distance from the baseline. If the absolute distance from the baseline were the determining factor, the normalized power of the first two Gaussians would be identical...... 50 xi

4.1 Log histogram for the significances from 105 blank pointings, over 2 mil- lion samples. The overlaid blue curve is a normal distribution with a mean of zero and a standard deviation of 1.032. The data are indistin- guishable from a normal distribution according to many tests such as the K-S test, D’Agostino’s test, etc ...... 53 4.2 This is an example of a type 1 excess, which consists mainly of an un- physical negative excursion. All negative excursions will be reconstructed with a positive component, since a function composed entirely of Haar wavelets must integrate to zero, however excesses in this class are clearly reconstructing a negative dip in the time series with positive spikes to either side of the dip to allow for the integral to be zero. The green points represent the measured data, and the blue and pink curves are two of the three overlapping reconstructions obtained with tiling for this excess. The third tiling is not displayed because the structure was not foundtobesignificantinthattile...... 57 4.3 This is an example of a type 2 excess, a spike with a physical appearance. 58 4.4 This is an example of a type 3 excess, an excess with a large gap in it. 58 4.5 This is an example of a type 4 excess, an oscillatory excess...... 59 4.6 This is an example of a type 5 excess, a spike with a symmetric appear- ance in the denoised series, with a negative spike that is around the same magnitude as the positive spike, and no other significant structure. . . 60 4.7 This is a histogram of the normalized power calculated using the custom trapezoid method, calculated for all of the physical-appearing excesses from the blank pointing sample. We have placed a cutoff (blue line) at a normalized power of 50. This is near the 33% sensitivity mark on our theoretical sensitivity cuve. We have chosen this value so that only one of the largest excesses is not distinguishable from physical flares by any of our other cuts, and also based on the results of our catalog in Ch 5. One excess over five years shows that we do not have to be concerned about background events overpowering our signal in the photon data. . 61 4.8 Three flares from 2006 were detected in the BAT monitoring data and published in (Tramacere et al. 2009) and marked on the plot with blue vertical lines (a) was a flare with small scale structure that was significant after denoising, with a normalized power of 791.02. (b) this flare was not nearly as strong of a detection, with a normalized power of 42.39. Tra- macere and collaborators had the flare beginning at MJD 53909.6, which is almost exactly the start time found in one of our tiled reconstructions. (c) While Tramacere et al. had this flare beginning at MJD 53847, we found instead a larger-scale excess beginning earlier at 53839. Since this excess overlaps the Tramacere et al. trigger time, we consider that a detection. The yellow trace in this figure is far below the data points simply because the significant structure that it finds has a much smaller amplitude than the rest of the data, i.e. the denoising is subtracting off a baseline that is found to be insignificant. The normalized power for thisflarewas135.1 ...... 63 xii

5.1 Sigmoid curve fit to sensitivity plot data with overlaid flares in blue. The green line represents the flare from Mrk 421 with a normalized power of 800thatisnotshownontheplot...... 66 ∼ 5.2 PKS 1510-089 flares in 2008 were seen in many different wave bands, including with the Swift BAT. The flaring was so significant in the BAT that an Astronomer’s Telegram detailing the flaring was issued. This flare was not detected with our wavelet methods because the data points were excluded form the sample due bad data quality flags set by the Swift team. The X-ray data does not seem to coincide with the flaring activity in the TeV energies as the R-band data do. Figure taken from Marscher etal.(2010) ...... 72 5.3 Here are first the three overlaid fits on the raw time series for 1ES 1741, then the raw time series (blue-green trace with star markers) overlaid on the three interpolated tilings (square markers), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in two of the three overlaid tiles (variation in the third tile is likely due to the oscillations in the sensitivity to the signal based upon its temporal placement in the window.) Two actual measured points are part of the detected excess. Each tile begins one-third of the way through the previous tiles time series, at the point in the raw data point that corresponds to that point intheinterpolatetimeseries...... 75 5.4 Here are first the three overlaid fits on the raw time series for 4C 06.69, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the excess was found to be significant in two overlapping time windows. This flare is composed of far more data points than the flare in 1ES 1741; it is far better sampled in the original time series(inblue)...... 76 5.5 Here are first the three overlaid fits on the raw time series for Mrk 421, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in two of the three overlaid tiles (variation in the third tile is likely due to the oscillations in the sensitivity to the signal based upon its temporal placement in the window.) The flare began well before the data-taking for IC40 did, so there is quite a bit of structure that is not included here...... 77 xiii

5.6 Here are first the three overlaid fits on the raw time series for the first of two flares from QSO B2356, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in three overlapping tiles, which is a very strong indication that the structure is physical. B2356 is an excellent addition to our catalog because it is the only Southern Hemisphere source from which we see significant flare, and we also see flaring at two different times duringtheIC40season...... 78 5.7 Here are first the three overlaid fits on the raw time series for the second flare from QSO B2356, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was again presentinthreeoverlappingtiles...... 79 5.8 UnphysicalflarefromQSOB0706+591 ...... 84 5.9 QSO B0829 also had a significant structure which turned out to be just a negative excess, an artifact of the source extraction process from the codedmask...... 85

6.1 A visual representation of the IceCube detector “uptime” compared to theflaretimes...... 88 6.2 Taken from Abbasi, et al, 2011, this figure shows the IceCube Point SpreadFunction ...... 90 6.3 Taken from Ackermann (2006), this figure shows how the declination band is situated on the sky with respect to the signal bin...... 92 xiv Acknowledgements

First and foremost, I want to thank my family and friends for all of their support, understanding, and patience with me as I finished this marathon. I would not have made it without you. I want to thank my thesis advisor Doug Cowen, who started me on the interest- ing path of particle astrophysics and helped me to blur the divisions between astronomy, physics, and statistics to learn some interesting things. Doug also gave me the op- portunity to attend a UNESCO summer school in Trieste, where I learned how many advantages and opportunities I had been given in comparison to some, and to always make the most of them. I want to thank the other members of the Penn State IceCube group throughout the years, and most especially Tyce DeYoung, Pat Toale, and Brendan Fox. Ty’s shared interest in astronomy kept me on the right path for this project and led to many inter- esting discussions, as did his passion for statistics. Ty was an especially great help at the very end of the thesis process, and I am appreciative of that. Pat Toale is a great person and a fine teacher, and he always had time to explain something for the first time or the hundredth time; he’s a man of great patience. Brendan is a tenacious researcher, incredibly detail-oriented, and a good friend. Brendan never gives up and will often put the needs and interests of others before his own. I doubt that this project would have been completed without Brendan’s help and advice. I especially want to thank Arsen Hajian for his continued interest and guidance for the past thirteen years. Arsen is always ready with sage advice and has always kept me on the right path with regard to developing skills and abilities that are universally applicable and useful in many industries and contexts. I want to thank my good friends Gustav Wikstrom and Martijn Duvoort for all of the fun and cooperation as we finished our IceCube theses, and all of the other fine people that I met through the IceCube collaboration. I also want to thank Brendan Miller for his invaluable help with editing and revisions. Finally, without the lessons learned in the classroom with Richard Wade, Mike Eracleous, and my fine professors at Rice in the statistics department, this project would never have gotten off of the ground. xv Preface

“The stars we see on earth are the mere scat- tered survivors that penetrate our misty atmo- sphere. But now at last I could realise the meaning of the hosts of heaven!” H. G. Wells, The First Men in the Moon xvi To my beautiful wife Marcela and my wonderful son Boaz. I did it all for you. 1

Chapter 1

Introduction

One of the great challenges facing physicists today is the mystery of the “cosmic accelerators”, which provide tremendous energies to protons and nuclei, some of which reach the Earth, known as cosmic rays. The question of how these ultra-high energy (UHE) particles can reach energies of EeV (1018 eV) or higher is still unanswered. These incredibly energetic nuclei are likely produced by some of the most extreme processes in the universe, and are a product of some of the most intense environments possible. It is thought that supermassive black holes (billions of solar masses) are involved in many of these processes, and can be found at the heart of most, if not all, galaxies in the universe. Studying these cosmic accelerators will also help us gain knowledge of extreme black hole environments, which due to their incredible gravity, density, surroundings, and distance from the Earth, can be particularly difficult to study. A correlation between flaring activity in high-energy photon sources and neutrino emission has been theorized (Rachen & M´esz´aros 1998); in addition, were a correlation to be seen with flares from AGN jets, it would be strong evidence for a highly accelerated proton component. Rachen and Meszaros write: “Photohadronic neutrino production is a result of the decay of charged pions originating from interactions of high energy protons with ambient low energy photons.” It is accompanied by the production of gamma rays from neutral pion decay. If protons can be proven to be a part of blazar jets, then a strong clue as to the identity of some of the cosmic accelerators will be obtained. At one point, results from the Pierre Auger observatory (Zavrtanik 2000) showed a rough correlation between cosmic ray directions and active galactic nuclei (AGN) (Abraham et al. 2008). Additional data collection proved the correlation was much weaker than originally thought, closer to a significance of 40% than the original 67% (Abreu et al. 2010). For this study, we used a wavelet-based technique to identify previously undetected flares from the Swift satellite, and then searched for correlations in space and time between these flaring objects and neutrinos detected by the IceCube Neutrino Observatory. There are many exciting possible discoveries to be made with IceCube, including the first ultra-high energy ( TeV) neutrino definitively originating from outside of the ∼ Solar System, the first confirmed ultra-high energy charged current neutrino cascade, and the first multimessenger detection (neutrino correlated with photon flare). While neutrinos from outside of the Solar System were discovered by Kamiokande in Japan after Supernova 1987-A, no TeV range neutrinos have been seen that can be attributed to sources outside of the Earth’s atmosphere, let alone outside of the galaxy. Further, as the field of astronomy and especially particle astrophysics evolves from its qualitative beginnings through an era of quantitative and simulation-based as- trophysics into an age of true astronomy experiments, such as the Large Synoptic Survey 2

Telescope (Krabbendam & Sweeney 2010), it is vital that tools for characterizing huge volumes of data be developed. In addition, it is crucial to develop tools for finding the most important and interesting periods to study in time series sampled multiple times per day over a period of years, thousands of samples per source. The Sloan Digital Sky Survey was a trailblazer in terms of processing an incredible amount of data, e.g. the seventh data release of Sloan included over 100,000 quasars with photometric observa- tions in five different bands covering 10,000 square-degrees of sky (Schneider et al. 2010). Sloan led to groundbreaking results such as z > 6 quasars (Fan et al. 2001), some of the most distant objects ever discovered. Also, repositories of public domain data and much freer access to cloud and cluster computing allow for a myriad of archival studies, which can make use of many of these same tools. The quantitative method for identifying flare periods in a years-long time series from hundreds of sources that we will detail in this thesis will be a valuable step forward in this process. Distinct “periods of interest”, where potential neutrino sources are in states of high photon emission could be correlated with neutrinos to search for physically and statistically significant correlations, which is the overall aim of this study.

1.1 Overview

The thesis will be structured in two parts: the first will focus on building a catalog of high-flux time periods from Swift monitoring data of active galactic nuclei, and the second will detail correlating these flaring periods with well-reconstructed muon neutri- nos from the 2008-2009 season of IceCube. The catalog was built using data from the Swift Burst Alert Telescope (BAT), which are archived on the web, and wavelet tech- niques specially adapted for data with uneven sampling in time and with well-determined error bars which vary with each observation. The wavelet techniques are implemented in R, a freeware statistical scripting language with a large community-developed library of useful add-on packages. The flares were then correlated in time and space with the point source neutrino sample from the 2008-2009 IceCube season, henceforth referred to as “IC40”, to look for evidence of neutrino production concurrent with X-ray flares from active galaxies. This study was an attempt to address the possible connection between photon and neutrino emission from blazars, to introduce a new technique for processing large and difficult-to-process time series to astrophysics, and to pave the way for more studies combining all-sky monitor data and high quality neutrino data. We hope to find more evidence to help determine the presence or absence of protons in AGN jets, as well as create a quantitative flare catalog from the Swift BAT.

1.2 A Brief Description of BL Lac Objects

Active galactic nuclei (AGN) have a very loose and inclusive definition: they emit radiation at all wavelengths and are variable across the spectrum. More specifically, most strong radio sources are elliptical galaxies (Peterson 1997). In the class collectively known as blazars, there are two distinct classes of objects: BL Lac objects and optically violent variables (OVV’s). In this study we are focusing on BL Lac objects. Classic BL Lac objects have a “featureless” spectrum, with a distinct lack of 3 emission or absorption lines. Every known blazar has a radio component to its spectrum (Peterson 1997). Radio emission is historically important when studying the discovery of the active galaxy zoo, however that discussion is beyond the scope of this thesis. In any case, the radio luminosity of AGN is far weaker than the UV/optical continuum, by a factor of three in the “radio-loud” objects and a factor of six in “radio-weak” objects. The radio emission likely comes from different physical processes than the ultraviolet and optical emission. Detailed studies of AGN in the radio show radio emission from the central object, as expected by the broad definition of AGN, but also complex and extended radio structures are found surrounding many active galaxies. These structures can be outflows of gas in clouds or an interaction between AGN-ejected material and the surrounding medium, but the structures that are of direct relation to this study are the jets from AGN (Peterson 1997). The jet structures in AGN, relativistic outflows of particles from the central disk along the magnetic field lines of the galaxy, are the main structures of interest with respect to this study. Years of careful study which led up to the unified geometric models of AGN showed distinct structures in the radio components of AGN. There was evidence of so-called “superluminal motion”, where projection effects cause narrow relativistic structures to appear to be moving faster than c, which then led to models of the relativistic energies in the jets (Tadhunter 2008). It was then postulated that these narrow jets would appear differently to observers at different orientation angles with respect to the AGN and especially to the jet (Blandford & Konigl 1979). While the radio observations did not give the whole picture of the interrelation- ships between the different types of AGN, the idea of a unified geometric model of an AGN evolved to its current state: a central supermassive black hole surrounded by a hot disk radiating as a multi-temperature black body, with gas clouds orbiting, some near to the nucleus and others far away. The model includes a torus of obscuring dust, a corona of high energy electrons, and powerful relativistic jets. Figure 1.1 below shows a way of characterizing AGN by radio loudness and “type.” The seminal review of AGN unification is Antonucci (1993), and the reader is referred there for in-depth coverage of AGN unification. Since the first radio “trails” were seen as weak emitters surrounding elliptical galaxies, they were thought to be caused by the galaxies’ sweeping up of intracluster gas as they moved through their clusters. It became apparent that some of the radio trails were continuously fueled. Better resolution showed knots and clumps in the jets, and it became clear that the trails in many cases were actually jets of relativistic particles emanating from the galactic nuclei. The jets needed to be relatively stable and traveled along the magnetic field lines of the galaxy, which keeps them collimated. (Begelman et al. 1979) The process by which protons could possibly be accelerated to relativistic speeds and thus be high-energy neutrino producers is known as Fermi acceleration. Fermi acceleration occurs when there is a bulk flow of charged particles, like in an AGN jet. The basic principle is that a majority of the material is moving in a bulk flow, but individual particles can get a “kick” in velocity due to collisions with the bulk flow. The kick is in a random direction, but some particles will continue to be kicked along the direction of the jets. Eventually, some of these particles will be accelerated to relativistic 4

Radio Quiet Radio Loud Radio Quiet Quasar Radio Loud Quasar Radio Lobe Types Broad Absorption Steep Radio Spectrum Type 1 Flat Radio Spectrum Line (BAL) Fanaroff Riley Class I Seyfert 1 Broad−line Radio Galaxy Fanaroff Riley Class II

Type 2 Seyfert 2 Narrow−line Radio Galaxy

Type 3 LINER Weak−line Radio Galaxy

Type 0 Blazars: BL Lac/OVV

Fig. 1.1 The AGN zoo by type and radio luminosity. The lower the type number, the more luminous the source class. Blazars are viewed head-on and thus display special properties such as relativistic beaming. Most of the sources explored in this study are blazars, however there are examples of radio loud quasars and one LINER galaxy, which stands for Low-ionization Nuclear Emission Region. Adapted from Tadhunter, 2008. 5 speeds. (Peacock 1981) The simple rationale for the bulk flow to be fast enough to produce an environment capable of kicking protons to relativistic speeds is that the process which accelerates the electrons to relativistic speeds while close in to the AGN accelerates any protons present, as well. The actual presence or absence of hadronic material as well as either a dense medium surrounding the jet or high enough energy photons being available for photohadronic processes are the factors in whether neutrino production is possible. The reader is referred to the review by Atoyan and Dermer (2004) for in-depth discussion of these topics. To get a handle on the processes occurring in an AGN, it is necessary to observe the complete spectrum in as many wavebands as possible, the spectral energy distribution (SED). These complex objects have structure on many different spatial scales and are composed of both thermal and non-thermal emitters. The original surveys for locating and identifying AGN were always focused on a particular waveband, and thus led to a biased sample which selected AGN with specific properties. Again, the optical properties of an AGN tend to correspond to very specific characteristics of the AGN and very specific structures (Wilkes 2004). While these properties are crucial for traditional studies of AGN and for determining the interior structures of the nucleus, we are most interested in the jets of AGN, which means the highest energy parts of the SED are crucial to understanding the physics in these extreme, relativistic, beamed structures. The most extreme processes in blazars produce very high energy photons, in the TeV range. The mechanism behind these emissions is not entirely clear, but studying the SED in the X-rays and gamma-rays of these objects will hopefully provide clues to the origin of these photons. The processes likely include inverse Compton scattering, where lower energy photons are scattered by charged particles and become much higher energy photons, and synchrotron self-Compton processes, where the same electrons that are emitting synchrotron radiation due to the presence of strong magnetic field lines and relativistic velocities of the electrons are also upscattering these same photons to higher energies. The reader is directed to Celotti et al. (2007) for a detailed description of how structures in the disc and heading outwards towards the jet produce high energy photons and result in certain features in the SED. The reader is then referred to Sokolov et al. (2004) and Sokolov & Marscher (2005) for a detailed description of hadronic and leptonic processes and their effects on the SED’s of blazars, and Chiang & Bottcher (2002) have a discussion of blazar synchrotron and synchrotron self-Compton processes.

1.3 Neutrino Production and Interaction

Neutrino production in AGN could take place in a few possible locations: the accretion disk (Bednarek & Protheroe 1999), or interactions within the jet or between the jet and the surrounding medium (Atoyan & Dermer 2004). While all of these scenarios for neutrino production are possible, it is most likely that the production of astrophysical neutrinos from AGN will come from either p-p interactions from collisions within the jet or from p-γ interactions between external x-ray photons surrounding the blazar jets. The three flavors of neutrinos, tau, muon, and electron, all interact through the weak force through two different channels: charged current and neutral current interactions. 6

While there are two interaction channels and three flavors of neutrinos, phe- nomenologically there are three distinct interaction signatures that IceCube will see. The first signature, and the easiest to reconstruct, is the track-like signature of the muon charged current interaction. The muon decay time is long enough that the parti- cle travels an appreciable distance through ice. Since the muons travel faster than the speed of light in ice, which is about 75% of the speed of light in a vacuum, Cherenkov radiation is produced. The radiation is produced all along the path of the muon, leaving a track-like signature in the detector. The second signature seen in IceCube is caused by the electron neutrino charged current interaction, along with the neutral current reaction from all three flavors. These reactions produce a near-spherical expanding ball of light known as a “cascade.” The direction reconstruction that is relatively straightforward for the track-like events is far more difficult in the cascade channel. However, the background from atmospheric cosmic ray interactions that is so prevalent in the track-like case is around two orders of magnitude lower in cascades. Occasionally, a bremsstrahlung interaction can occur in the track-like case, and a combined track and cascade signature is seen. The final interaction channel is the charged current interaction from tau neutri- nos. The decay time for a tau particle is far shorter than that of a muon, so a track-like signature is not seen below E 100TeV. Instead, two cascades very close together ν ∼ is the signature of this interaction (several other signatures are possible, but will not be discussed since this analysis focuses on track-like events). See Cowen & the Ice- Cube Collaboration (2007) for a detailed summary of the different tau interactions and their branching ratios. Only the muon track signature was used in this analysis. There are two branches of particle interactions from which these neutrinos would be created, photohadronic processes and hadron-hadron processes. The first neutrino production channel is the p-γ or photohadronic process. When a proton and photon combine to form a short-lived delta resonance, the products are either a proton and a neutral pion or a neutron and a charged pion. The neutral pion decays to two photons, but the charged pion will decay first to a muon and a muon neutrino, and then the muon decays to an electron plus another muon-flavored neutrino and an electron-flavored neutrino; three neutrinos are produced in total(Atoyan & Dermer 2003). Experimental measurements of properties of the ∆(1232) resonance are the basis for predictions on production cross-sections for pions and used to determine the ratio of energies in produced neutrinos to produced photons and protons. The cross-section for the ∆ resonance at an energy of 232 GeV is 500 µbarns, and the ratio of neutral to charged pion production is 2:1. The pions then decay and produce photons and neutrinos with a ratio of Eγ : E of 3:1. These decays are known as electromagnetic cascades and the photon energy ν P gets re-processed through these reactions to produce an SED with a spectral slope of P α = 2. This re-processing through a second resonance and multiple interaction sites in an AGN jet leads to quite a different Eγ : Eν of 1:1. Thus we can assume that the output energy in neutrinos is roughly the same as that in photons. (Mucke et al. 1999). P P As for the proton-proton interactions, they will result either in a π0 and two protons or a neutron, a proton, and a π+. The pions then decay as described above (Rose et al. 1987). 7

Dumm (2011) contains the effective area (Aeff ) for a 40-string Icecube detector in the muon neutrino channel from sources at various declinations at various energies, as shown in Figure 1.2. Once the neutrinos are produced, they likely pass undisturbed through cosmolog- ical distances due to their extremely low interaction probability. This unique property of neutrinos is what makes them so well-suited as astrophysical messengers. This low interaction probability is a double-edged sword, however. An incredibly large detector volume is necessary to achieve a reasonable probability of detection. It is for this reason that a cubic kilometer-scale detector such as IceCube is necessary to detect astrophysi- cal neutrinos. When high-energy neutrinos do interact within the IceCube volume, it is generally with quarks in the nuclei in the ice. While the interactions discussed above for dense environments produce one muon neutrino for every two electron neutrinos through photohadronic processes and only electron neutrinos through hadron-hadron interactions, this is not the expected flavor ratio for observations on Earth. The ratio of νe:νµ:ντ is approximately 1:2:0 at the production site, but through neutrino flavor oscillation, 1:1:1 is the expected ratio on Earth. Neutrino flavor oscillation was originally proposed as the solution to the so-called “solar neutrino” problem. In 1968, Davis, Harmer, and Hoffman attempted to measure the solar neutrino flux. A dearth of neutrinos from the sun was seen; the flux was around 2 to 3 times smaller than expected. (Davis et al. 1968) The answer to this problem is neutrino flavor oscillation; over time, neutrinos change flavor as they travel through space from a distant source towards the Earth. Muon neutrinos are the easiest to reconstruct with high precision for a few specific reasons. First of all, the interaction length is too short for a muon that forms in the Northern Hemisphere to pass through the Earth and enter IceCube from underneath. Using the Earth as a filter, we can be confident that all “upgoing” muons, those origi- nating inside of the Earth, have come from neutrino interactions and not from cosmic ray interactions in the atmosphere of the Northern Hemisphere. This filter allows for a considerable reduction in the constant background of 2,600 trigger events per second due to down-going atmospheric muons. Downgoing νµ, those originating in the Southern Hemisphere, are much harder to distinguish from the cosmic ray background. Above an energy of 1 PeV, however, the distinction becomes clearer due to a sharp decline in the atmospheric muon flux at these high energies (Halzen 2006). The decline is due to the fact that these high energy muons enter the Earth prior to decaying. The muons then lose energy while traveling through the rock and then decay in the ice at lower energies (Halzen & Klein 2010). See Halzen (2006) for a detailed discussion of the interactions in the Earth and atmosphere of cosmic ray muons and neutrinos. In most scenarios, we expect muon neutrinos to be present when UHECR pro- duction is taking place, so we look for muon charged-current interactions in IceCube, as they are the easiest to detect and their direction can be reconstructed with the best pre- cision. The challenge in detecting neutrinos in general is separating the small amount of signal from an enormous background of muons produced from cosmic ray interactions in the atmosphere. In the case of astrophysical neutrino detections, atmospheric neutrinos are a source of background, even though there are important physics analyses based on atmospheric neutrinos. The keys to detecting astrophysical neutrinos and distinguishing 8 them from the background are timing information and directional reconstruction. Even when the downgoing muon background has been mostly eliminated through event cuts based on Monte Carlo simulations as well as data, atmospheric neutrinos and astrophysi- cal neutrinos are identical particles. Astrophysical neutrino candidates can be correlated with photon observations from likely neutrino sources, as atmospheric neutrinos are es- sentially evenly distributed in time. If a neutrino source has an increase in neutrino flux with a corresponding increase in photon flux, a time window can be placed around the photon flare and since the background is constant with time and the neutrino flux increases, the signal to noise ratio in that window should be much higher.

1.4 Feasibility Calculation and Summary

To show that this neutrino analysis is a feasible study, we will calculate a simple expected number of neutrinos from an AGN flare with reasonable physical parameters. Mrk 421, considered by many to be a prime source for neutrino production has a declina- tion of 38.21◦. This places Mrk 421 in the declination band from 30◦ to 60◦ in Figure 1.2. As explained in Chapter 2, IceCube’s effective area for neutrino detection is reasonably constant across large bands of declination. IceCube has an effective area (A ) of 10m2 ν ≈ at this declination, for a range of energies from 10 TeV to 1 PeV, according to Figure 2 1.2 (Dumm 2011). For this feasibility calculation, we will use a constant Aeff of 10m . We will use the careful derivation of neutrino flux from a photon flare from Kappes et al. α (2007) to do our calculations. First, an E− energy dependence with a cutoff energy ǫp is assumed for a spectrum of accelerated protons:

α dNp Ep − Ep = kp exp − (1.1) dEp 1T eV ǫp

12 1 2 1 The variable k is a normalization constant with units of 10− TeV− cm− s− . The ǫp corresponding neutrino spectrum produced is then (where ǫν = 40 ):

Γν dNν Eν − Eν = kν exp (1.2) dEν 1T eV −s ǫν

The values for kν in Kappes et al. (2007) generally range between 1 and 2, so we will calculate a value of the expected number of neturinos for both values. The rate of neutrino production can then easily be found: dN dN ν = dE A ν (1.3) dt ν eff dE Z ν Finally, we integrate over time to obtain a total number of events in the example flare: dN N = R dt ν (1.4) ν Θopt dt Z 9

where RΘopt is a factor to account for the inefficiencies of the signal bin placed around a point source. We numerically integrated dNν for energies between 10 TeV and 1 PeV dEν (the valid range from Kappes et al. (2007)) and found a rate of 0.05 k A neutrinos/second. Since the spectrum is constant in time we can just · ν · eff multiply the result by the total length of the flare in seconds and the efficiency factor R: N = A T (0.05 neutrinos/sec) R k . We obtain an expectation of 0.00093 to 0.0018 ν eff · · · · ν neutrinos depending on the value chosen for kν for a three-day flare. While this is not a large number of expected neutrinos per flare, detecting neutrinos coincident with multi-day flares is not outside the realm of possibility. 10 ed ysical , for the / GeV µ ν E pled with the theory from Kappes et al. 10 log e area for neutrino detection in the muon channel for astroph of a given length from a given AGN at a given energy. Each color ) ) or a given declination band on the sky, as a function of energy ° ° ) ) ) ° ° ° ) ° , -0 , -60 , -30 , 60 , 90 ° ° ° ° ° , 30 ° = (0 = (-30 = (-90 = (-60 = (30 = (60 δ δ δ δ δ δ 2 3 4 5 6 7 8 9 4 3 2 1 -1 -2 -3

10

µ Effective Area [m Area Effective

] 10 10 10 spectra in various declination bands. This information cou

ν 10 10 10 2 2 − Fig. 1.2 Taken from Dumm (2011), this figure shows the effectiv neutrino sources with E (2007) allows for a calculationtrace of corresponds an to expected the flux40-string from effective a IceCube neutrino flare detection detector. area f 11

We have introduced the concept of AGN jet physics as well as the production methods for neutrinos in AGN jets. We have also briefly described the main background that is seen with the IceCube observatory, downgoing muons. Using cuts described in Chapter 6, the main background of downgoing muons is effectively eliminated, leaving a flux almost entirely composed of atmospheric neutrinos. The atmospheric neutrinos occur at a constant rate, in our sample at about 60 per day. The atmospheric neutrinos can be used for many interesting physics analyses, but in a search for astrophysical neutrinos, they become background. If information beyond the neutrino reconstructions could be used to identify astrophysical neutrinos then they could be distinguished from atmospheric neutrinos. In this thesis, we have used temporal information obtained from studying the high-energy X-ray flux from blazars to identify periods with significant excess photon flux. If the proportionality between neutrino emission and photon emission in blazars discussed above holds true, then we expect a higher flux of neutrinos from the blazars during these flaring periods. Since the background is constant in time and we are setting strict time limits on possible excesses of astrophysical neutrinos, we find significant gains in signal-to-noise ratio. The next chapter discusses the instrument used to observe the high-energy X-rays and neutrinos. 12

Chapter 2

Instrumentation

2.1 Swift BAT- X-ray Instrumentation

The Swift satellite, headquartered at the Pennsylvania State University, is com- posed of three different detectors, the Burst Alert Telescope (BAT), the X-Ray Telescope (XRT), and the UltraViolet/Optical Telescope (UVOT) (Hurley 2004). We will focus almost exclusively on the BAT detector because all of the photon data analyzed in this study were collected solely by BAT, and come from the online BAT Monitoring Cata- log(Krimm 2010). Hurley writes: “The Burst Alert Telescope (BAT) covers the 15 150 − keV energy band and will detect < 100 bursts per year. It comprises a CdZnTe (CZT) detector array with an area of 5200cm2 and a coded aperture mask covering 1.4 sr of the sky.” Positions fit by the BAT are accurate to one to four arcseconds (Barthelmy et al. 2005). The CZT detector is masked by over 50,000 lead tiles. The mask is around five times the area of the detectors, and serves to cast a shadow on the detector. Vigneau writes: “To cast a distinct shadow on the detector array, the mask panel needed to allow 35% transmission of X-rays at 10 keV while the tiles blocked about 90% of the X-()rays at 150 keV.” The key to a successful coded-mask detector is a random but known pattern so that photon incidence directions can be reconstructed (Vigneau & Robinson 2003) The difference between a coded-mask detector and a standard imaging detector is that the point spread function (PSF), the response of the detector to a single point source, is spread across the entire telescope (Skinner 2004). Skinner writes: “The disadvantage of the multiplexed approach is that reconstruction of the intensity at a particular point in the field of view involves harvesting photons from all over a detector.” It is important to note that random noise will contaminate every pixel in every event due to the unique PSF. Coded mask methods are necessary since it is not possible with current technology to focus photons with energies of these magnitudes for a conventional imaging system (Barthelmy et al. 2005). Even if focusing systems are developed, they will not have the enormous sky coverage of coded-mask detectors which is vital for monitoring transient sources (Skinner 2004). When the BAT is not in alert mode and pointed at a burst or a transient, it observes a large number of sources across the sky, making full use of the wide field-of-view of the instrument. Once every five minutes, all 32,786 elements of the detector are producing an individual spectrum. (Barthelmy et al. 2005) These spectra become part of a deep all-sky survey as well as being compiled in a transient monitoring database online (Krimm et al. 2008). The BAT data collected are still the shadows collected by the coded mask system. The Fourier transform of the image is actually a map of the sky after some further processing. An algorithm is used to detect bright sources in the sky map, then these sources are iteratively removed, backfilled with an estimate of the background spectrum behind the source, then further sources are sought 13

(Barthelmy et al. 2005). The peak detection algorithm and background calculation can cause “negative” photon counts which are merely artifacts of the process and do not represent a physical measurement. In addition, the errors in the photon counts produced by the algorithm follow a Gaussian distribution, in contrast to a pure photon counting experiment where Poisson errors are expected. Both the negative photons and the Gaussian errors are important to wavelet analysis of the monitoring data. While the All-Sky Monitor (ASM) on the Rossi X-ray Timing Explorer (RXTE) satellite (Swank 1999) does produce similar data to the Swift BAT monitoring data, the measurement errors on the data are not as accurately determined as they are for the Swift BAT(Fidelis 2011). Because the RXTE ASM data do not have error bars that are extremely well-determined, we have chosen not to use these data for this study and to focus solely on the Swift BAT monitoring results. The Swift/BAT Hard X-Ray Monitor page (http://heasarc.nasa.gov/docs/ swift/results/transients/) collects all of the orbital measurements and daily average fluxes for 939 known X-ray sources over the entire lifetime of the Swift mission into one convenient resource. The data have a quality flag based on extremely negative counts or large error bars. There are daily and orbital average curves plotted for all the objects; these plots are useful for monitoring “at a glance”, and each source has all of its observations stored in ASCII files in table form for easy offline processing. This monitoring repository makes Swift the ideal instrument to use for an all-sky flare search since its data products are so readily available. In addition, a detailed analysis was performed and is documented on the web page, enhancing the scientific utility of the data (Krimm et al. 2009a). The BAT had already detected flaring behavior from the blazar Mrk 421 on at least two occasions. The first was a series of flares in 2006 (summarized below in Table 2.1), culminating in a huge flare seen in a wide range of energies from optical up to TeV gamma-rays (Tramacere et al. 2009). The flaring behavior duration was on the order of months and Mrk 421 reached the highest X-ray flux ever recorded until that date. These types of flares are easily apparent and do not require special algorithms to detect. The Swift online triggering system flagged them as transients as well (Palmer 2011). While these flares are not invisible to the casual observer, they do provide solid evidence that significant flaring from blazars can be seen by Swift and detected in the monitoring data. The Swift team in fact published an Astronomer’s Telegram (Lichti et al. 2006) to announce the flare to the community and to mobilize follow-up observations from a myriad of other instruments. The second flare we will discuss occurred in March 2008, and was announced by an Astronomer’s Telegram as well (Krimm et al. 2008). This flare is of great interest because it occurred during the IceCube 2008-2009 season and thus is a candidate to be correlated with neutrino data, assuming it is detected by the wavelet-based flare detection algorithm. Below in Figure 2.1 is a diagram of the Swift BAT. 14

Fig. 2.1 Schematic representation of the BAT detector - the coded mask casts a shadow on the detector so that the direction of incoming photons can be determined with a Fourier signal processing algorithm. Source: Krimm (2004)

Table 2.1 Adapted from Tramacere, et al, 2009 - this shows the very bright and active nature of Mrk 421 during the spring and summer of 2006. Asterisks indicate events which the workers declared would have “triggered” the BAT. ObsId Date Start UT(s) XRT Exp(s) UVOT Exp(s) BAT Exp(s) 00206476000(*) 04/22/06 (*) 04:21 AM 10329 10337 15156 00030352005 04/25/06 06:22 AM 4885 1214 4927 00030352006 04/26/06 03:29 AM 3526 878 3567 00030352007 04/26/06 10:48 PM 1328 329 1343 00030352008 06/14/06 12:21 AM 3187 788 3318 00030352009 06/15/06 11:42 AM 5427 1336 2787 00030352010 06/16/06 12:33 AM 23327 5868 23693 00030352011 06/18/06 12:52 AM 33288 32468 33671 00030352012 06/20/06 11:59 PM 15009 0 15379 00030352013 06/22/06 01:08 AM 20213 20430 0 00030352014 06/23/06 09:25 AM 7916 0 7221 00215769000(*) 06/23/06(*) 03:44 PM 1109 1049 5207 00030352015 06/24/06 01:37 AM 12944 0 13191 00030352016 06/27/06 03:17 AM 3046 0 3080 00219237000(*) 07/15/06(*) 04:54 AM 1916 1915 6224 15

2.2 IceCube: Neutrino Instrumentation

The IceCube neutrino telescope is located at the Earth’s geographic south pole, and now consists of roughly a cubic km of instrumented polar ice. Glass pressure spheres contain large photomultiplier tubes as well as on-board electronics for timing synchro- nization, in-ice pulse digitization, and calibration sources known as “flashers.” These spheres and the associated electronics are known as Digital Optical Modules (DOM’s). The photomultipliers are produced by Hamamatsu Photonics and are 10 inch diameter R7081-02 photomultiplier tubes (PMT) (Abbasi et al. 2010). See Figures 2.2 and 2.3 below for a photo of a DOM and the schematic of the DOM design. The DOM’s are connected to sturdy cables and 60 of them are strung together to form what is known as a string. A hole in the ice cap is melted using a specially designed hot water drill, and the strings are lowered into the ice and tested through the deployment process. The ca- bles then collectively run into the IceCube Laboratory, where racks of specialized servers called DOMHubs collect all the raw pulses and pass them along to a triggering system. IceCube consists of three main parts, the IceTop array on the surface, the main IceCube array, and a densely-instrumented low energy section known as DeepCore for its location in the center of the main detector, lower down than the start of the main strings to avoid nearly all of the atmospheric muon background. The complete, main IceCube array consists of 78 strings of 60 DOM’s, plus 320 DOM’s frozen in blocks of ice in surface tanks (2.5 m2 circular tanks) for the IceTop array, and DeepCore provides another eight strings of 60 DOM’s for a total of 5480 DOM’s in the entire IceCube detector. The IceCube strings are instrumented from 1.45 km to 2.45 km below the surface, and the spacing between IceTop tanks is around 125 m (Abbasi et al. 2010). Figure 2.4 shows how the DOM’s hang on the strings. Relative timing between photon detections, known as “hits”, in a given event, as well as accurate time measurements for each event are crucial to the accuracy of IceCube detections and for correlation with photon events in multimessenger studies. In-ice dig- itization of detected pulses from the PMT’s helps with this synchronization, as signals are recorded immediately after detection and their integrity remains intact. In IceCube’s predecessor, AMANDA, signals were sent up to the surface in the main with an analog format, and the long travel through cabling often distorted the signal. The number of photoelectrons (NPE) reconstructed in a given event is a derived quantity; the NPE is found by integrating calibrated waveforms from the DOM’s. The DOM’s have two digitizers to allow for one to read out data while the other is recording. The DOM’s do have a saturation point, above which it becomes more difficult to determine an accurate NPE. The simpler reconstructions, which are also less computationally expensive, recon- struct the waveform from each DOM as if it came from a single photoelectron (SPE). More complicated reconstructions try to determine the number of individual photoelec- tron pulses represented by a waveform and are known as multi-photoelectron (MPE) reconstructions. When a high energy muon interacts with the ice in the instrumented volume of IceCube, Cherenkov light is generated along the path of the muon. This light is emitted at a characteristic angle, 41◦ from the track angle, which is known as the Cherenkov angle. Muons over 1 TeV in energy will create photon yields that are proportional to 16

Fig. 2.2 The last DOM deployed on the 86th string of IceCube. 17

Fig. 2.3 Schematic of the inner workings of a DOM. The DOM is a glass pressure sphere housing a photomultplier tube and on-board electronics to digitize the signals from the PMT and send them to the DAQ system on the surface via Ethernet cables. the energy of the muon. DOM’s close to the track of the muon receive the light directly, with no scattering, in a pulse of around 50ns in duration. As the light travels to DOM’s which are further away, they will scatter more, on a scale of 25m. DOM’s that are 160m away from the track will receive light on a pulse scale of 1ms (Abbasi et al. 2010). The in-ice digitization of events keeps the relative timing of events calibrated to the order of nanoseconds, but the absolute timing of events is calibrated with a system that sends and receives short pulses to the in-ice DOM’s, as shown below in Figure 2.6. Every minute or so, the mainboard on each DOM’s timer needs to be synchronized to GPS time with nanosecond precision to allow for proper intra-detector timing. A circuit on the surface sends a signal at a GPS-time, which is designated t1. The time at which the pulse arrives at the DOM is designated t2. A circuit on the DOM that is identical to the circuit on the surface sends the same pulse at a time designated t4. The cable (t4 t1 δt) transmission time t = − 2 − (Abbasi et al. 2009b). The accurate time resolution, both absolute time and relative, in-ice time, allows for precise reconstruction of muon track events in the IceCube detector. See Ahrens et al. (2004) and Neunhoffer (2006) for detailed descriptions of likelihood methods for timing and energy reconstructions in neutrino analyses. Specifically, while the orbital length of the Swift satellite is around 40 minutes, and nanosecond precision would seem to be unnecessary for correlating photon flares with neutrino events, the reconstruction of the muon track position to an accuracy of less than a meter is needed to reconstruct the direction from which the neutrino came. Errors in the reconstruction of the track 18 position as a function of time would lead to errors in the reconstructed angle from which the muon originated, and would hinder point source analysis by reducing the resolution.

2.3 Detector Configuration

This study was performed using the IceCube dataset from the 2008-2009 cam- paign which used 40 deployed strings of IceCube, and was known as IC40. Just under half of the instrumented volume of the detector had been deployed, with a map of the layout in Figure 2.7. The 22 string detector which was the configuration for the 2007- 2008 campaign (IC22) was essentially trapezoidal, and the 18 strings added for IC40 were arrayed in a fairly regular hexagon. The 40 string detector was quite regular in bands at constant Y in Figure 2.7; this lead to a homogeneity in declination in terms of instrumented volume as well as effective area; these are defined as declination bands. The IC40 season ran from April 4, 2008 until May 20, 2009, and was followed by a 57 string campaign from 2009-2010.

2.4 Previous Time-Dependent Searches for Point Source Neutrinos

The first underwater (or under ice) Cherenkov telescope ever deployed was Bail- kal in 1993 (Belolaptikov et al. 1997), in Lake Baikal, Russia. The first Baikal detector deployed had 36 photomultiplier tubes (PMTs) arrayed on three strings. As of 2008, operating with 200 PMTs, Baikal had not detected a significant point source of neu- trinos.(Wischnewski 2008). Thirty Burst and Transient Source Experiment (BATSE) GRB’s were correlated in time with Baikal detections that occured from 1998 until 2000. No coincidences were found, but a limit on the diffuse flux was found, which was 1.1 6 2 10− GeV/cm /s/sr (Avrorin, A. for the Baikal Collaboration 2009). This limit was · not competitive with limits set by the Antarctic Muon And Neutrino Detector Array (AMANDA) which will be discussed below, but it was 100 times lower than the limit set by Super Kamiokande, a detector optimized for lower energies (Swinbanks 1993). AMANDA (Abbasi et al. 2009c) was completed in 2000, located in the South Polar ice cap, at the geographic South Pole. AMANDA was comprised of 19 different strings of optical modules (OM’s) containing 20 cm photomultiplier tubes (PMT’s), a total of 677. AMANDA had an analog data acquisition system (DAQ) and used a variety of hardware and cabling to transmit signals to the surface. In 2003, the Transient Waveform Recorder (TWR) was implemented, allowing for the entire waveform from the PMT to be recorded for each hit OM. AMANDA ceased operation in August, 2008. Seven years of MuonDAQ data (data where properties of the waveforms are extracted and stored but the entire waveform is not recorded) from 2000 to 2006 were combined for a point source analysis over 1,387 days of uptime. Flux limits were found for 26 possible neutrino-producing AGN, including Markarian 421 and M87. No point sources were detected, and the one source that overlaps with our study, Mrk 421, was found to have an upper bound of 8 2 2.54 10− GeV/cm /sec . · ANTARES, (Aguilar et al. 2007), consists of 12 strings of 900 photomultiplier tubes, and construction was completed in 2008. ANTARES, like Baikal and in constrast to AMANDA, is an underwater Cherenkov telescope located off the coast of France. Five 19 out of 12 strings were deployed in 2007, and were used in the initial point source search, consisting of 140 days of live time. Both an all-sky scan and a pointed observations from likely neutrino sources were performed. Twenty-four sources were chosen for pointed observations, most of them located in the southern hemisphere, since unlike AMANDA, ANTARES is located in the northern hemisphere. Comparing these results to the Ice- Cube results is not easily done since the upper limits published by ANTARES are in number of neutrino events detected and not in units of flux(Salesa-Greus & ANTARES Collaboration 2011). The first IceCube point source search was performed with the 9 string detector with data from June until November 2006 (IC9). The most stringent limit set was on 7 2 neutrino flux from the Crab Nebula, at 2.2 10− GeV/cm /sec. Only around 10% of the · instrumented volume of IceCube was active for that study, which was mainly an analysis prescription for future data obtained by IceCube (C. Finley & for the IceCube Collabo- ration 2007). Time-dependent point source searches were first published by IceCube in Abbasi & Collaboration (2011). An untriggered search based purely upon potential sta- tistically significant excesses in the neutrino rate occurring within time windows of length up to 100 days was performed, both an all-sky search and a search based upon sources that are known to flare in the X-ray and gamma-ray bands. No significant excesses were found. However, the pointed search did result in upper limits on over 40 AGN. The tightest fluence limit was placed on PKS 2325+093 at 0.33 GeV/cm2. The other study published in that paper was based upon photon flare information. The Maximum-Likeli- hood Blocks method (Scargle 1998) was used to denoise the light curves. The hypothesis that the photon emission is correlated with neutrino emission was then used so that the light curves became neutrino probability distribution functions. Fluence limits were placed on eight AGN based on data from both IC22 and IC40. The tightest bound on fluence was found for PKS 1502+106, with 0.37 GeV/cm2 over an 8 day flare. 20

86-string Configuration 40-string Configuration 600 22-string Configuration

400

200

0 Y (Grid North) [m] -200

-400

-600 -600 -400 -200 0 200 400 600 X (Grid East) [m]

Fig. 2.7 Taken from Abbasi & Collaboration (2011), this figure illustrates the position of all 86 deployed strings of IceCube. The 2006-2007 season ran with 22 deployed strings and was known as IC22, represented by black circles. The blue circles represent the 40 string detector (IC40) which ran from 2007-2008, and the white circles represent the full detector as currently deployed 21

‘

Fig. 2.4 Drawing of a DOM’s positioning on a string. The orientation of the DOM is important because the DOM contains LED’s that are used for calibration and emit in the ultraviolet to mimic Cherenkov radiation. 22

Fig. 2.5 Schematic diagram of the entire IceCube array, including the IceTop surface tanks and the low-energy extension known as DeepCore.

Fig. 2.6 Taken from Kestel (2004), this figure illustrates the timing of short pulses sent from the GPS clock in the IceCube Laboratory on the surface down to DOM’s hundreds of meters deep in the ice cap to keep the internal DOM time accurate. 23

Chapter 3

Statistical Technique

Having established in Chapter 1 that a timing flare-based analysis easily increases signal-to-noise discrimination for neutrino detectors, and the theory behind tying X-ray flare times from an all-sky monitor to possible neutrino emission, we will introduce the concept of the wavelet transform as a method of finding flare times and eliminating noise to build a catalog. We begin with a definition of wavelet transforms and their similarities to Fourier methods, then we move on to denoising, then to a specific method of denoising that is well-suited to astronomical survey data, and then finally we use Monte Carlo simulations to test the efficacy of the denoising and other cuts in separating signal from background. We find that we can quantify the performance of the algorithm on a given flare based only on a derived quantity proportional to the integrated square of the flux, regardless of signal shape or the width-to-height ratio of the flare. Finally, we find that we can increase the sensitivity to lower fluence flares by using sample windows that overlap in time when denoising the full time series of observations for a given object. All time series analysis in this study was performed in the R scripting language (R Development Core Team 2009a), a freeware statistical scripting language with a large user-supported set of libraries for a variety of statistical and scientific endeavors.

3.1 Theory and Example

In essence, a wavelet transform is a generalized version of the Fourier transform. A standard Fourier transform is performed by convolving a function or discrete series with a sinusoid, a function of infinite width. In contrast, a wavelet transform uses a compact function, the wavelet, to preserve time information in the wavelet domain. This is impossible with a Fourier transform, due to the infinite range of sinusoids(Kovac 1998). A wavelet transform allows for the efficient represention of functions in a manner as localized as possible in time while preserving information in the transformed domain (Strang 1989). In this study, we make use of the Haar wavelet, which is the most basic wavelet, shown below in Figure 3.1. A Haar wavelet has a very simple physical interpretation: the discrete wavelet transform of a dataset using the Haar wavelet has coefficients equal to the difference between adjacent time bins. Haar wavelet coefficients represent the magnitude of the difference in the time series at the time represented on a given scale. In all cases, location in time is preserved in the wavelet domain so that a given wavelet coefficient corresponds to a defined set of points in the time domain. The transform to the wavelet domain records coefficients on different time scales dyadically (by powers of two), from all of the points in the series down to sets of two points. The complete set of wavelet detail coefficients, along with a complementary set of coefficients 24 known as approximation coefficients, as explained below, represents the entire time series uniquely. The largest wavelet coefficients correspond to the location in time and scale of the most significant structures in the time series. If a coefficient is found to be statistically significant, it indicates that the data points past the midpoint of a given Haar wavelet (i.e. at a given start time and on a given dilation scale) are significantly different from those before the midpoint. 25

1.0

0.5

Ψ 0.0

-0.5

-1.0

0.0 0.2 0.4 0.6 0.8 1.0 time (normalized)

Fig. 3.1 The Haar wavelet, the first conceived and simplest of all. In physical terms, the wavelet sums all the points in each of two adjoining bins and finds the difference between them. Ψ represents the relative height of the wavelet function; the function is normalized by an extra factor of 1 for each level of additional detail. √2

Since we are working with discrete time series in this study and not continuous functions, we will use the Discrete Wavelet Transform (DWT). The DWT is analogous to the Discrete Fourier Transform. When the discrete wavelet transform is used to compare 26 scales from two points up to the entire length of the time series it is known as the multi- level decomposition (Mallat 1989b), because it finds detail at all levels from the finest to the sum total of the series. “Detail” is the structure at a given time on a given scale (a length of 2i). Separating significant signal detail from background noise is the goal of any denoising. There are j 1 levels of decomposition for a given time series, where the − length of the series is defined as n = 2j . The coarsest level of decomposition is level 0, which corresponds to the entire data series and has just one coefficient. The finest level of decomposition, j 1, has 2j 1 coefficients and each corresponds to exactly two data − − points in the time series. The discrete wavelet transform has an exact inverse, just like the Fourier transform, which will convert a multi-level decomposed data set back into the original time series. See Figure 3.2 below for a schematic representation of the various levels of decomposition. We provide one more important definition: a “realization” is one particular “draw” from a statistical distribution, e.g. rolling a die and getting a “5”. The probability mass function (the equivalent of a probability distribution function for a 1 discrete set of outcomes) for a fair die is 6 for each face, but the single roll is a realization from that probability mass function. For a continuous distribution, a realization is a single sample from that distribution, and for a white noise Monte Carlo simulation, selecting a noise value for each simulated flux measurement is a realization. The DWT is usually calculated with an efficient method known as Mallat’s pyra- mid algorithm /citep192463. This method functions by decomposing the data level-by- level, using two matrices. The decomposition operates as a recursion, each iteration operating on the output from the previous, finer level of detail each time. The “detail” at a given level is stored in the wavelet decomposition, and a low-pass filter passes the remaining data on to the next coarser level of decomposition. The detail is removed like layers of an onion, and the next coarser level is found below. An important note is that at any given level of the decomposition, the data from all the coarser levels can still be obtained, as the low-pass filter essentially smooths out detail by factors of two at each recursion. Mallat’s algorithm provides an efficient recursive method of obtaining the wavelet transform of the astronomical data we input (Modi et al. 2004). 27

Fig. 3.2 Figure reproduced from Modi et al. (2004) This figure demonstrates the dyadic nature of the wavelet transform and the way that the levels represent different scales in the time series.

The following equations define a simple time series example that we will refer to several times:

y = 0.75, x = 0.4375, 0.625 = 1.5, x = 0.5, 0.5625 = 0, otherwise

This sample input time series is seen in Figure 3.3. Every data point is evenly spaced in time and all have the same measurement error of 0.1 in arbitrary units. The DWT was performed on the data set, the results of which are in Figure 3.4. A cutoff in absolute value is then applied, a value of 0.6, to all coefficients, and any coefficient with an absolute value which falls below this threshold is set to zero. This is known as a universal threshold, and thresholding will be described in detail below. The inverse transform was next performed, and the result is in Figure 3.5. It is clear that some of the structure in the original time series was not significant to the level of the universal threshold that was used, so that structure was deemed noise and removed from the time series. 28

1.5

1.0 y

0.5

0.0

0.0 0.2 0.4 0.6 0.8 1.0 time

Fig. 3.3 This sample input time series with measurement errors demonstrates how the multi-resolution decomposition is performed when combined with Figures 3.4 and 3.5 below.

We now describe in more detail the calculation of the DWT. The pyramid algo- rithm uses two matrix filters, labeled G and H, which are used respectively to remove each level of detail on a given timescale to obtain wavelet coefficients, and then to smooth out the time series so that the next coarser level of detail can be obtained. For a Haar wavelet, the matrices have a block diagonal form that is extremely simple. At the finest level of detail for this time series, level 3, the low-pass filter, the matrix that obtains the wavelet detail coefficients is 29

Wavelet Decomposition Coefficients Resolution Level 3 2 1 0

0 2 4 6 8

Standard transform Haar wavelet

Fig. 3.4 The result of the multiresolution decomposition of the time series in Figure 3.3. The vertical black lines represent the detail coefficients. Each X-axis point represents a different spatial scale from left to right in the original time series. The relative sizes of each coefficient within a level of detail are important, but the comparison of coefficient magnitudes is not possible from this plot because the scale is different for each level. All coefficients are subject to the same universal threshold, at the proper scale for the level. 30

1.5

1.0 y

0.5

0.0

0.0 0.2 0.4 0.6 0.8 1.0 time

Fig. 3.5 Shown in this figure is the inverse transform of the thresholded time series. The structure at y=0.75 was not significant with respect to the universal threshold of 0.6 that was applied, so those points now have a y-value of zero.

G: 1 1 00000000000000 √2 √−2 0 0 1 1 000000000000  √2 √−2  1 1 0 0 0 0 − 0000000000  √2 √2   000000 1 1 00000000   √2 √−2   00000000 1 1 000000   √2 √−2   1 1   0000000000 − 0 0 0 0   √2 √2   000000000000 1 1 0 0   √2 √−2   1 1   00000000000000 −   √2 √2    The corresponding “bandpass” matrix, which is essentially an average over the timescale at the given level, that then smooths out the data to the next coarsest scale is 31

H: 1 1 00000000000000 √2 √2 0 0 1 1 000000000000  √2 √2  0 0 0 0 1 1 0000000000  √2 √2   000000 1 1 00000000   √2 √2   1 1   00000000 √ √ 000000   2 2   0000000000 1 1 0 0 0 0   √2 √2   000000000000 1 1 0 0   √2 √2   1 1   00000000000000   √2 √2    For each coarser level of detail, there are two fewer wavelet detail coefficients, until level 0, which has only one coefficient. The single coefficient at level zero represents the difference between the right half of the entire time series and the left half. The dimensions of the successive G and H matrices are reduced by a factor of two for each recursion to achieve this. For Haar wavelets, G is intended to obtain the mean difference n j 1 between adjacent bins of size 2 − − and H is meant to take an average, where again n is the length of the input data series, n = 2j . These are intuitive conclusions based on the shape and normalization of the Haar wavelets, i.e. the wavelet is a subtraction of the left half of the included data from the right half, multiplied by 1 to normalize √2 n j 1 the sum. Because each coefficient only corresponds to 2 − − data points, the matrices have a block diagonal form. R’s sparse matrix code allows for efficient calculation of the wavelet transforms due to the block diagonal nature of the matrices. The values of the coefficients for this specific example at the finest level of detail are found by G c where c is the time series vector:

0 0 0 1 1 0 0 0 √−2 √−2   Coarser levels of detail are obtained by multiplying by H once for each level of coarseness beyond the finest level of detail (i.e. to obtain the coefficient at level 0, you would multiply G4H3H2Hc. In this particular notation, the exponent j represents the j 1 reduction of the dimensions of the block-diagonal matrices by 2 − ). For our example time series, this is equal to zero. In other words, G4 means that eight rows and eight columns are removed from the original bandpass matrix. Figure 3.4 shows a visual representation of the multi-resolution decomposition of the example time series. The detail coefficients that are extracted at each step, and not the structure left behind, are what are crucial to the denoising and are of the most interest. Harnessing the power of these numerical techniques, a technique known as “de- noising” or “thresholding” is used to remove noise contributions in the wavelet domain. Denoising relies on the fact that the wavelet transform of pure white noise is also white noise. Therefore if the noise coefficients, those below the threshold of significance, are zeroed out, what is left behind in the time domain is solely the signal contribution. A significance threshold is defined, below which the coefficients are considered indistin- guishable from pure background noise, and in our analysis, coefficients below threshold 32 are zeroed out before performing the inverse transform(Ogden 1996). There are many choices of thresholds to use in denoising, and the choice is made based upon character- istics of the data and the desired results of the denoising. The simplest threshold is a universal threshold, which is applied equally to all coefficients. Further refinements to the method include level-by-level thresholding, where a distinct threshold is calculated for each level in the multiresolution decomposition, and soft thresholding, where the significance is then used as a weight, and rather than an all-or-nothing calculation, each coefficient’s magnitude is reduced according to the calculated contribution from noise. Thresholding which is “all-or-nothing” is known as hard thresholding. We have chosen the Visushrink threshold, a universal threshold defined below, as it is the method that gives the greatest noise suppression possible (as discussed in Donoho et al. (1995) in great detail, at a scope far beyond this thesis), allowing us to look for signals that are lost to the naked eye but are still statistically significant(Kovac 1998). We now present a slightly more complex example of wavelet denoising to demon- strate the techniques described thus far. We have used traditional wavelet techniques, assumed a constant measurement error for all data points and evenly spaced in time. We begin with a simple sine wave, sin x, from X=0 to X=4.095, sampled in time (X) in increments of 0.001. The number of samples is key as it must be a power of two for traditional wavelet methods. The error bars are set deliberately to give each measure- ment an uncertainty of 0.05. The multi-resolution decomposition is then found for the ± time series, shown below in figure 3.6, and in this case, colored lines have been overlaid to show where the threshold lies with respect to the coefficients shown in figure 3.7. The absolute value of a coefficient must be greater than the hard threshold or the coefficient is set to zero. The threshold at each level of decomposition is represented in the figure below as the red and blue horizontal lines intersecting the wavelet detail coefficients. Coefficients above the red line or below the blue line are deemed to represent significant physical structure and are retained. Removal of insignificant coefficients, or denoising, is then done, followed by a reverse transformation. It is clear in Figure 3.8 that not all of the structure of the sine wave was statistically significant because of the measurement error, and therefore the red line representing the denoised series only contains the structure that is significant. The “stair-step” shape of the reconstructed series arises from the bipolar, rectangular nature of the Haar wavelet, as seen in Figure 3.8. 33

Fig. 3.6 Input sine wave for denoising, error bars=0.05; the thickness of the trace is due to the error bars on each point of the densely sampled curve. A sine wave was chosen because the shape of the curve is familiar to the reader and the effect of the denoising is obvious in Figure 3.8 34

Wavelet Decomposition Coefficients Resolution Level 6 5 4 3 2 1 0

0 512 1024 1536 2048

Translate Standard transform Haar wavelet

Fig. 3.7 In this figure, the red and blue lines are the positive and negative thresholds for each level. Coefficients that extend beyond the threshold lines are statistically distinct from white noise. Those that fall in between the colored lines are zeroed out since they are deemed to be noise coefficients. The y-scale varies for each level of decomposition, but the relative heights of each coefficient in a given level can be compared on the same scale. 35

Fig. 3.8 The red trace is the output of the inverse transform of the denoised time series from Figure 3.7. The error bars=0.05, and the thickness of the gray trace is due to the error bars. The errors are accounted for in the denoising technique, and the shape of the reconstructed series differs from the sine curve because the insignificant wavelet coefficients have been zeroed out.

We used the Visushrink threshold, √2 ln nσ (where n is the number of measured · points and σ is the calculated uncertainty for a given coefficient), for our physics analysis because it is the denoising technique that eliminates the most background possible, as explained below. In fact, simple properties of the Gaussian distribution allow for theoretical predictions on the rate of surviving coefficients due to pure white noise. This threshold is not very useful for function estimation (following the trend of the original data) because it is so aggressive. When the purpose is to look for large outliers, in this case flares, the noise suppression is quite desirable and the loss of small scale structure is acceptable. The “Strong Law of Large Numbers” states that the average of a large enough sample of numbers from a given distribution will approach the expectation value (Bauer 1996). It applies to the maximum absolute value of the wavelet coefficients for a pure white noise data set. Given that each time series Xn when transformed will have coeffi- cients that are also pure white noise, the following applies max X lim n 1 (3.1) √2 ln n → · 36 i.e. the largest noise value obtained will approach √2 ln n for large n. (Newland 1993) · We now need to appeal to Parseval’s theorem: the integral of the square of the time series is equal to the integral of the square of the wavelet coefficients, and this quantity is known as power. While more commonly used in Fourier methods, Parseval’s theorem is also applicable to wavelet transforms (Newland 1993). This power is also known as “energy”, and this theorem is known as the conservation of energy theorem for transforms (Modi et al. 2004). This theorem declares that the wavelet transform of white noise, which will integrate to zero, is white noise as well. Finally for large n, the following inequality applies (with c as an arbitrary tuning parameter):

√ √ 2 P ( Xn > c ln n) c 1 (3.2) | | ∼ n 2 − √cπ ln n (Vidakovic 1999). The optimum threshold for noise suppression (according to Vidakovic) is when c = 2, so the threshold (τ) is set to τ = √2 ln n, and a noise coefficient will · survive with probability 1 , or one in every four to five realizations for most data √2π ln n sets (the value is quite insensitive to n since the √ln n is a relatively flat function) (Vidakovic 1999). Thus, we have quantified the noise contribution in the cleaned time series. To try and understand the behavior of wavelet coefficients on a given signal with random white noise added, we may select a function chosen so that at the maximum shift (defined below), the maximum coefficient is exactly equal to the Visushrink threshold, √2 ln n. The theoretical survival rate for that particular coefficient would be 50%, since · the detail coefficients vary about their true values with a normal distribution, i.e. half of the time the value will oscillate above the threshold. Because the bulk of the noise contribution is assumed to be Gaussian (which we will confirm in the next chapter) , and we can find the true (expectation value) coefficients for noise-free functions by taking the wavelet transform of the original function with no noise added, and since the Visushrink threshold is well defined, it should be possible to predict the passing rate for a given input function with a fixed measurement error placed at a given shift in the sample window. However, the pass rate is not determined solely by the largest coefficient. Noise fluctuations can drive the second-largest, third-largest, or even smaller coefficients over threshold. Since again by Parseval’s theorem, white noise data translates to white noise in the wavelet domain equally distributed to all coefficients, we can calculate the conditional probabilities for any single one of the largest several coefficients to exceed threshold, which simply add since the coefficients are assumed to be varying independently. Below is a simple example to illustrate the theoretical pass rate, and results from Monte Carlo simulations to confirm the pass rate. In Figure 3.9 there is a square wave with a height of 0.5 and a width of 80 points, and the sample window has n = 1024 samples. We define a quantity called “maximum coefficient magnitude” (MCM) , which is the coefficient with largest absolute value. In this case there is an MCM of 1.8119. Since √2 ln 1024 = 3.7233, (1024 is the number · of points in the time series) we can solve for σ50%, the value of the error bars where we expect the coefficient to survive 50% of the time. In this case, that value is 0.4867, 37 the quotient of the MCM and the threshold. σ50% is the value ofσ ¯ so that half of the maximum coefficients are elevated above threshold by noise. The next two smaller coef- ficients have magnitudes of 1.5625 and 1.4375, and differ from the MCM by 0.2495 and 0.3745 respectively. We state the “average error” because we simulate the error bars on each point to vary on a uniform distribution to add another layer of realism to the simulations. The wavelet coefficients will vary with a normal distribution, as explained earlier. For the MCM, the fluctuations will cause half of all realizations to produce a coefficient larger than the true coefficient, and thus passing threshold. For the next two coefficients, less than half of the realizations will exceed threshold, because a larger pos- itive fluctuation is required for the coefficient to exceed threshold. Each coefficient has the following survival probability, with the lower limits adjusted to reflect the relative magnitude of the coefficients:

P = 1 ∞ N(0, 0.4867) = 0.5 1 − 0 R P = 1 ∞ N(0, 0.4867) = 0.304 2 − .2495 R P = 1 ∞ N(0, 0.4867) = 0.221 3 − .3745 R In the above equations, N(a, b) is a normal distribution with mean of a and standard deviation of b. The sum of the probabilities for all the permutations where at least one of the first, second, or third largest magnitude coefficients passing threshold yields a total probability of 0.729 that one or more surviving coefficients exits after denoising. Out of 120 Monte Carlo realizations run to test this prediction, 89 of them had surviving coefficients, or 74.2%. In this case as well as many others tested, the theoretical passing rate is quite accurate.

3.2 Wavelets and Astronomical Data

In this study, however, we are working with astronomical data, which tend to have two aspects that make traditional wavelet denoising techniques less-than-ideal for noise reduction: astronomical data tend to be sampled irregularly in time, and astronomers tend to obtain careful measurement errors, which can vary for each data point in an observation. Traditional wavelet techniques do not account for error bars at all, let alone heteroscedastic (varying) errors. A novel approach to wavelet denoising was developed by Kovac & Silverman (2000) which addresses these serious issues. This method differs from traditional wavelet methods because the errors on the input series, if known, are also decomposed. The wavelet decomposition provides the covariance matrix for each level of decomposition. Thus it is possible to propagate the measurement errors from the astronomical data into the wavelet domain and to obtain an error on each coefficient. Significance testing on these coefficients becomes much more powerful because we know how certain we are of the value of each coefficient. To account for the uneven sampling, a simple linear transformation is used to interpolate the data. Furthermore, since the interpolation is linear, the errors propagate 38 in quadrature, so the covariance is very easy to calculate using only the two points located on either side, leading to a covariance matrix with a block-diagonal form. Once a covariance matrix is calculated for the interpolated data, the Mallat’s Pyramid algorithm is applied to the covariance matrix to obtain the progressively smaller matrices for each level of decomposition. The diagonal of each transformed matrix is the variance for the coefficients at that level. In addition, wavelet techniques require an input data set with a length of 2n, as seen with the dyadic nature of the wavelet, so interpolation allows for datasets that are originally of arbitrary length. We chose a linear regression for several reasons, as other models such as an au- toregressive fit could have been used instead. First, Kovac and Silverman used a linear interpolation in the literature, and the corresponding R code for linearly interpolating the time series data and then passing it to the Kovac-Silverman wavelet technique was already available. Second, the ease of error analysis has already been mentioned. Third, while an autoregressive model potentially could better predict the structure between the samples, it would impose a parametric structure on the analysis that we had studiously tried to avoid. Fourth, we did not wish to further complicate the algorithm numerically, as a simple technique has value when it is presented to the wider community. If we start with a covariance matrix Σ for the input data (a diagonal matrix of the squared measurement errors, since the observations are assumed to be independent and thus have no covariance terms, and a block-diagonal after interpolation), it is postulated that we can obtain the variance for individual coefficients at any level by using the 2D wavelet transformation to propagate the errors exactly from level to level (Vannucci and Corradi 1999). The 2D transform is performed first across the columns of the matrix and then across the rows, with additional detail available in Vannucci and Corradi (1999). Since we knew the exact measurement errors for each measured (and then interpolated) data point, we obtain exact standard errors (error bars) for each coefficient. In practice, the 2D wavelet transform is performed by multiplying the filter matrices described earlier with the covariance matrix GΣGT . An assumption in most wavelet denoising methods is a constant variance for all data points, i.e. all data have the same measurement uncertainty. Ideally, you will adjust the threshold for regions of higher uncertainty to be more stringent, and to give more credence to regions that have smaller errors. Kovac and Silverman have developed a way to propagate the measurement errors through to the wavelet domain (Kovac & Silverman 2000). However, in many situations the errors are unknown, and many methods have been created for determining an estimate of the overall variance instead. Once the overall variance is determined, it is possible to determine the relative variance for different regions up to a constant (Kovac & Silverman 2000). Besides correcting for uneven sampling, the other key advantage to using the Kovac and Silverman method on data with carefully measured errors is the calculation of both “within level” (between coefficients at the same level of detail) and “across level” (between coefficients at different levels of detail) covariance. Most analyses, including many in the Kovac and Silverman references, are done with data where the measurement error is unknown, and so the variance is estimated. Since the Swift BAT data do have known measurement errors, our denoising can be more precise. The error bars are entered into the covariance matrix after they are calculated for the interpolated time series; this 39 is a straightforward calculation since the errors add in quadrature. We have written the code to perform the 2D wavelet transform on the covariance matrix and to extract the errors on the coefficients at each level of decomposition. The errors on the coefficients are the diagonals of the covariance matrices that are reduced in dimension by a factor of two at every level of decomposition.

3.3 Sensitivity plots

Now that the method has been defined, we will measure its performance on Monte Carlo simulations and real data. We created sensitivity plots to quantify the performance of the algorithms on signals of various shape profiles and flux, or more accurately, flux di- vided by the measurement error. This quantity, which we have defined as the significance of a measurement, is used because it normalizes all of the various flux measurements with respect to their accuracy. The significance is thus a good unitless quantity for comparing heteroscedastic flux data. Often, data are standardized by subtracting the mean value from each sample before dividing by the measurement error. However, in the Monte Carlo data, the mean of the background is equal to zero which would actually lower the baseline by the mean of the input signal thus accomplishing little. The same is true of the real data, which are shown in Chapter 4 to be indistinguishable from a Gaussian distribution with a mean of zero. Two sets of sensitivity plots, which determine the fraction of signals with a given significance that survive our cuts, were produced; one to map out the performance under ideal conditions that require knowledge unavailable from real measurements, and the second to more accurately represent real observations. Both of these were based on tests of Monte Carlo simulated signals with white noise added to approximate real observed signals. In summary, these plots show the theoretical fraction of signals of a given fluence that will pass all cuts. To create a sensitivity plot, we first calculate a white noise only dataset of 1024 points, and check for surviving coefficients and false positives. Surviving coefficients are those that remain after denoising, while false positives are structures that remain following an additional physics cut defined below. We then use the same random number seed to add the same noise realization to a simulated data set with an injected signal added. We then denoise again and see if there are more coefficients that survive all the cuts than the noise-only realization. If so, this signal realization has passed the cuts and the algorithm is sensitive to the signal. While investigating sensitivity curves, we discovered that the wavelet transform has significant positional dependence, i.e. the position of the signal in the sample window affected the passing rate. The positional dependence caused a suppression of signal passing. In fact, when a noise-free signal is run through the transform, and the three largest wavelet coefficients are obtained, we find a fascinating result: there are periodic oscillations in the magnitudes of the three largest coefficients, and therefore the passing fractions for signals that occur at different times within the sample window will differ. The pass rate for a given signal shape and fluence is directly related to the value of the largest coefficient in the wavelet decomposition. The maximum coefficient varied up to 50% in magnitude in our testing. For signals that are well above threshold, this variation is not significant. The variance due to position in the sample window will not suppress 40 the pass rate as these coefficients will be larger than 1.5x the denoising (threshold plus a cushion for the 50% fluctuation) threshold no matter where in the sample window the signal occurs, making them insensitive to the oscillations. In other words, these coefficients will be so far above threshold that the positionally-dependent fluctuations in the MCM will not bring them below the denoising threshold. However, when searching for signals very near the threshold, the start and end times for the window used for denoising can have quite an effect on signal detection probability. Figure 3.9 shows a sample signal with no noise added and Figure 3.10 the “max- imum coefficient” plot obtained by “sliding” the center of the signal one time sample at a time to the right of the center of the sample window. For each position in the sample window, the coefficient with the largest absolute magnitude was recorded. The wavelet coefficients from a discrete signal with no noise added are “true” coefficients; an inverse transform of those coefficients returns the original function exactly. The maximum co- efficient plots show a clear oscillatory trend , indicating “sweet spots” in the sample window where the passing fraction for pulses near threshold is at a maximum. As noise is added to the input data, the measured coefficients will oscillate around the true values with a normal distribution, so the mean value of each coefficient over many realizations approaches the true value. 41 yin 0.0 0.1 0.2 0.3 0.4 0.5

0 200 400 600 800 1000

Time (samples)

Fig. 3.9 Input time series for the Maximum Coefficient Magnitude plot, this is a square wave across 80 samples, shifted 238 samples from the center of the time series to sample 750. 42

Fig. 3.10 This Maximum Coefficient Magnitude plot shows the oscillation of the sensitiv- ity of the algorithm as a function of the position of the input signal in the sample time window. A clear oscillatory pattern is shown in this plot, and there is a clear minimum as well as a maximum, demonstrating the importance of the tiling to try and increase the sensitivity of the algorithm. The x-axis contains the horizontal shift away from the center of the sample window, and the y-axis represents the absolute value of the three largest coefficients in the multiresolution decomposition. Triangles represent the largest coefficient in a given decomposition, asterisks the second largest, and circles the third largest. Even though these coefficients are obtained from square wave input data, the oscillatory pattern in the MCM’s is angular.

The first set of sensitivity plots we created is called the “ideal” sensitivity plot. These plots are ideal because they assume knowledge that is unknown for real measured data, namely the position in the sample window where detection of the signal has the highest probability. Implicit in these tests is the assumption that the shape and fluence of the input signal are known, which is not true for real data. The ideal shift for the input signal is used for each simulated realization so that the greatest possible passing rate is achieved, hence the name “ideal”. Figure 3.4 again shows a maximum coefficient oscillation plot for one particular square wave signal. While the ideal plot in Figure 3.11 shows the upper limit of the performance of the wavelet algorithms, it is instructive as well to simulate the performance under realistic circumstances. Real observed fluxes do not have known maximum coefficient distributions and so will be observed at time shifts where the power from the maximum coefficient is not optimized. This will lead to a lower passing rate overall, because the power will be spread out among more coefficients in the multiresolution decomposition than it would be at the optimum location in the sample window. Thus more structure 43 will be removed due to denoising. To achieve the less-than-optimal maximum coefficient, the signal is placed directly at the center of the time sample window for each realization. Surveys of a wide range of maximum coefficient distributions show that the exact center of the sample window is rarely the optimal signal position. The sensitivity plots that are obtained in this fashion are called “simulated measurement” sensitivity plots. Real excesses will occur at random points in each sample window, but by selecting the center of the sample window, we have chosen a less than optimal position for testing. A more accurate representation of measured data might have been obtained by randomizing a signal’s position in the sample window, but that would be much more computationally expensive, and if the tiling algorithm is as effective as our results show it to be, these tests would add little to our understanding of the algorithm’s sensitivity. We used the tiling method, as described below, to overcome some of the sensitivity loss due to the likely less-than-ideal position of the test signal within the sample window. The goal of the tiling algorithm is to over-sample the data set by overlapping sample windows, so that a given potential signal is tested three different times at different positions in each sample window. If the signal is at a “cold spot” in terms of maximum coefficient magnitude in a given window, sampling at different points in each window will hopefully mitigate this effect. Signals that are close to threshold are of high interest as preserving more of them will increase the overall sensitivity of the algorithm. Before we could plot the efficiency of the algorithms on signals of various profiles (shapes) and fluences, it was important to try to determine a variable that could describe a signal’s overall fluence regardless of shape or parameters of the signal (e.g. width or amplitude). We used Parseval’s theorem along with some trial-and-error to develop our “fundamental axis” for sensitivity plotting. Parseval’s theorem when applied to wavelets states that the signal power P x2dx , where x is the flux, is identically equal to ≡ the power in the wavelet domain. Power in the wavelet domain in the case of the R multiresolution decomposition using the DWT is the sum of the squares of the detail coefficients plus the square of the zeroth level scaling coefficient. Note that no mention is made of time; the spacing on the x-axis is evenly sampled after interpolation, ergo the wavelet transforms and the integral of the power are one-dimensional. To allow for heteroscedasticity, we divide it by the average measurement error squared, σ¯2. We ≡ obtain a unitless quantity which expresses the power in terms of the measurement error, and allows for a reasonable comparison between signals of different shapes and sizes. The fundamental axis for sensitivity allows for one-dimensional curves for sensitivity to be plotted, because the pulse’s width in time and total fluence are both represented in the power. The sensitivity curves lead us to a powerful conclusion: regardless of the pulse profile or width-to-height ratio of a pulse, the sensitivity of our algorithms to signals is determined almost entirely by just the power normalized in terms of the average measurement error. We used three very different signal profiles to test how signal shape affects the detection probability for these algorithms. The three shapes chosen were square waves, Gaussians, and “sharkfin” pulses, defined below in equations 3.3 and 3.4 . The sharkfin pulses are an important test for the algorithm because they are asymmetric, the square wave pulses test the algorithm’s ability to detect sharp edges, and the Gaussians test 44 sensitivity to rounded pulses. In addition, the sharkfins show the fast rise, slow decay that is seen in many observed flares.

y = √x 1

Table 3.1 For three different Gaussians with σ not divisible by two, 250 realizations with white noise were created, and the passing rate with and without tiling was recorded, with a significant improvement due to tiling Gaussian Width # passing without tiling # passing with tiling Improvement % 17 199 239 20.1% 33.5 183 238 30.1% 57 169 228 34.9% structure at a sensitivity which, regardless of height-to-width ratio or profile shape, only depends on the normalized power. We have shown that white noise alone passes denoising at the theoretically predicted rate of around one in every five realizations. We are confident that the varying error bars that we see in the data from Swift will average out to the sensitivity curves we have obtained through more simulations. We also have a working method for overcoming the varying sensitivity to a given signal based upon where in the sample window the flare occurs, known as tiling. We are satisfied that our Monte Carlo testing has shown the theoretical power of our algorithms, and the next step is to look at blank pointing data, observations from the Swift BAT that should be comprised entirely of background noise. 46 nown. s ideal t. ent for the start and end times of the underlying flares is not k e placed at the highest MCM location in the sample window. Thi Fig. 3.11 Ideal sensitivity plot, where the input signals ar sensitivity is not achievable inAll the data data points as had the a ideal constant measurement placem error for this plo 47

1.0

0.8 Passing Fraction 0.6

0.4

0.2

0.0 0 50 100 150 200 250 300 350 Power/Sigma_bar**2

Fig. 3.12 Sensitivity plot for the simulated measured Monte Carlo data. The sensitivity plots for the three different signal profiles: square wave, Gaussian, and “sharkfin” all follow the same curve. This allows us to state that we can determine the sensitivity of the algorithm to signals of arbitrary shape and extent in time. The black trace represents a Gaussian signal with σwidth = 0.879, the blue and purple traces are sharkfins with a width=50 and 25, respectively, and red and green are square waves with width=8 and 4, respectively 48 879, the blue . = 0 width σ tively, and red and green are square waves with width=8 and 4, th the same axes. k trace represents a Gaussian signal with Fig. 3.13 Sigmoid curve fit to sensitivity plot data - The blac and purple traces arerespectively. sharkfins These with are a the width=50 same and data 25, shown respec in Figure 3.12 wi 49

To ensure that we used the exact same method to determine the normalized power for MC events that will be used on the real data, we will no longer useσ ¯ as an average measure of the normalized power for the second set of sensitivity plots. Instead, the algorithm that will be used is known as the “custom trapezoid” method for determining normalized power: The custom trapezoid method that we developed uses the errors on each mea- surement to more accurately normalize the integrated power. We average the errors on the two observations that make up the trapezoid, and then normalize the power integral just over that interval with our new localized average error. This method takes into account the heteroscedasticity of the data and thus puts more credence in more accurate measurements. We find that when we place the normalized powers for real flares onto the ideal sensitivity curve, the custom trapezoid method gives us a figure that more closely matches the MC pass rates.

0.5(b a)(Y (a)2 + Y (b)2) Normalized power = − (3.5) 0.5(σa + σb) X where a and b represent the two x-axis points between which the area is being determined, σ is the error bar for each point, and Y is the flux at those x-axis values. Now that we have introduced and explained the statistical theory behind the wavelet denoising and quantified the algorithm’s performance on signals of arbitrary shape and duration, we will in the next chapter test our methods on real data from the Swift BAT. One flaw in our calculation of normalized power was that it had the implicit assumption that the baseline (i.e. mean) for a given sample window is zero. This is true of all of our Monte Carlo simulations, so our sensitivity plots are not affected. This is also true to a lesser degree for most of the physical point sources that we have studied. A simple test run on three Gaussians shown in Figure 3.14 demonstrated the possible pitfalls of using a power variable that is not standardized (e.g. mean-subtracted as well as normalized by the measurement error). The normalized power was found for Gaussian with a mean of zero, a σ of 1, and an amplitude of 0.4, which was 40960. The same time series was shifted on the y-axis by 0.2, and the power became 102320. Finally, the time series y-values were divided by two and then shifted up by 0.2, and the normalized power was 122800. If the baseline did not affect the normalized power, the first two Gaussians would have identical normalized powers. However, we will show in the catalog chapter that the flares that we detect are not seriously affected by this flaw. 50

Fig. 3.14 Three Gaussians integrated to find the normalized power: the first is an ordinary Gaussian with σ = 1 and an amplitude of 0.4. The second Gaussian is identical to the first except 0.2 is added to all the y-values. The third Gaussian is the same as the first Gaussian except the y-values are all divided by two and then are added to 0.2. The normalized powers for the Gaussians are respectively 40,960 , 102,320, and 122,800. These results show that the normalized power is not standardized, meaning that the baseline is not subtracted off of the time series. However, the baseline for all of the positive detections in our catalog is close enough to zero that this should not be a significant effect on our catalog, as the absolute value of the flux measurements affects the normalized power, not the absolute distance from the baseline. If the absolute distance from the baseline were the determining factor, the normalized power of the first two Gaussians would be identical.

Example Gaussian Example Gaussian Plus 0.2 Example Gaussian Divided by 2, Plus 0.2 Flux (arbitrary units) Flux (arbitrary units) Flux (arbitrary units) 0.0 0.1 0.2 0.3 0.4 0.2 0.3 0.4 0.5 0.6 0.20 0.25 0.30 0.35 0.40

−4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4

Time (Arbitrary Units) Time (Arbitrary Units) Time (Arbitrary Units) (a) (b) (c) 51

Chapter 4

Verification of Methods using Swift BAT Data

In the previous chapter, we characterized the algorithm performance using MC simulations. We developed the concept of the normalized power, and characterized the sensitivity of the wavelet algorithm to any signal with a given normalized power, regardless of profile. We found that the wavelet technique could achieve admirable background suppression in large, unevenly sampled time series with varying error bars for each observation. The effectiveness of the algorithm in separating signal from noise in MC events encouraged us to apply the method to real observations. In this chapter, we will now demonstrate the algorithm’s effectiveness on Swift data.

4.1 Blank Pointings

Our testing began with the Swift BAT “blank pointings”, which consist of 105 locations chosen across the sky which were selected by the Swift BAT team to be at least 10 arcmin from any known X-ray source. These 105 pointings were observed just like the sources in the BAT source list, several times per day over the entire lifetime of Swift. This allows for an assumption of X-ray dark sky in each pointing. We then ran tests on data from Markarian (Mrk) 421, a source which is well-known to have had flaring activity in the BAT data (Tramacere et al. 2009). We processed these data to determine if the structure we detected corresponded to the BAT trigger time, as these data presented us with an opportunity to confirm the presence of signal that we expected to see. At this point, we will introduce the data quality cuts that the Swift team imposed on data in the monitoring catalog. Most importantly, events that were more than 10σ less than zero, or events with error bars at least four times larger than the average error for a Swift BAT monitoring measurement were flagged with a poor data quality flag. Other cuts eliminated data points from the catalog entirely. These cuts include data points where the star finder malfunctioned or the satellite was missing altitude data, data points where less than 10000 pixels were active or more than 15 pixels were considered ”hot” (meaning that they were overly saturated), events where a source is occulted by the Earth, and data points where the object in question covers less than 10% of the detector, known as the partial-coding fraction.(Krimm 2011). The utility of the blank pointings becomes clear through a comparison to flat field measurements in optical astronomy. A flat field observation is taken by pointing a telescope at a white background such as a sheet of paper and taking a long exposure. The Charge-Coupled Device (CCD) will respond unevenly to a uniformly illuminated surface, due to inevitable inefficiencies in the electronics; the flat field is used to calibrate later physics observations, as the CCD’s response due solely to a uniform input is then known. 52

The flat fields show how the detector sensitivity varies across the CCD. In a similar fashion to flat fields, the Swift blank pointings can be used to determine the detector response to a field that has no expected sources in it. Unlike flat fields, however, it is possible as well for a signal detection to occur in the blank pointing data. A source below the normal flux threshold of the BAT could be elevated to a detectable level by a flare, for instance, or a transient event could occur in the blank field. Disregarding such rare events, the statistical properties of more than five years of observations in 105 pointings can be used to characterize the detector performance over the course of several orbits. To prove that these data were suitable for wavelet analysis and to properly un- derstand the error properties of the detector, it was crucial to duplicate the findings of Krimm (2011). We collected significance measurements from 105 pointings, 2,077,495 measurements in total. We only looked at data points which passed the Swift data quality cut on negative measurements and error bar size (details of these cuts were not provided). Simple descriptive statistics were calculated including the sample mean of the flux measurements along with the standard error on the mean. The mean value should be indistinguishable from zero within 1σ of the mean for a truly Gaussian data set. We also found the third moment, or skewness, of the distribution using the formula:

(Y Y¯ )3 skewness = i − (4.1) (N 1)s3 P − in the above equation, Y represents a normalized flux measurement, Y¯ is the average of all of the normalized flux measurements, s is the sample standard error, and N is the total number of measurements. The skewness, as the name suggests, determines if the data distribution is more heavily tailed on one side of zero or the other. A p-value for the t-test is calculated as well. This statistic indicates if the the skewness is statistically distinguishable from zero, and it is known as D’Agostino’s test (D’Agostino 1971). We find the data to be Gaussian. We find a mean of 0.00018, a standard deviation of 1.032, and an error on the mean of 0.027, so the mean is not distinguishable from zero. We find a skewness of 0.00083, and a value for D’Agostino’s test of 0.313, meaning that we cannot reject the null hypothesis of a zero skewness, since 0.313 is far greater than a reasonable p-value of 0.05, for instance. These data are plotted below in Figure 4.1. The “wings” out past 5σ on the histogram are not as severe as they may appear since the Y-axis has a logarithmic scale. Even eliminating events with bad data quality flags, we are only removing data points that are 10σ below zero, so the excess of points > 5σ and < 10σ away from zero is not affected. A tougher outlier cut would eliminate these points, but since the data are essentially normally distributed, it is not necessary. We find using a KS test that the distribution of significances is indistinguishable from a normal distribution shown in blue. Also, the mean value of the distribution is statistically indistinguishable from zero, and the skewness is indistinguishable from the skewness of a Gaussian distribution. The skewness for the data including those flagged for bad quality is 0.0007, so the distribution is slightly more right-skewed after eliminating large negative values, as expected. Krimm found that the systematic errors were underestimated by 30%, and this measurement was used to adjust all of the measurement errors in the BAT monitoring data set before the data are posted in the monitoring database, so the 53 underestimated systematic error is now accounted for. By replicating Krimm’s results, we have shown that we are accurately processing the Swift BAT data. Having confirmed the BAT team’s findings, we continued to test the normality of the data set. A Kolmogoroff-Smirnoff (KS) test was performed, comparing the vector of wavelet coefficients of the blank pointing flux significances to the theoretical distribution of the standard normal. The value of the KS statistic indicates whether or not the two input distributions, in this case the wavelet coefficients from 7200 time windows and a standard normal distribution, are statistically distinguishable. We have found that the distribution of the data is very much Gaussian-like and indistinguishable from a normal distribution. These data are remarkably close to a standard normal, only with a slightly higher variance.

Blank Pointing Significances, 2077495 samples from 105 pointings Log−density −15 −10 −5

−5 0 5 10

Sigma Blue curve is Gaussian (0,1.03)

Fig. 4.1 Log histogram for the significances from 105 blank pointings, over 2 million samples. The overlaid blue curve is a normal distribution with a mean of zero and a standard deviation of 1.032. The data are indistinguishable from a normal distribution according to many tests such as the K-S test, D’Agostino’s test, etc

To reduce the number of false positives in the blank pointing data, we instituted simple cuts to try and eliminate seemingly unphysical structure while preserving what should be caused by actual flares from AGN. These cuts were in addition to the overlap- ping coefficient cut discussed previously. The first cut we implemented was to require that a structure appear in at least two overlapping sample windows. One benefit of this simple cut is that false positives caused by pure white noise should be automatically eliminated. Even in overlapping sample windows, the distribution of white noise to the 54 various detail coefficients will differ greatly. The expected excess that occurs once in every five sample windows in the MC occurs at the same rate, regardless of whether the sample windows overlap in time. The final cut that we developed was a simple check to determine the sign of the flux measurement with the largest magnitude in the interpo- lated data, without regard to error bars. If this value was negative, then the flare was rejected, because observing less than zero photons on a CCD is physically impossible and thus an artifact of the data processing. We processed data from the first day that Swift monitoring of the blank pointings took place, April 13th, 2005, until March 4th, 2010. There were 7720 sample windows of 1024 interpolated samples representing several months per window over a period of more than five years in total. Out of those 7720 sample windows, we detected false positives in 35 sample windows, leading to a “fake rate” of 0.45%. However, we have theoretically removed nearly all or all of the pure white noise contributions from the dataset. There remained a possibility that some of the significant structure could not be classified as noise. Some of the structure could have been due to a physical X-ray source. This source could be a transient such as a below-threshold GRB or a steady source that is ordinarily below the threshold which flared and became detectable. The surviving excesses in the blank pointings came from 34 different pointings and showed a total of 35 excesses: one source had two excesses. Table 4.1 below shows the pointing coordinates, the dates on which flaring occurred, and the sources are labeled if the excesses occurred during the IC40 season. Plus, several of the flares occurred around MJD 53790. This leads us to believe that something may have been happening with the detector during that period of time since it is inconceivable that an event would occur over a period of several days in so many directions. However, the Swift team members that we contacted were not aware of anything out of the ordinary. While this is an interesting and unexplained result, these excesses did not occur during IC40, and so we will not pursue the matter further. We then sorted the excesses into five different categories. We then eliminated those excesses from the categories which were deemed unphysical to determine our final blank pointing excess sample. Figures 4.2 through 4.6 show representative examples of each category, summarized below in Table 4.2. We have determined that two of the classes are categorically unphysical (they are summarized in Table 4.3), and have excluded them from the final blank pointing sample. The excesses that contain extremely large, week-scale gaps have been eliminated, as have the excesses that represent negative excursions, i.e. categories 1 and 3. The first category is simple, it is unphysical negative excesses. Two of the excesses fit this category, with an example below in Figure 4.2. The raw data for these cases clearly shows that at least one large negative outlier was the cause for these excesses to be statistically significant. 55

Table 4.1 34 different blank pointings showed 35 total significant excesses, 29 of them were classified as possible physical excesses. The first two columns of the table give the coordinates of the center of the blank pointing bin, the next column provides the starting MJD for the flare, the fourth and fifth columns note whether or not an excess occured near MJD 53790 or during the IC 40 season, and the final two columns are the category in which we have placed the excesses and the normalized power for the excess.

Source RA (hrs) Dec (◦) MJD of flare start Near 53790 IC 40? Flare Cat. Norm. Power 2.61 70.14 53786.00 Y N 5.00 9.84 3.13 -13.04 53791.00 Y N 4.00 4.92 4.48 65.26 53783.00 Y N 2.00 41.78 4.48 6.01 53525.00 N N 4.00 11.10 4.56 6.04 54519.00 N N 5.00 22.09 4.60 50.24 53510.00 N N 4.00 86.50 4.60 -7.38 54861.50 N Y 2.00 10.05 5.09 22.54 54436.00 N N 5.00 12.18 5.30 -32.39 54790.00 N Y 4.00 3.92 6.02 18.45 53785.00 Y N 4.00 8.01 6.02 18.45 53807.00 N N 5.00 8.51 6.07 60.56 54761.00 N Y 4.00 3.81 6.97 13.04 54855.00 N Y 4.00 16.12 8.46 -75.29 54844.50 N Y 2.00 6.05 8.56 -8.55 54980.00 N N 4.00 44.80 8.97 -16.03 54235.50 N N 5.00 2.65 10.20 -74.30 55172.50 N N 2.00 9.96 12.09 74.18 55174.50 N N 2.00 28.29 12.12 -15.04 53475.00 N N 2.00 4.69 12.69 12.05 54887.50 N Y 4.00 4.13 12.89 -1.05 53785.50 Y N 4.00 16.16 14.23 8.51 53787.50 Y N 2.00 8.38 15.36 -51.31 54721.25 N Y 2.00 5.09 15.47 -33.12 54583.50 N N 4.00 12.80 17.37 -0.23 53784.25 Y N 4.00 4.20 19.15 62.35 54434.50 N N 2.00 10.95 20.59 -70.07 54814.00 N Y 4.00 13.93 21.00 0.35 54284.25 N N 4.00 2.25 21.45 63.55 55040.00 N N 4.00 4.30 23.04 -61.22 53513.00 N N 4.00 8.10 56

Table 4.2 Categories of excesses and the number of occurrences in the blank pointings. These categories were subjective and determined by eye. No sophisticated numerical scheme for identifying the classes was needed since negative excesses and large gaps were the only two categories to be outright rejected, and these events can be easily identified by eye. Excess Type Count Dips 2 Peaks 6 Gaps 4 Oscillations 20 Symmetric 3 Total 35

Table 4.3 This table summarizes the results for flares classified as unphysical. The first two columns provide the coordinates for the blank pointing bin, then the next two columns show if the excess occurred near MJD 53790 or during IC 40, and the final column shows the category we have placed the excess in.

Source RA (hrs) Dec (◦) MJD of start Near 53790 During IC 40 Cat. 0.70 59.18 53786.00 Y N 3 0.74 50.19 53781.75 N N 3 15.11 20.07 53787.75 Y N 1 17.37 -0.23 53784.25 Y N 3 18.756 4.52 53522 N N 3 19.58 11.19 54839.75 N Y 1 57

XXXJ1506.4 +20.07 Type 1 Excess

0.02

0.00 Flux (counts/sec/cm/cm •0.02

•0.04

54719 54720 54721 54722 54723 54724 MJD

Fig. 4.2 This is an example of a type 1 excess, which consists mainly of an unphys- ical negative excursion. All negative excursions will be reconstructed with a positive component, since a function composed entirely of Haar wavelets must integrate to zero, however excesses in this class are clearly reconstructing a negative dip in the time series with positive spikes to either side of the dip to allow for the integral to be zero. The green points represent the measured data, and the blue and pink curves are two of the three overlapping reconstructions obtained with tiling for this excess. The third tiling is not displayed because the structure was not found to be significant in that tile.

The second category is “spikes”, excesses that seem to be real, physical detections. Eight of the excesses from the blank pointings fell in this category, and in a way represent an irreducible background, as they are indistinguishable from flares from real sources, unless another cut is added. An example from this category is seen below in Figure 4.3. These excesses could represent transient events, below-threshold sources which flared above the threshold and became detectable, or other physical events, but we cannot determine that from the BAT data alone. 58

XXXJ1909.1 +62.35 Type 2 Excess

0.04

0.02 Flux (counts/sec/cm/cm 0.00

•0.02

54432 54434 54436 54438 54440 54442 MJD

Fig. 4.3 This is an example of a type 2 excess, a spike with a physical appearance.

The third category is excesses that contain large gaps in the time series. These week-scale gaps are large enough to affect the reconstruction and cause a false positive detection. These gaps are likely detector issues where no observations were taken for a long period of time. These excesses are easily identified and removed from the final sample, and there are two of them in all. An example is shown below in Figure 4.4. Gaps in the data can also be caused by the maneuvers of Swift to avoid exposure to the Sun. Sources that lie near the Sun’s position will be observed at the edges of the detector and thus will have smaller partial-coding fractions. The sources may even be unobservable for a few weeks per year. The signature of these time periods is a large gap bookended by points with large error bars, due to a low partial-coding fraction (Romano et al. 2011). These gaps are easy to identify by eye and vary in duration; a selection by eye made the most sense as a technique for eliminating flares containing such gaps.

XXX1845.4 +4.52 Type 3 Excess

0.01

0.00

Flux (counts/sec/cm/cm) •0.01

•0.02

•0.03

53518 53520 53522 53524 MJD

Fig. 4.4 This is an example of a type 3 excess, an excess with a large gap in it. 59

The fourth category for the excesses is a distinct oscillatory pattern in the recon- structed time series. This signature is best explained with an example, seen in Figure 4.5. All denoised time series which were found using Haar wavelets will be symmetric about zero because the Haar itself is symmetric about zero. However, type 4 excesses do not just integrate to zero, there is no clear peak in the reconstructed series, neither positive nor negative. It is not clear what causes this signature, but it is not seen in the data from known sources, so we can assume it is an artifact that appears when the telescope is observing blank sky. However, we cannot prove that these excesses are unphysical, either, and so they remain in the blank pointing excess sample.

XXXJ1722.1 •02.30 Type 4 Excess

0.03

0.02

0.01

Flux (counts/sec/cm/cm 0.00

•0.01

•0.02

•0.03 53782.5 53783.0 53783.5 53784.0 53784.5 53785.0 53785.5 53786.0 MJD

Fig. 4.5 This is an example of a type 4 excess, an oscillatory excess.

The fifth and final category describes positive excesses like category one does, however these excesses also have a very symmetrical negative component to them. An example of one of these five flares is seen below in 4.6. The unphysical flares are sum- marized in Table 4.3. This category is designed to fit noise-like fluctuations. The Haar wavelet is symmetric about zero, so all reconstructions that consist of a series of Haar wavelets will be symmetric about zero. If only a small structure survives, it will be quite symmetric and will not resemble the physical excesses, where a large peak tends to be bookended by shallow “troughs” to average to zero. 60

XXXJ0858.3 •16.03 Type 5 Excess 0.03

0.02

0.01

Flux (counts/sec/cm/cm 0.00

•0.01

•0.02

54235.2 54235.4 54235.6 54235.8 54236.0 MJD

Fig. 4.6 This is an example of a type 5 excess, a spike with a symmetric appearance in the denoised series, with a negative spike that is around the same magnitude as the positive spike, and no other significant structure.

After categorizing the excesses and eliminating the unphysical flares, data files containing the detector status tables from Swift during the 35 excesses were checked for roll angle irregularities (Krimm 2011), where the telescope would be pointed in the same direction for a period of time on the order of a day. Noise fluctuations that normally would be averaged out across the whole detector were several pointings to occur during the day would instead build up in the same regions of the detector. The files were in the Flexible Image Transport System file format, which was originally conceived to transport astronomical data on magnetic tapes (Grosbol 1988a), and processed using ftools (Pence et al. 1993), a NASA package for manipulating FITS files. All of the files showed roll angles that varied throughout the day so that noise “pile-up” as a source of a false positive was eliminated. Finally, we plotted histograms of the normalized power of the blank pointing excesses, seen in Figure 4.7. We have placed a cut on the normalized power of an excess, requiring a value above 50. The cutoff was set at 50 to preserve all of the flares seen from blazars that are presented in Chapter 5, while eliminating nearly all of the excess seen from the blank pointings. All of the excesses that appear physical are all eliminated by this cut except for one. This one event over a period of five years averages to less than one quarter of an event per year, making the background from the blank pointings and thus from sources other than the AGN in the source bin an acceptable one-in-twenty for the IC40 season as presented in Chapter 5. 61

6 Counts 5

4

3

2

1

0 0 10 20 30 40 50 Normalized Power

Fig. 4.7 This is a histogram of the normalized power calculated using the custom trape- zoid method, calculated for all of the physical-appearing excesses from the blank pointing sample. We have placed a cutoff (blue line) at a normalized power of 50. This is near the 33% sensitivity mark on our theoretical sensitivity cuve. We have chosen this value so that only one of the largest excesses is not distinguishable from physical flares by any of our other cuts, and also based on the results of our catalog in Ch 5. One excess over five years shows that we do not have to be concerned about background events overpowering our signal in the photon data.

4.2 Mrk 421 Data from 2006

Having shown that that background noise and unidentified flaring objects cause excesses that pass all of our cuts at a rate of less than once per year, it was then important to show that the algorithm detected flares that were known to have been detected. There were three BAT triggers from Mrk 421 within three months during 2006, i.e. events that were comparably bright in hard x-rays to a GRB. While the BAT monitoring program and the BAT all-sky survey observed AGN regularly in between gamma-ray bursts, it rarely triggered from “always-on” x-ray sources like AGN, so these events from 2006 are notable. The workers on the Tramacere, et al study detected these flares by delving into the BAT FITS files and looking for the text: “OBJECT = ‘Automatic Target’” (Tramacere, 2011), which denotes events that had flux levels equivalent to those that would trigger the BAT to slew towards a transient. Seen below in Figure 4.8 are the results from the wavelet algorithm on Swift BAT data from Mrk 421 in 2006 during these flaring periods. Seen in Figure 4.8a is the most significant flare, with a normalized power of 791.02. This is is an enormous amount of power and if the algorithm did not detect this flare, there would have been serious concerns as to its effectiveness. The flare falls well within the 100% expected pass rate regime of the sensitivity curve, and its enormous power is the reason why even small details in the shape of the flare were very well reconstructed. Flare 2, Figure 4.8b, has a normalized power of 42.39. This falls in the low pass rate regime ( 10%) of the ∼ sensitivity curve, and it appears that it was fortunate that our algorithm detected this 62

flare. It would not have reflected poorly on the algorithm had the flare not been seen, as it would have been suppressed by our severe wavelet threshold. Flare 3, Figure 4.8c, has a normalized power of 135.31 , which places it in the high sensitivity( 90%) regime ∼ of the sensitivity plot. It was a strong confirmation of the algorithm’s effectiveness for this flare to have been detected because this flare is very wide and has a low maximum flux, demonstrating that the algorithm does not just detect narrow, high-amplitude flares. The extreme length of this flare, on the order of a month, is what allows for the integrated power to have such a high value. Short, high fluence flares have more power than longer, lower flares, but since this flare had a length of weeks, the power is quite large. The low amplitude of the excess is the reason that very little smaller scale structure is reconstructed over the length of the flare. The success in detecting all three of the flares published in the Tramacere study is an excellent confirmation of the effectiveness of the wavelet technique.

4.3 Other Tests and Summary

Having confirmed these results from 2006, another important check on our results was a comparison of our detected flares with the Swift team’s definition of flare detec- tions, those worthy of a Gamma-ray burst Coordinates Network (GCN) notice (Palmer 2011). A GCN (Barthelmy et al. 1995) is an automated alert sent out to the larger astronomical community with coordinates and characteristics of a gamma-ray burst or similar transient. The Swift-team-designated flare periods are on a timescale that just barely intersects that of the monitoring observations. The Swift team used the individ- ual photon arrival times to define their flaring periods to an accuracy of a few seconds, whereas the minimum length for the orbital observations is on the order of a half an hour. We can still check the orbit-by-orbit data for integrated fluence across the single-orbit bin during which the Swift team flare occured. It is however an average over the entire bin and the peak can get “washed out” by the rest of the observations, but we were still able to check our sensitivity to these flares. We find that we detect no flares from the monitoring data which overlap with the GCN-level flare times from the Swift team, due to the huge difference in average observation length (seconds for the Swift team, tens of minutes for the monitoring data). Finally, we examined 39,500 pure white noise samples to determine the influence of white noise spikes on the passing rates of data through our algorithm. We find no significant excesses in 39,500 white noise pointings after running them through our entire algorithm and selection process, so we can be confident that there was no white noise contribution at all in the final sample, since we tested over five times as many realizations and found no excesses. Thus, the 35 excesses found from the blank pointing sets must be from other factors such as large gaps in the measured data, non-Gaussian noise, off-axis GRB’s, etc. Palmer et al. (2007) and Stamatikos et al. (2007) are examples of BAT triggers from non-physics related excesses (in both cases, cosmic rays striking the detector). However, 34 of the flares had unphysical characteris- tics, low normalized powers, or both, and were thus eliminated from the final sample, in which just one excess remained. In summary, we determined a final version of physics-based cuts for a production catalog by optimizing them on the results from the blank pointings and from Mrk 421. 63

Fig. 4.8 Three flares from 2006 were detected in the BAT monitoring data and published in (Tramacere et al. 2009) and marked on the plot with blue vertical lines (a) was a flare with small scale structure that was significant after denoising, with a normalized power of 791.02. (b) this flare was not nearly as strong of a detection, with a normalized power of 42.39. Tramacere and collaborators had the flare beginning at MJD 53909.6, which is almost exactly the start time found in one of our tiled reconstructions. (c) While Tramacere et al. had this flare beginning at MJD 53847, we found instead a larger-scale excess beginning earlier at 53839. Since this excess overlaps the Tramacere et al. trigger time, we consider that a detection. The yellow trace in this figure is far below the data points simply because the significant structure that it finds has a much smaller amplitude than the rest of the data, i.e. the denoising is subtracting off a baseline that is found to be insignificant. The normalized power for this flare was 135.1 Mrk 421 Flare in 2006 #1

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We decided to eliminate category one excesses in particular, since negative fluctuations are unphysical, and we determined that white noise would make no detectable contribu- tion to the background in this study. We eliminated 34 of the 35 detected excesses from the blank pointing sample, leaving a total of 1 in a time period of around 5 years. This leaves an average of one excess every five years from unknown origins. These results are from 105 pointings over five years; our data sample had 193 sources from a period of one year. We see one excess in approximately 2.5 times as many pointings, which shows that we should not be concerned about excesses that do not originate from X-ray sources. Having thoroughly characterized and eliminated nearly all of the background contamination possible in our catalog, we then began building a flare catalog. 65

Chapter 5

Results: Catalog

We chose to use a mainly Swift-based selection of source candidates for this study, since the flare periods are being selected based upon Swift BAT monitoring data alone. The monitoring catalog contains all sources labeled as BL Lac or Blazar on the Swift BAT monitoring web page. This list of sources makes up the bulk of the source candidate list for this analysis. However, we have chosen to supplement this list with sources that have a reasonable possibility of being neutrino sources. As mentioned in Chapter 2, we did not use any RXTE data for this analysis, so the RXTE catalog was not used as part of our source selection. We first looked at the first year results from the AGILE satellite (known as agilecat) (Pittori et al. 2009) for gamma-ray detected AGN that were not included in the list at that point. In its first year of operation, AGILE detected 13 blazars. Comparing the list of detected AGN with the list of sources monitored by Swift, we were able to add 5 more sources to the candidate list, and they are listed below in Table 5.1 along with the other sources. The sources listed in the first-year results of AGILE include 8 that are already in the source list from Swift, 2 that were not seen by Swift, and 3 that were not in the source list because Swift had classified them as other objects. To round out the sample, the sources labeled by the Swift team as “radio galaxies” were included in the sample, as well. However, for non-blazar AGN, the geometry for neutrino production in the jet is different because the jet does not point directly at the Earth. It is possible that the neutrino jet is wider than the photon jet, and this would allow for radio galaxies to be seen as point sources of neutrinos by IceCube. A second possibility is neutrino production in a different structure of the AGN, such as the disk (Bednarek & Protheroe 1999). However, since we did not know how many sources or which classes would show significant flaring, we wanted to have a large and diverse catalog to provide a better chance for finding excesses. 66

1.0

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Fig. 5.1 Sigmoid curve fit to sensitivity plot data with overlaid flares in blue. The green line represents the flare from Mrk 421 with a normalized power of 800 that is not ∼ shown on the plot. 67

Table 5.1: Sources for the Wavelet-based Catalog

Source Identifier RA(degrees) Dec. (degrees) Object Type IC40 Flare 1ES 0120 +34.0 20.79 34.35 BL Lac No 1ES 0229 +200 38.20 20.29 BL Lac No 1ES 0414 +009 64.22 01.08 BL Lac No 1ES 0502+675 76.98 67.62 BL Lac No 1ES 0806 +524 122.46 52.32 BL Lac No 1ES 0927 +500 142.66 49.84 BL Lac No 1ES 1011+496 153.78 49.48 BL Lac No 1ES 1101 -232 165.91 -23.49 BL Lac No 1ES 1218 +304 185.34 130.1770 BL Lac No 1ES 1255 +244 194.383 24.21 BL Lac No 1ES 1426+428 14:29 42.67 BL Lac No 1ES1727 +502 262.08 50.22 BL Lac No 1ES 1741+196 265.99 19.58 BL Lac Yes 1ES 1959+650 300.0 65.13 BL Lac No 1ES 2344+514 356.77 51.70 BL Lac No 1H 0717 +714 110.48 71.33 BL Lac No 3C 273 187.28 2.05 Radio-loud QSO No 3C 279 194.05 5.78 Radio-loud QSO No 3C 309.1 224.78 71.67 Sy 1 No 3C 345 250.75 39.81 Radio-loud QSO No 3C 371 271.71 69.82 BL Lac No 3C 390.3 280.55 79.77 Sy 1 No 3C 445 335.96 -2.10 Sy 1 No 3C 454.3 343.49 16.15 Radio-loud QSO No 3C 66A 5.6651 43.0355 BL Lac No 4C 04.42 185.59 4.22 BL Lac No 4C 06.69 327.02 6.96 Radio-loud QSO Yes 4C 11.69 338.15 11.73 FSRQ Blazar No 4C 14.60 235.20 14.80 BL Lac No 4C 15.05 31.20 15.23 FSRQ Blazar No 4C 21.35 186.23 21.38 Radio-loud QSO No 4C 34.47 260.84 34.30 Sy 1 No 4C 40.24 147.23 40.66 Radio-loud QSO No 4C 47.08 45.90 47.27 BL Lac No 4C 50.55 321.18 50.97 Radio Galaxy No 4C 56.27 276.03 56.85 BL Lac No 4C 67.05 37.21 67.35 FSRQ Blazar No 4C 71.07 130.35 70.90 Radio-loud QSO No 4C 73.18 291.95 73.97 Sy 1 No 7C 0059 +5808 15.69 58.40 FSRQ Blazar No Continued on next page 68

Continued from previous page Source Identifier RA(degrees) Dec. (degrees) Object Type IC40 Flare 7C 1308 +3236 197.62 32.35 BL Lac No 7C 1415 +2556 214.49 25.72 BL Lac No 7C 1424+2401 216.75 23.80 BL Lac No 8C 1803+784 270.19 78.47 BL Lac No AO 0235+16 39.66 16.62 BL Lac No B3 0650+453 103.22 45.16 Radio Gal., Fermi No B3 2247+371 342.52 38.41 BL Lac No B3 2322+396 351.32 39.96 BL Lac No BL Lac 330.68 42.28 BL Lac No BWE 0708+5038 108.18 50.56 BL Lac No BWE 0907 +3341 137.65 33.49 BL Lac No BWE 1051+2227 163.63 22.18 Fermi source No BWE 1118+4228 170.20 42.20 BL Lac No BWE 1133+6753 174.13 67.62 BL Lac No H 1517+656 229.45 65.42 BL Lac No KUV 00311-1938 8.39 -19.36 BL Lac No M87 187.71 12.39 LINER No Mrk 180 174.11 70.16 BL Lac No Mrk 421 166.11 38.21 BL Lac Yes Mrk 501 253.48 39.77 BL Lac No MS 1050.7+4946 163.43 49.50 BL Lac No NGC 1275 49.95 41.52 Sy 2 No NGC 612 23.49 -36.49 Radio Gal. No NRAO 190 70.65 -0.28 FSRQ Blazar No OJ 287 133.70 20.11 BL Lac No PG 1246+586 192.08 58.34 BL Lac No PKS 0118-272 20.13 -27.0 BL Lac No PKS 0244-470 41.50 46.86 Radio gal., Fermi No PKS 0301-243 45.86 -24.12 BL Lac No PKS 0332-403 03:34 -40.13 BL Lac No PKS 0426-380 67.1680 -37.9390 BL Lac No PKS 0447-439 72.3530 -43.84 BL Lac No PKS 0454-234 74.26 -23.41 BL Lac No PKS 0528+134 82.73 13.53 FSRQ Blazar No PKS 0548-322 87.67 -32.27 BL Lac No PKS 0823-223 08:26 -22.50 BL Lac No PKS 0907+022 137.42 2.00 BL Lac No PKS 1057-79 164.68 -80.07 BL Lac No PKS 1127-14 172.53 -14.82 FSRQ Blazar No PKS 1144 -379 176.76 -38.20 BL Lac No Continued on next page 69

Continued from previous page Source Identifier RA(degrees) Dec. (degrees) Object Type IC40 Flare PKS 1213-17 183.95 -17.53 Poss. Blazar No PKS 1335-127 204.42 -12.96 FSRQ Blazar No PKS 1510-089 228.21 -9.10 FSRQ Blazar No PKS 1622-253 246.45 -25.46 FSRQ Blazar No PKS 1717+177 259.80 17.75 BL Lac No PKS 1830-211 278.42 -21.08 FSRQ Blazar No PKS 2005-489 302.36 -48.83 BL Lac No PKS 2023-07 306.46 -7.59 FSRQ Blazar No PKS 2155-304 329.73 -30.22 BL Lac No PKS 2233-148 339.14 -14.56 BL Lac No QSO B0033+595 8.97 59.83 BL Lac No QSO B0048-09 12.67 -9.49 BL Lac No QSO B0109+224 18.02 22.74 BL Lac No QSO B0208-5115 32.69 -51.02 BL Lac No QSO B0317+183 49.97 18.76 BL Lac No QSO B0323+022 51.56 2.42 BL Lac No QSO B0422+004 66.20 0.60 BL Lac No QSO B0446+113 72.28 11.36 BL Lac No QSO B0521-365 80.74 -36.46 BL Lac No QSO B0537-441 84.71 -44.09 BL Lac No QSO B0647+250 102.69 25.05 BL Lac No QSO B0706+591 107.63 59.14 BL Lac No QSO B0716+714 110.48 71.33 BL Lac No QSO B0754+10 119.28 9.94 BL Lac No QSO B0808+019 122.86 1.78 BL Lac No QSO B0814+425 124.57 42.38 BL Lac No QSO B0829+047 127.95 4.49 BL Lac No QSO B0954+65 149.70 65.57 BL Lac No QSO B1028+511 157.83 50.90 BL Lac No QSO B1212+078 183.80 7.54 BL Lac No QSO B1215+303 184.47 30.12 BL Lac No QSO B1413+135 214.00 13.34 BL Lac No QSO B1437+398 219.82 39.55 BL Lac No QSO B1440+122 220.70 12.01 BL Lac No QSO B1514-241 229.42 -24.37 BL Lac No QSO B1533+535 233.76 53.35 BL Lac No QSO B1542+614 235.74 61.50 BL Lac No QSO B1553+113 238.93 11.19 BL Lac No QSO B1722+119 261.27 11.87 BL Lac No QSO B2008-159 302.82 -15.78 FSRQ Blazar No Continued on next page 70

Continued from previous page Source Identifier RA(degrees) Dec. (degrees) Object Type IC40 Flare QSO B2136-428 324.85 -42.59 BL Lac No QSO B2149-306 327.98 -30.46 FSRQ Blazar No QSO B2356-309 359.78 -30.63 BL Lac Yes QSO J1512-0906 228.21 -9.10 FSRQ Blazar No RBS 0319 36.82 2.033 BL Lac No RGB J0136+391 24.14 39.10 BL Lac No RGB J0152+017 28.17 1.79 BL Lac No RGB J0214+517 33.58 51.75 BL Lac No RGB J0643+422 100.86 42.24 BL Lac No RGB J0738+1742 114.53 17.71 BL Lac No RGB J1012+424 153.185 42.4997 BL Lac No RGB J1058+564 164.66 56.47 BL Lac No RGB J1341+399 205.27 40.00 BL Lac No RGB J1413+436 213.432 43.6625 BL Lac No RXJ 1117.1+2014 169.28 20.24 BL Lac No RXJ 1211.9+2242 182.994 22.7089 BL Lac No S4 1250+53 193.30 53.02 BL Lac No TXS 0141+268 26.14 27.09 Fermi source No W Comae 185.38 28.23 BL Lac No

Out of all of these sources, nine showed flaring behavior according to our algorithm during the live time of IC40, all of them blazars: Mrk 421, 1ES 1741 +19.6, 4C 06.69, 4C 34.47, 7C 1415+2556, QSO B0706 +591 , QSO B0829 +047, QSO B2356 -309, and QSO J0738+1742. All data from April 4, 2008 until May 20, 2009 were considered, however we can only look for neutrino coincidences while the IceCube array was collecting good quality data. The uptime for IceCube is discussed in Chapter 6. The properties of these flares are summarized in Table 5.2 below. All of the flares detected are on the order of a day in length, with the longest flare occurring in Mrk 421. The duration of this flare was 4 days during the IC40 data season. The flare actually began just prior to the beginning of data taking for the IC40 season. We determined flare start and end times by eye, but these determinations were based upon studying the three overlapping reconstructions for each flare; We looked for the flare structure to settle back down to the baseline, a qualitative determination. More quantitative methods such as finding the inflection point of the discrete series are available, or even sophisticated techniques such as Bayesian Blocks (Scargle 1998) or change-point analysis. However, for the purpose of the study, the fits-by-eye are quite sufficient because the data are unevenly sampled thus interpolated before fitting, and we have added additional time to the start and end of the flares, which makes the exact start and end times flexible. The start and end periods are the first classification data we collected for each flare. We have also allowed for a “pad” of 12 hours before and after the flare times that we determined by eye in order to allow for the possibility that the neutrino production mechanisms are not completely simultaneous with processes that 71 produce X-ray flares. Also, time windows for denoising were limited to 1024 samples for ease of computation. The distribution of the sources on the sky is also interesting and used to classify each source. The most important distinction between the sources is the hemisphere in which they are located; Northern Hemisphere sources have the Earth as a filter as dis- cussed in Chapter 1 and therefore much lower energy neutrinos can be reliably detected. The energy cutoff for neutrino detection for Southern Hemisphere sources is far higher, at 1 PeV (as explained in chapter 1 with regard to downgoing muons), which affects both the expected neutrino flux as well as the point-spread function (PSF) for IceCube, as explained in the next chapter. The only surviving Southern Hemisphere source is QSO B2356 -309, and it is exceptional because it is the only source from which we have detected more than one flare during the IC40 season. The normalized power, as described in the previous chapter, is also found for each flare. It was important for us to keep the normalized power unitless for real data as well as for the simulations for the sake of consistency. To make the time axis unitless, the MJD is replaced with a sample number, ranging from 1 to 3072, since each set of tiles has three windows of 1024 samples, in the interpolated series. The custom trapezoid algorithm described in Equation 3.5 is then used to find the normalized power for these flares. The flares are then placed onto the final sensitivity plot in Figure 5.1. Each flare is a single “realization” on the sensitivity curve, so it is represented by a vertical line at a given value of normalized power. The normalized power distribution for the flare sample indicates that the theoretical sensitivity curve has some empirical confirmation; four of the five total flares that pass all cuts had a theoretical passing probability of 50% or above. We had expected most of the flares that passed all cuts to have normalized powers of 100 or more since the sensitivity curve reaches values of 75 to 100% at these powers. Finally, members of the Swift BAT team were consulted to determine the status of Swift on the MJD’s when the flares occurred (Krimm 2011) and if Swift had auto- matically flagged any flares during the time periods in question (Palmer 2001). We want to be sure that no aberrant detector behavior occurred during the flares, even a minor malfunction, as discussed in Chapter 4. The Swift team informed us that normal opera- tions were occurring during each of the detected flares, so this is not a concern. However, during two of the flares, the roll angle of Swift stayed the same for the duration of the flare, those from 7C1415+2556, and QSO J0738+1742. We removed them from our final sample due to the possibility that they could be caused entirely by noise. Also, we want to know if any of the flares that we detect were already known to the Swift team from their automatic flare detecting algorithm. Other than the Mrk 421 flare, which was significant enough for an Astronomer’s Telegram to be issued about the event (Krimm et al. 2008), none of the other flares we detect were found by the Swift team. Also, one other Astronomer’s Telegram describing a BAT flare was issued during IC40, (Krimm et al. 2009b) which was for PKS 1510-089. This flare was not detected in the wavelet catalog, likely because many of the orbital observations were marked with bad data quality flag and thus not included in this study. The published plots from the multi-wavelength study in Marscher et al. (2010) appear to indicate that the BAT band observations are not coupled well to those in the γ-ray band like the 72

R- band observations appear to be. Since neutrinos are predicted to more closely follow the TeV emission timescale (with the logic that the highest energy events are most likely to produce neutrinos), these may not have been the best flares to examine in any case due to the lack of correlation between X-ray and TeV flaring. Figure 5.2 below shows the X-ray, TeV, and R-band observations of the flaring in PKS 1510-089.

Fig. 5.2 PKS 1510-089 flares in 2008 were seen in many different wave bands, including with the Swift BAT. The flaring was so significant in the BAT that an Astronomer’s Telegram detailing the flaring was issued. This flare was not detected with our wavelet methods because the data points were excluded form the sample due bad data quality flags set by the Swift team. The X-ray data does not seem to coincide with the flaring activity in the TeV energies as the R-band data do. Figure taken from Marscher et al. (2010)

In summary, once a profile of each flare had been assembled and the literature had been searched for other detections from Swift in 2008-2009, decisions were made as to which flares were to be included in the final sample. The flares were judged on integrated power, peak flux, Swift detector status, proximity of the flare to large gaps in the data collection, and the morphology of the flare. If a flare had a shape that appeared to be very un-physical, e.g. a reconstruction that deviated significantly from the interpolated time series, that was deemed indicative of noise. All of these considerations led to the 73 formation of the catalog shown below in Figures 5.3 to 5.7. Figures 5.8 and 5.9 below show images of rejected flares along with the reason for which we decided not to include it in our sample.

5.1 Source Characteristics

We will discuss here the sources from which we have detected significant excesses during IC 40. They will be listed alphabetically by catalog identifier. The first source we see a flare from is 1ES 1741+196. 1ES 1741 is an elliptical galaxy that is one of the brightest galaxies to host a blazar AGN, as well as one of the most luminous(Heidt et al. 1999). 1ES 1741 is likely interacting with two other nearby galaxies; one is a spiral and the other is an elliptical. Interacting galaxies, star formation, and active galactic nuclei are known to have some correlation (for instance Lonsdale et al. (1993) and Hernquist (1989)) but that discussion is beyond the scope of this thesis. The flare from 1ES 1741 is seen in Figure 5.3. 4C 06.69 is a radio-loud quasar located at z=0.99. It has two lobes in the radio that represent large-scale jets. Strong radio fluctuations over a period on the order of months are seen. Variability on the order of a Jansky was seen during single night observations at 36.8GHz, and variability in the visible light is seen as well. The AGN in 4C 06.69 is considered a blazar as well, so it is like 4C 34.47, discussed below. (Volvach et al. 2009) It is possible that 4C 06.69 is actually a blazar AGN viewed head-on, with two off axis jets making up the radio lobes.(Marscher et al. 2010) The short time period fluctuations support this theory as the blazar jet would have a very small angular extent. The flare from 4C 06.69 is seen in Figure 5.4. Mrk 421 is one of the best studied AGN. Mrk 421 was the only object of the four to be labeled as a transient source by the Swift BAT team (Krimm 2010). The criteria for this are a mean rate above 0.00022 counts/cm2/sec, or at least nine days with a significance above 5σ, or the highest rate recorded from the source is 0.00275 counts/cm2/sec. The flare from Mrk 421 is seen in Figure 5.5. QSO B2356 -309 is a γ-ray blazar within an ellipitical galaxy at a distance of z=0.165. The high energy emission from QSO B2356 is very bright, even compared to its emission in the radio. Very high energy gamma-rays, those in the HESS energy range around 10 TeV, are seen, but the VHE spectrum seems not to vary much with time, which is unusual. The HESS collaboration maintains that their results strongly support an electron synchrotron self-Compton model of emission for B2356, so it is actually a very interesting test case to correlate with a neutrino sample to try and refute their leptonic prediction. (Abramowski 2010). The flares from QSO B2356 are seen below in Figures 5.6 and 5.7. Of all of the sources from which flaring was detected, only Mrk 421 was included in previous IceCube point source searches. Thus we are exploring time periods and direc- tions that have not yet been searched for neutrino correlations, making this study of even more interest to the community. This will also eliminate most of the blindness concerns that will be discussed in the next chapter and makes our study more non-parametric than previous IC-40 point source analyses, as we have placed fewer constraints on our object selections and are not using the light curves as probability distribution functions 74

(Abbasi & Collaboration 2011). The object selection process for IC-40 considered fac- tors such as X-ray spectrum, sky location, theoretical predictions of neutrino production from a source, etc. We have instead relied solely upon Swift as our catalog input data and have kept all other concerns, physical and logistical, out of our selection process. We now provide some additional detail on the objects which are part of the final sample, beginning with Mrk 421. Mrk 421 is the only source in the catalog to have been detected by the EGRET instrument on the Compton Gamma-Ray Observatory satellite, and it is seen by Fermi as well. Up until the early 2000’s, before the success of AGILE, Swift, and Fermi, EGRET was the best source of information about the highest energies in the AGN SED. Markarian 421 has been known to have been an exciting blazar source for decades. It is also detectable in the TeV gamma-ray range, by ground Cherenkov arrays such as HESS and HEGRA (Aharonian et al. 2003) and MAGIC (Aleksi´c2010). Swift also announced flaring activity in 2008 (Krimm et al. 2008), and this flaring activity coincided with the earliest part of the Mrk 421 flare included in the catalog. This Astronomer’s Telegram lends credence to our detection, as well as to the method itself. QSO B2356 -309, the lone Southern Hemisphere blazar, is not part of the EGRET catalog. However, B2356 has been seen in the gamma-ray band by Fermi, as published in the First Fermi AGN Catalog (Abdo et al. 2010). B2356 is a TeV blazar as well, as it was first seen by HESS in 2006 (Aharonian et al. 2006). HESS is a useful detector as it gives TeV photon coverage in the Southern Hemisphere, allowing us to study sources such as B2356. The other two sources, 1ES1741 and 4C 06.69 have not been detected in either the gamma-ray or TeV gamma-ray bands. 75

5.2 Flare results and characteristics

Fig. 5.3 Here are first the three overlaid fits on the raw time series for 1ES 1741, then the raw time series (blue-green trace with star markers) overlaid on the three interpolated tilings (square markers), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in two of the three overlaid tiles (variation in the third tile is likely due to the oscillations in the sensitivity to the signal based upon its temporal placement in the window.) Two actual measured points are part of the detected excess. Each tile begins one-third of the way through the previous tiles time series, at the point in the raw data point that corresponds to that point in the interpolate time series. 1ES1741 Flare during IC40 0.10

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By far, the brightest and most extensive flare occurred in Markarian 421. The flare, which as described above warranted an Astronomer’s Telegram due to its high fluence, began before the IC 40 season did, during the IC22 season. However, the flare 76

Fig. 5.4 Here are first the three overlaid fits on the raw time series for 4C 06.69, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the excess was found to be significant in two overlapping time windows. This flare is composed of far more data points than the flare in 1ES 1741; it is far better sampled in the original time series (in blue).

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Fig. 5.5 Here are first the three overlaid fits on the raw time series for Mrk 421, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in two of the three overlaid tiles (variation in the third tile is likely due to the oscillations in the sensitivity to the signal based upon its temporal placement in the window.) The flare began well before the data-taking for IC40 did, so there is quite a bit of structure that is not included here. Mrk 421 during IC40

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Fig. 5.6 Here are first the three overlaid fits on the raw time series for the first of two flares from QSO B2356, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was present in three overlapping tiles, which is a very strong indication that the structure is physical. B2356 is an excellent addition to our catalog because it is the only Southern Hemisphere source from which we see significant flare, and we also see flaring at two different times during the IC40 season. QSO B2356 Flare during IC40

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Fig. 5.7 Here are first the three overlaid fits on the raw time series for the second flare from QSO B2356, then the raw time series (black trace with black star points) overlaid on the three interpolated tilings (square points), and then each of the three tiled reconstructions overlaid on the raw time series (brown points). The overlaid fits show that the structure was again present in three overlapping tiles. QSO B2356 Flare #2 during IC40 0.06

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•0.06 54864 54865 54866 54867 54868 (e) MJD 80 was so enormous, a normalized power of 3451.4, that we felt compelled to include it. For reference, we predict that any signal with a normalized power above 200 will be positively identified essentially 100% of the time. While most of the structure is before IC40 began, an integrated power of 854.6 still continued on into the IC40 season. The significant structure took the form of an elevated baseline, with no smaller scale structures. Before this study, Mrk 421 was not considered to be flaring more than a month after the ATel times, so this will be a very interesting test of the possible correlation of elevated x-ray emission to an increased muon neutrino flux. The elevated baseline, with flux value around 0.01 counts/cm2/sec is an order of magnitude higher than the mean for all of the data points for Mrk 421 with good data flags for Swift’s lifetime, which is 0.0016 counts/cm2/sec. This mean is an order of magnitude above that for 1ES 1741, 4C 06.69, and B2356 (0.00014, 0.00015, 0.00008 respectively) which indicates that Mrk 421 has an intrinsically higher baseline than the other sources, but this flare should still be quite significant. The small means for the other three sources means that standardizing the power (as discussed in Ch 4) would not substantially affect our results, although it should be done for future studies. Since Mrk 421 is one of the brightest Swift sources, we do not expect more sources to have had significant flaring were standardized power to be used. The second largest flare as measured by normalized power is from QSO B2356, and it occurred from February 3rd until February 6th, 2009, MJD 54865 to 54868. This flare had a normalized power of 149.5, which gives it a high probability of detection; in our sensitivity testing, around 75% of signals with that normalized power passed all of our cuts. The peak flux is a relatively large 0.06 counts/cm2/sec, and the maximum is over 3σ away from zero. This flare may not have been detected with other flare-finding techniques since it only consists in the measured time series of a single observation (a single observation in the Swift monitoring catalog is a flux measurement over an entire orbit, not a single photon). The wavelet technique allowed us to compare this observation and its significance with the surrounding measurements to determine that it is in fact a significant flare. This flare was also significant in all three tilings, making a strong case for its inclusion into the catalog. The third largest flare came from the object 1ES 1741, with a normalized power of 106.6, and the highest peak flux of any flare at 0.1 counts/cm2/sec. The flare is detected in two overlapping tiles. The flare from 4C 06.69 has some smaller scale structure in the raw time domain which is not present in the wavelet fits, but it is important to remember that the wavelet threshold that we are using was selected for its maximal noise rejection properties, with the understanding that it would lead to reconstructions that did not necessarily represent the original time series well. There is still a significant fluence above zero across the first narrow peak that begins during MJD 54912, and the second peak that begins around MJD 54913.5 is captured in more detail in two overlapping tiles. Again, all of the observations during the flare are considered significant as they led to the surviving wavelet coefficients, even if the smaller scale structure is not present in the reconstruction. This flare had a modest normalized power of 69.1, and a peak flux of 0.05 counts/cm2/sec. The other flare from QSO B2356, which began on MJD 54639, had the lowest normalized power of any of the flares in the catalog at just 57.76. This flare is however 81 notable because it was detected in three overlapping tiles, the only such flare in the catalog besides the larger flare from B2356 to be seen in three overlapping tiles. Two of the flares did not make the cut for the catalog because of their physical structure - they just did not resemble the time series or seemed to be a reconstruction of a negative photon “dip” in the data. The first significant excess to be excluded was in QSO B0706 +591. The flare, seen in Figure 5.8, very much resembles a noise fluctuation, due its nearly symmetric shape and the presence of a large negative measurement in the significant region. The significant structure from QSO B0829 +047 was similarly rejected, as the reconstructed shape clearly shows that is a negative excess, or “dip”. These two un-physical “flares” have been eliminated from our sample, as seen in Figure 5.9 as well. 82 d Comments Power comes from one strong flux point Main peak consists ofLong, several low orbits flare, likeDetected an in elevated baseline all 3Detected overlapping in tiles all 3 overlapping tiles 90.00% 50.00% 35.00% Sensitivity 100% 98% avelet based catalog search. The normalized power, start an Duration 3 days 3.5 days 3.5 days 3 days 1.5 days 54602 54915 54868 54641 54564.5 End MJD 54599 54561 54865 54911.5 54639.5 Start MJD 69.1 57.6 106.6 854.6 149.5 Normalized Power Source 1ES 1741 4C 06.69 Mrk 421 QSO B2356 QSO B2356 end MJD, duration, and comments are included for each flare. Table 5.2 Summary of the findings of the Swift BAT Monitoring w 83

This catalog of flares from blazars as seen by Swift is important for many rea- sons. The Swift BAT monitoring catalog provides valuable information on the hard X-ray emission properties of a myriad of sources both galactic and extragalactic, but a literature search indicates that few large-scale studies of this catalog have been published. 300 days of data from over 100 sources sampled multiple times per day is an immense data sample, and we have identified what we consider to be the 13.25 most interesting days out of the year in four different directions. We have also provided a blueprint for creating future catalogs from Swift as well as other instruments. In addition, literature searches indicate that these particular wavelet techniques have not yet been applied to astronomical data. These techniques have allowed for a quantitative determination of the statistical significance of structures in these BAT observation time series, whereas in the past flares were detected either based upon individual photon data or qualitatively. The survey can quickly and easily be expanded to the entire lifetime of Swift and any other large dataset of monitoring time series data. 84

QSO B0706 Flare during IC40

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QSO B0829 Flare during IC40

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Fig. 5.9 QSO B0829 also had a significant structure which turned out to be just a negative excess, an artifact of the source extraction process from the coded mask. 86

Chapter 6

Neutrino Analysis

After the X-ray, wavelet-based catalog was completed, we correlated the X-ray flares with a high quality neutrino sample (Abbasi et al. 2011b). As previously discussed in Chapter 1, the neutrino data set that we chose was from the 40 string IceCube campaign which lasted from April 4th, 2008 until May 20th, 2009. Data collected during the established flare periods from the wavelet catalog were checked for quality against the IceCube monitoring data and the “Good Run List”, which is a master list of all IceCube data collection runs along with comments on if/why the runs failed quality checks. The vast majority of runs during the wavelet catalog flare periods were considered “GOOD” runs and included in the point source neutrino sample. However, runs 110790 and 110791 during the flare from Mrk 421 did not have the usual accompanying monitoring information collected and were checked manually and cleared for use in analysis. Further, run 111204 is missing from the neutrino sample because one of the IceCube strings, string 59, was not collecting data during that run. In addition to anomalous runs, there were also some periods during the flares where IceCube was not collecting any data. Strip charts are below in Figure 6.1 illustrating the uptimes of IceCube and the flaring periods. The IceCube data, which is digitized in the polar ice cap and then transmitted via Ethernet cables to the surface, goes through several layers of quality cuts before reaching what is known as “neutrino level”, where all events present are considered well- reconstructed neutrino signatures. IceCube filters data directly after triggering due to the sheer volume of data handled by the data acquisition system (DAQ). The filtering keeps the data throughput of the detector below the bandwidth limit for data transmitted from the South Pole. Data is sent over the Tracking and Data Relay Satellite System (TDRSS) and eventually arrives at the University of Wisconsin data warehouse. Each physical signature expected to be observed in the detector is given a filter stream with basic cuts on simple reconstructions to reduce the data volume to a manageable rate. Relevant filters to this analysis are the muon filter and the extremely-high energy (EHE) filter. The EHE filter is quite simple: all events that consist of more than 630 reconstructed photoelectrons in the reconstruction run at the South Pole are considered EHE and pass the filter. The event rate for this filter is 1.4 Hz, and the background rate is around 107 times the expected signal rate after the filter. The EHE filter is meant to detect neutrinos with energies 1PeV (Abbasi et al. 2011a). ≥ The second filter, known as the muon filter, is used to select promising track-like events from the triggers arriving at the DAQ in the TeV energy range. The online filter is based upon a few simple derived quantities. The waveforms are recorded and the “hits” are extracted, and then SPE likelihood fits are performed with two initial guesses: a fit seeded with a guess based upon the time of the first hit in the event (SPE1) and a fit based on a seed with a direction that is 180◦ away from the first seed (SPE2). The 87 online filter has two branches. Branch 1 is designed for upgoing muons of all energies, and will accept Southern Hemisphere events, but only with an energy cut that increases with decreasing zenith angle. For Branch 1 acceptance, events must either consist of at least 10 hit DOM’s and have a reconstructed zenith angle from SPE1 and SPE2 80◦ ≥ or at least 16 hit DOM’s and a reconstructed zenith angle from SPE1 and SPE2 70◦. ≥ Branch 2 is designed for higher energy events. To this end, all events passing the branch 2 cuts must have an average of 5 hits or more per DOM hit. In addition, the events must have either at least 10 hit DOM’s and one of SP1 or SPE2 with a reconstructed zenith angle 70◦, or at least 20 hit DOM’s and one of SP1 or SPE2 with a reconstructed ≥ zenith angle 50◦. Generally, the more hit DOM’s in the event, the less stringent the ≥ zenith cut is. Then, cuts were applied to the muon neutrino filter stream as well as the extremely high energy filter stream to obtain a final point source sample that was developed by the Point Source Working Group of IceCube and published by the IceCube collaboration as the official IC40 point source search results (Abbasi et al. 2011b). The cuts which produced the sample of 39,500 events used in this analysis were based upon a more accurate (and time-consuming) reconstruction called the multi-pho- ton electron (MPE) reconstruction. The cuts were based up on nine derived quantities as described below:

Zenith Angle This is the value as reconstructed by the MPE fit. • Reduced Log Likelihood and Modified Reduced Log Likelihood the “goodness- • of-fit” obtained by the MPE reconstruction is normalized by the number of DOM’s hit in the event minus the number of parameters in the muon fit, which is five. Simulations showed an energy dependence in the reduced log likelihood which was eliminated by re-adjusting the degrees of freedom to 2.5.

Angular uncertainty This quantity is calculated using the paraboloid sigma method • detailed in Neunhoffer (2006). A confidence ellipse is constructed based upon the likelihoods calculated from the position reconstruction. An estimate of the space angle error between the true direction of the muon and the reconstructed track can be calculated from this ellipse with a few simple geometric constructions.

Reconstructed Muon Energy Proxy Because the interaction position is not pre- • cisely known for detected muons, an exact reconstruction of the energy is not possible, however an accurate proxy for the energy can be calculated. Energy loss as a muon travels through the ice is proportional to muon energy above 1 TeV, and so this proxy can be calculated by considering ice properties, distance to the DOM’s from the muon track, and the PMT’s angular acceptance.

Bayesian odds ratio Since the downgoing muon rate is six orders of magnitude higher • than the neutrino rate, we can weight our log-likelihood ratios accordingly.(Hill 2001). 88

Fig. 6.1 These five plots represent the IceCube detector uptime during the detected flares. A value of “1” indicates that the IceCube detector was running nominally, and a value of “0” indicates that the detector was not collecting analysis quality data. The blue dashed rectangles on each plot represent the beginning and end of each particular flare. IceCube uptime varied due to many factors such as stray light in the detector, data acquisition hardware problems, etc. a) 1ES 1741, b) 4C 06.69, c) Mrk421, d) B2356 Flare 1, e) 2356 Flare 2 1 1

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Number of Direct Hits (Ndir) A direct hit is defined as one that arrives at a DOM • within -15 to 75ns from the expected time for an unscattered photon leaving the reconstructed muon track. Length of Direct Hits (Ldir) This is the maximum length between two direct hit • photons along the best-fit muon track. Split-reconstruction Zenith Each event is reconstructed again, with the hits split • into two distinct halves. This reconstruction is first done with the hits separated into halves by time, and again with the hits separated geometrically at the midpoint of the reconstructed track. The minimum zenith value from all of the reconstruc- tions is used as a cut parameter. Further details are available in (Dumm 2011) and (Abbasi et al. 2011b). Even though this analysis could possibly be considered “a posteriori”, we tried as much as possible to preserve the principle of blindness throughout the process. A collaboration- wide unblinding process had already taken place on the IC40 point source data set, so the assumption is that the findings from those analyses could subtly influence our study design and the findings we produced. The driving force behind blindness is the desire to prevent the worker’s bias from contaminating the analysis. Certain aspects of the data are kept hidden until the entire analysis method is completed. Testing can be achieved on data not used in the final analysis, known as the “burn sample”, or on Monte Carlo simulations. For an excellent review of blindness procedures, see Klein & Roodman (2005). For this analysis, we used a histogram of event times which all fell within time periods where IceCube was functioning normally, and then selected random times from that histogram. The random times replaced the recorded event time, and the right ascension was then recalculated since the zenith and azimuth of the muon track was fixed. All cuts were then first run on the scrambled times and right ascensions, and fluxes in the signal bins as well as the declination bands were recorded, just as they were for the final analysis. The high-energy particle physics scripting and programming language known as ROOT (Brun & Rademakers 1997) was used for the neutrino portion of the analysis, as well as for all of the final plotting for this work. ROOT files containing the neutrino level sample for the point source analysis were provided by the Point Source Working Group. We then applied a simple date based filter for all of the neutrino events, based on the date of the selected events, then applied a spatial filter to determine which events fit within. The first step in the spatial cut analysis was to examine the PSF from Figure 6.2, and using Equation 6.1, we then calculated the ideal bin size for the IC40 detector configuration for events from both hemispheres of the Earth. Using methods explained in Alexandreas et al. (1993), we first tabulated the total number of events during IC40. We then assumed that all of the flares will be on the order of one day length, which based upon the catalog in Chapter 5, is a safe assumption. We also assumed that the reconstruction error angle (reconstructed direction minus actual track direction) had a Gaussian distribution. We used an order-of-magnitude estimate for the duration to obtain one uniform bin size for all of the sources in a given hemisphere. The root- mean squared (RMS) value for the Gaussian distribution occurs when the cumulative 90

1 0.9 0.8 0.7 0.6 40 Strings: 10 TeV < E < 100 TeV 0.5 ν 40 Strings: 1 PeV < E < 10 PeV 0.4 ν Cumulative Fraction 86 Strings: 10 TeV < E < 100 TeV 0.3 ν 86 Strings: 1 PeV < E < 10 PeV 0.2 ν 0.1 00 1 2 3 4 5 6 ∆Ψ [°]

Fig. 6.2 Taken from Abbasi, et al, 2011, this figure shows the IceCube Point Spread Function 91 distribution function reaches 68%. Using the PSF, we find a value of 1.5◦ for TeV energy neutrinos and 1◦ for PeV neutrinos. We then need to determine an order-of-magnitude estimate for the area of the signal bins, which we set at 10 square-degrees. There are 132 neutrinos per day across the entire sky on average in this data sample, so in 100 square degrees, we expect 0.06 neutrinos on average per day per signal bin. Finally, we refer to Equation 4 from Alexandreas et al. (1993) :

0.88N 0.36 r = (1.58 + .7 e− ) σ (6.1) opt · ∗ where σ is the RMS value we have obtained from the PSF and N is the expected number of neutrinos, to obtain the optimal bin radius. The final values we obtain are 2.0◦ and 3.01◦ as the optimal bin radius for the Southern and Northern Hemispheres, respectively. This equation was derived through Monte Carlo simulations of single particle arrivals on a detector. The curve was fit to a plot of optimal bin size as a function of total number of expected events (Alexandreas et al. 1993). Once we had determined the optimal bin size for point source detection, we needed to quantify the background expectations for those bins so that we could determine the significance of an excess in neutrinos that we might find. The method we used to calculate these expected values involved integrating all of the neutrinos across the entire sky within a given declination band during the associated flare periods. This analysis is discussed in great detail in Ackermann (2006). The width of the declination band is twice the optimal bin size in declination, and includes all right ascensions minus those within the actual signal bin. While the detector properties may change over time, and the detector sensitivity may not be uniform across the entire array, it has been shown that relative stability at a given time is present across a given band in declination. According to Ackermann (2006), “existing azimuthal efficiency variations are washed out by the rotation of the earth.” Further, since the expected flux in a given flare window is rather low ( 1 neutrino), integrating over the entire declination band allows for reasonable ≪ statistics to be collected. Figure 6.3 below shows a schematic of how the declination bands relate to the signal bins.

d⇀ d⇀ = cos ψ < cos ψ (6.2) s · ν 0 Equation 6.2 shows the criterion for accepting events into the signal bin. The angular distance between the origin of the reconstructed neutrino track and the position of the point source cannot exceed the bin size. The angular distance is found using the dot product. A 1 cos Ψ µ = searchbin N = − 0 (6.3) b A bg,band sin δ +Ψ sin δ Ψ N dec.band s 0 − s − 0 bg.band Equation 6.3 provides the effective background in a search bin, µb, which is the ratio of the search bin area to the declination band area multiplied by the number of counts present in the declination band. The second equation for µb is merely the spherical trigonometry necessary to calculate the area of the search bin and then the declination band minus the search bin. 92

Fig. 6.3 Taken from Ackermann (2006), this figure shows how the declination band is situated on the sky with respect to the signal bin.

The results of collecting the declination band statistics and the signal bin statistics are shown in Table 6.1. Once the neutrino counts (both on-source and in the declination band) were obtained, we could use the final significance formula found in Li & Ma (1983) to determine the statistical meaning of finding one neutrino apiece from 4C 06.69 and QSO B2356. Equation 6.4 below shows this formula in detail. The other two sources, Mrk 421 and 1ES 1741, had no neutrinos within the signal bin during the flare windows, we instead use Alexandreas et al. (1993) to find Equation 6.5, which we then use to find the probability of finding at least one neutrino in the signal bin during the flare windows. The results, much less than 5σ for the positive detections, and less than 15% for both of the probabilities indicate that the scrambled data produce no significant detections, the expected result from blind data.

1+ α Non Noff S = √2 Non ln[ ( )] + Noff ln[(1 + α) ] (6.4) · s α Non + Noff Non + Noff where α is the ratio of on-source neutrinos to background neutrinos, which are Non and Noff respectively.

αns (N + n )! P = 1 Ns B s (6.5) ns=0 N +n +1 − (1 α) B s NB!ns! X − In this equation, NB is the number of background counts, ns is the number of on-source neutrinos for which the probability is being calculated, and Ns is the total number of on-source neturinos for which the probability is desired. 93 e mn ’s he source ν 0.06 0.14 N > P NA NA 1.44 0.28 Significance (sigma) NA NA 0 1 1 0 Signal Counts 3 7 16 41 the sources, since no on-source counts were seen, so the colu ast as many counts as were detected in the signal bin due to pur talog sources. Mrk 421 and 1ES 1741 did not have any on source nstead, the probability of detecting at least 1 neutrino in t Background Counts 6.96 19.59 38.21 -30.63 Declination 3 2.5 5.5 3.5 Duration (days) Source 1ES 1741 4C 06.69 B2356 Flare 1 Mrk 421 reads “NA.” The finalnoise. column is the probability of seeing at le neutrinos, so a significance for the result cannot be found. I Table 6.1 This table shows the blinded results for the four ca bin is given. The significance cannot be calculated for two of 94

Chapter 7

Unblinded Results, Summary and Conclusions

This chapter will contain discussion of the final results of the analysis, summa- rize the entire analysis, and then will feature conclusions based upon our results and suggestions for future work. Up until the unblinding, we had demonstrated the power of the wavelet technique to separate true excesses in the time series data from Swift and to suppress unphysical and noise-based excesses. The effectiveness of the technique was demonstrated on both Monte Carlo simulations and blank sky pointing data, and then a catalog was produced of probable physical excesses during the 40 string IceCube season. We then developed an analysis prescription using scrambled times and right ascensions from our neutrino data, and prepared to calculate our final results and look for significant increases in neutrino flux.

7.1 Final Results

Once results had been obtained from the blinded data, summarized in Table 6.1, we were confident in the parameters of our analysis and moved on to unblinding the data set. The unblinding process was a simple yet crucial step in this analysis. The ROOT script used to filter the neutrino sample by time and location on the sky was modified to sort the events by the true event time and measured right ascension, which removed the scrambling. The important step of finalizing all analysis steps before “opening the box” and unblinding the data had been completed, and results could be obtained. The results of the unblinded analysis are shown below in Table 7.1. Seventy-one background neutrinos were seen in the four declination bands, and zero on-source neu- trinos were found. This strongly supports the null hypothesis of no signal neutrinos present during these flaring periods. Based on the background counts seen in the dec- lination bands, we find an expected background neutrino fluence of 0.185, 0.351, 0.153, and 0.359 neutrino counts per source bin for 1ES 1741, 4C 06.69, Mrk 421, and QSO B2356 respectively. Using the Alexandreas et al. technique discussed in Chapter 6, we found a probability of seeing at least one background neutrino for 1ES 1741 of 17.9%, for 4C 06.69 of 30.4%, Mrk 421 of 15.5%, and QSO B2356 of 31.0% based upon an assumption of background only neutrinos present in the sample. However, there is a noticeable difference in the declination band counts for the blinded and unblinded data that cannot be explained by simple Poisson fluctuations. The difference lies in a subtle error in the blind analysis. When the times were scrambled, they were randomized using a histogram of possible event times that all occurred while the IceCube detector was up and running. In reality, as seen by the strip chart in Chapter 6, there are noticeable downtimes during each of the flares, during which no data would have been collected. The unblinded data were actually collected over larger periods of time than the flare 95 lengths, however this just caused the blind analysis to have a more conservative result than the final analysis. In the future, this mistake will be avoided. 96 e for the bin n the significances ) b N 0.18 0.30 0.16 0.31 | ν 1 > P( 0 0 0 0 ν On Source 0.18 0.35 0.15 0.36 c. band counts which is the expected number of neutrinos in number of counts in the entire declination band surrounding en in the source bin during the flares, the seventh column is th the probability of seeing at least one background neutrino i Effective Background e in degrees, the third column is the ratio between the source e source name, the first column is the RA coordinate in degrees d. 9 ast one neutrino given the null hypothesis is calculated; no 13 26 23 Dec. Band Counts A 0.014 0.014 0.017 0.016 6.96 19.59 38.21 Dec -30.63 RA 265.99 327.02 116.11 359.78 Source 1ES 1741 4C 06.69 Mrk 421 QSO B2356 source, the fifth columnthe is source the bin, product the of sixth A column and is the the number number of of de neutrinos se number of on-source neutrinossignal seen, bin and during the the eighth flare column time is given the effective backgroun Table 7.1 Unblinded results: The probability of seeing at le are found because nothe on-source source, neutrinos were the seen. secondand After column the th is rest the of declination the of declination band, the the sourc fourth column is the 97

Therefore, our observation of zero on-source neutrinos is completely within range of these predictions. While we cannot claim any discoveries based upon this analysis, the analysis prescription we have prepared is a very significant contribution. Limitations of this study included the possible “a posteriori” nature of the neutrino analysis due to previous unblinding, photon energies limited to a maximum of 50 keV, only 40 strings of IceCube operational during this period of time, and the previous unblinding of the point source sample. A truly blind analysis can be performed in the future before the point source data from later seasons is unblinded, the sensitivity of the detector will increase when more strings are present during the data collection, and higher energy photons are more likely to correlate with neutrino emission. We can also find an upper bound (as defined by Kashyap et al. (2010)) on potential signal flux from each source using results from Abbasi & Collaboration (2011), since the previous IC-40 time dependent flare study used the same detector configuration and thus would have the same effective area. As mentioned in Chapter 1, the effective area of the IC40 detector was relatively constant over large bands in declination, 30◦ wide. The flux bound is declination dependent, as shown in Chapter 1 from the effective area plot. The methods of Feldman and Cousins (Feldman 1998) were used to obtain these estimates; when zero neutrinos are observed in a bin with Poisson arrival probabilities and an expected flux of zero, the 90% confidence level upper bound on neutrino fluence during each flare is 2.4. We attempted to use sources in the same declination bin as the sources in this study to obtain the flux estimates in Table 7.2 below, since we have observed zero on-source neutrinos for sources in the same declination band as sources published in the IC40 Point Source analysis, the upper bound for these sources will be the same as the sources with published limits. In other words, for a null detection, the upper bound calculation for a source observed by the same detector configuration (IC40) and in the same declination bin can be used. These are the comparable sources listed in Table 7.2, but for 1ES 1741, 4C 06.69, and QSO B2356, these are the first flux bounds measured for these sources. Once upper bounds on the neutrino flux had been found, it was then possible to calculate upper bounds on the neutrino luminosities of the AGN. It is important to note that the blazar emission in photons and most likely in neutrinos as well would be highly beamed and therefore calculating an isotropic luminosity will seriously overestimate the luminosity, but it is still a physically interesting result. The redshifts of these AGN were found using SIMBAD (Wenger 1985), and the luminosity distances were then found using the cosmological calculator known as CosmoCalc (Wright 2006) with the open universe settings. Using the standard formula for luminosity, L = 4πr2F , where F is flux and L is luminosity, the isotropic luminosities found in Table 7.2 were calculated. 98 Limit Comparable Source W Comae W Comae Mrk 421 PKS 0454-234 GeV/sec GeV/sec GeV/sec GeV/sec 49 52 48 49 10 10 10 10 · · · · on figures from Abbasi & Collaboration (2011) 07 53 02 1 iso . . . . L 6 1 6 2 /sec /sec /sec 2 /sec 2 2 2 GeV/cm GeV/cm GeV/cm GeV/cm 6 7 6 6 − − − − 10 10 10 10 · · · · 91 82 82 . 23 . . . Upper Bound on Neutrino3 Flux 3 .2 3 6.96 38.2 19.59 -30.63 Declination Source 1ES 1741 4C 06.69 Mrk 421 QSO B2356 Table 7.2 Upper bound on neutrino flux in the source bins based 99

7.2 Conclusions and Future Possibilities

Because the results from this study come in the form of upper bounds on muon neutrino flux from AGN during X-ray flare periods, limited statements can be made on the implications for neutrino production theories. Also, because the Swift BAT energies are lower than the second peak in the SED of most blazars, it is possible that the lack of coincident neutrino flux is simply because the search was too low in photon energy. Since the photons detected are 150 keV or less and the neutrino sensitivity really begins in the TeV energy, it is difficult to draw direct conclusions about the energetics of the photon and neutrino production methods. However, competitive limits on the flux of three blazars, 1ES 1741, 4C 06.69, and QSO B2356, were found, as well as the same limit as was previously seen for Mrk 421. The future applications for this analysis prescription are many and varied. The wavelet techniques developed here can be used on the Swift monitoring catalog for differ- ent source classes, such as microquasars, soft gamma repeaters, etc. Fermi, the gamma- ray Great Observatory, observes the universe in energies that are closer to the second peak of the SED for many blazars, and thus the photon flaring may be better tied in with neutrino production, assuming a hadronic model. Fermi data are not stored in a format that is as easily accessible and mass processed as the Swift monitoring data; a Fermi-based investigation could require more extensive data processing and likely col- laboration with experts from the Fermi team. The possibilities for the application of our methods to the thriving field of astronomical data mining are very exciting (McConnell et al. 2011). In the future, the HAWC array will allow for large sky coverage observations in the high energy ( TeV) gamma-ray regime, leading to a large increase in duty cycle ∼ length and sky coverage in that waveband, which could be crucial to identifying the most promising flares for correlation with neutrinos. Another logical extension of this study would be to use data from later IceCube seasons, where the data are from a more complete array and also remain unblinded. Greater sensitivity and a more homogeneous detector than the 40 string configuration (IC40) could help reduce background contamination. If data with fewer cuts are used, specialized cuts for the wavelet analysis could be developed, as the point source sample used for this study was already cut down to what is referred to as “neutrino-level.” If flares are on the order of days, then the neutrino candidate sample could be increased by a factor of two orders of magnitude, and the timing cuts would bring the rate back to neutrino level. Specialized cuts could increase the possibility of detecting correlated neutrinos with AGN flares. This would allow for looser physics cuts since the time cuts would be used to eliminate the background, and so there could be more on-time neutrinos to test. In addition, the binned search approach used in this study could be replaced with an unbinned search method, where the reconstruction error on each neutrino is factored into the calculation of its position with respect to a given point source. Publications from this study could include a methods paper on the wavelet technique and a scientific paper on the entire analysis prescription and results. Future publications would come from redoing the study with IC59 or even the full IceCube detector. In the end, while no significant results were discovered, our analysis has served as a trailblazer for similar analyses in the field of particle astrophysics. Future astronomical 100 instruments will collect larger and larger amounts of data, even petabytes per day in some cases. Automated data analysis tools and data mining techniques are key to exploring the massive data sets of today and in the future. Our technique allows for 142 objects over a period of a year to be reduced to a catalog of five significant flares. It is possible that refinements to the wavelet technique (e.g. a more sophisticated mother wavelet than the Haar wavelet or a looser, more tuned wavelet threshold) could lead to further sensitivity increases for the algorithm. Furthermore, with the background of a neutrino telescope relatively constant with respect to time at the neutrino level, well-defined time windows for correlations with neutrino samples are promising techniques for possible discoveries. The possibilities for multi-messenger astrophysics with IceCube are truly exciting, with a breakthrough discovery a distinct possibility. In comparison to the previous studies discussed in Chapter 1, this study has introduced a new flare identification method, set upper bounds on neutrino flux from 4 AGN which previously did not have limits, and was likely the first of its kind to search for neutrino coincidences with photon flares of such short duration, on the order of half an hour. 101

Appendix

Source Code 102 blankcsvmaker.R: Converts Swift Monitoring Data to a CSV file #This script converts the Swift input files into CSV files to be read into ROOT datain=read . table ( ”C: /cygwin/home/Steve/ blanksource /XXXJ1506 . 4 p2007. orbit . lc . txt”, header=FALSE) filelen=21487 #replace this with the number of lines in the file #convert Swift mission time into JD JD=datain$V1/ 60.0 / 60.0 /24.0+2451910.5 #convert JD to MJD MJD=JD 2400000.5 − MJDa=MJD datainaV3=datain$V3 datainaV2=datain$V2 thesedata=datainaV2 datainaV11=datain$V11 picky=datainaV2# mean(datainaV2) Uncomment to baseline − subtract the data indices=c ( 1 : length (picky)) goodones=indices [ datainaV11==0] #only keep the entries that have good data quality flags sigmaall=datainaV3[goodones ]; #use this array to select the proper sigma entries x=(MJDa[ goodones ]) #same for x entries picky=(picky [goodones])#;same for y values ii=matrix ( data=c (x,picky ,sigmaall),nrow=21487, ncol=3) # put all the data in a matrix for output write . csv (ii , file=” c : root 1506.4. csv”, col . names=F, row . names= \\ \\ F) #write the outfile customtrap.R: Calculates the custom trapezoid integral for normalized power customtrap2=function (xarray1, array0, sarray1, beg, endit) { #xarray1 is the input x series #array0 is the input y series #sarray1 is the input error arry #beg is the point to start integrating #endit is the point to stop integrating array1=array0 #don’t overwrite the input data thesum=0 # this variable represents the total normalized power for (aind in c ((beg+1): endit)) { #do the power calculation thesum=.5 (xarray1[aind] xarray1[(aind 1)]) (array1 [aind]+ ∗ − − ∗ array1 [(aind 1)]) /(mean(sarray1 [(aind 1):aind ]) 2)+thesum − − ∗∗ } return (thesum) #return the normalized power 103

} supportfuncs3.R: Supporting functions #add white noise to a time series, given an array of sigmas noisemaker< function (pickyz ,sigmas) − {

#pick values from N(0,sigmas) to add noise for (ycount in c ( 1 : length (pickyz))) { #pick Gaussian noise tempval=rnorm(1 ,mean=0,sd=(sqrt (sigmas[ycount]))) #add it in pickyz[ycount]=pickyz[ycount]+tempval } pickyz }

#function to directly apply sqrt(2 log(n)) sigma to each ∗ ∗ wavelet coeff dumbthresh< function (thresh, len) − { newthresh< thresh − #loop over all coeffs for (threshiter in c (1:( length (newthresh$D)))) { #apply Visushrink if ( ( abs (newthresh$D[threshiter]) /sqrt (newthresh$c [ threshiter]) /sqrt (2 log (len))) <= 1) newthresh$D[ ∗ threshiter]=0

} #return a wd data type with the denoised coeffs class (newthresh)< ”wd” − newthresh } #for use with MC data, jitters the x axis of the time series to − be more realistic xscrambler< function (x,gridsize) − { thislength=gridsize xholder=c ( ) totalshift=0 #keep track of the cumulative offset 104 evenx=c (0:( thislength 1) )/(thislength 1) 12 #this gives an − − ∗ evenly sampled x vector #from zero to 1 minspacing=1.0/ thislength 6 ∗ samplerate=1/ gridsize xholder=c (xholder ,0) for (count1 in c (2: thislength)) { #pick a uniform random variable to decide if a point jitters testvar=runif (1) # pick a uniform variable if (testvar >(1 jitterfraction)) #make a gap or squish − { spacing=(rnorm(1))/ thislength 3 #divide by 3 so that the ∗ points don’t #overtake each other totalshift=totalshift+spacing if ( count1==1) #first point either jitters or doesn’t { #no need to worry about falling behind xholder=c (xholder ,evenx[count1]+totalshift) } else { if ((evenx[count1]+totalshift)>=xholder [ length (xholder ) ] ) { #tests to see if the jittered point is ahead in time of the previous point xholder=c (xholder ,evenx[count1]+totalshift) } else { totalshift=totalshift spacing+minspacing ( − − samplerate ) xholder=c (xholder ,evenx[count1]+totalshift)

} } } else xholder=c (xholder ,evenx[count1]+totalshift)

} xholder=xholder/(max(xholder)) x=xholder x 105

} #points to signal shape function datafiller< function (x,y,choice ,gridsize) − { if (choice==”flatfunc”) { y=flatfunc(x,y, gridsize , maindex, scaleind ) } if (choice==”gauss”) { y=gaussfunc(x,y, gridsize , maindex) } y } reversep-useR-nn.R: Overlapping coefficient cut function #overlapping coefficient cut function #Input: wavelet coefficients from irregwd, the coarest lev el of decomposition to checck for overlapping coeffs , and a verbose boolean flag reverseuseRnn< function (wdin,bigsize , verbose=F) − { #copy the input wavelet coefficients into the output variab le wdout=wdin #reset the test variable trigger=0 #fill a list , each element contains vector of values of wavele t coefs. nlevels=ceiling ( log ( length (wdin$D) )/log (2)) 1 − if (verbose) print ( paste (”nlevels”, nlevels ) ) deconstructit=list (accessD(wdin,0) ) minlevel=nlevels floor ( log (bigsize)/log (2)) − if (verbose) print ( paste (minlevel ,minlevel)) lookedat=wdin lookedat $D=rep (0 , length (lookedat $D) )

#main loop here for (qindex in c (minlevel:( nlevels 1))) − { if (verbose) print ( paste (”q trigger”, trigger)) #make a vector of indices for the length of the coefficient vector at this level of decomposition indices=c (1:2 qindex) ∗∗ #which elements are non zero, don’t waste time looking at the − zero coeffs nonzeros=indices [ abs (accessD(wdin,qindex)) > 10 8] ∗∗− 106

if (verbose) print (nonzeros) for (zindex in nonzeros) { #look for coefficients that overlap if (accessD(lookedat ,qindex)[ indices [zindex ]] < 1) { trigger=0 #this happens if no nonzero coeffs exist at that level of detail if ( length (nonzeros) > 1) #if non zero ccoeffs exist , look for adjacent coefficients if ( 1 %in% abs ((nonzeros nonzeros[zindex ]))) − trigger=1 {

} if (verbose) print ( paste (”accessD trigger”, trigger)) #loop over all the levels for (rindex in c ((qindex+1): nlevels ) ) { if (verbose) print ( paste (”comparing” ,qindex ,”to ”,rindex)) if (verbose) print ( paste (”r trigger”, trigger))

startpt=2 (rindex qindex) (zindex 1)+1 ∗∗ − ∗ − if (startpt >1) startpt=startpt 1 − stoppt=2 (rindex qindex) zindex ∗∗ − ∗ if (stoppt 10 ∗∗ 8) − { trigger=1 if (verbose) print (”trigger”) } #lookedput is a parallel structure to the wavelet coefficie n t matrix #it is to keep track of whether a coefficient has been looked at before #by setting lookedput=1 for any coeff that has been looked at before , we #save on CPU time by preventing redundant comparisons between coeffs lookedput=accessD(lookedat , rindex) lookedput[ startpt:stoppt]=rep (1 ,(stoppt startpt+1)) − if (verbose) print ( paste (”lookedput”,lookedput)) lookedat=putD(lookedat ,rindex ,lookedput) if (verbose) { print (”accessD this R” ) 107

print ( paste (”accessd”,accessD(lookedat ,rindex))) }} if (verbose) print ( paste (”trigger”,trigger)) if ( t r i g g e r ==0) { if (verbose) print (”untrigger”) for (rindex in c ((qindex): nlevels ) ) { if (verbose) { print (”zeroing”) print ( paste (”starting pt”, rindex)) print ( paste (”ending pt”, nlevels ) ) } #trigger=0 means no overlapping coeffs were foiund, so we zero out the row startpt=2 (rindex qindex) (zindex 1)+1 ∗∗ − ∗ − stoppt=2 (rindex qindex) zindex ∗∗ − ∗ innerind=c (1:2 rindex) ∗∗ if (verbose) { print ( paste (”startpt”, startpt)) print ( paste (”stoppt”,stoppt)) print (innerind) } lookedput2=rep (1 , length (innerind)) lookedput2[ startpt:stoppt]=rep (0 ,(stoppt startpt+1)) − if (verbose) print (lookedput2[startpt:stoppt])

#lookedput2 is a parallel structure to the wavelet coeffici e n t matrix #it will have a 1 for values that should be retained and a zero for values with no overlapping coeffs #at the end we multiply them together, thus zeroing out any coeffs that don’t overlap lookedput=accessD(lookedat , rindex) #multiply them together to zero out the coeffs with no overlap wdout=putD(wdout, rindex , lookedput2 (accessD(wdout, rindex))) ∗ if (verbose) print (accessD(wdout, rindex)) }} }} } if (verbose) { print (”looked at”) print (accessD(lookedat , nlevels ) ) print (lookedat $D) print (”wdout”) print (accessD(wdout, nlevels ) ) } 108

#lnz checks the finest level of decomposition; there will be coeffs at finer levels to compare with, #but if there are two coefficients in the finest level that are non zero and adjacent to each other − #they will be saved lnzinds=c ( 1 : length (accessD(wdout, nlevels ) ) ) lastnonzero=lnzinds [ abs ((accessD(wdout, nlevels ) ) ) > 0 ] keepers=c ( ) for (lnz in lastnonzero) { if (1 %in% abs (lastnonzero lnz)) keepers=c (keepers ,lnz) − } #makes sure that all coefficients that were never checked are zeroed out. #coeffs that were never checked therefore have no overlappi ng coeffs and are zeroed out wdout$D[1:(2 nlevels )]=wdout$D[1:(2 nlevels ) ] lookedat $D[1:(2 ∗∗ ∗∗ ∗ nlevels ) ] ∗∗ return (wdout) } reversesharkfin.R: Sharkfin function #”sharkfin” asymmetric input function for sensitivity plo t s #A and C are scaling factors, and there is a verbose flag reversesharkfin< function (A,C, verbose=F) − { xrang=c (1:A) #A sets the width firsthalf=c (1:(A/2) ) if (verbose) print (firsthalf) #inverse square root for the second half, square root for the first half , and make sure that they intersect newfirsthalf=((firsthalf 1)/ ( (A/2) 1) 9)+1 − − ∗ totaly0=c ( sqrt (newfirsthalf) ,1/( sqrt (newfirsthalf))) totaly=c ( ) for (revind in c ( length (totaly0):1)) { totaly=c (totaly ,totaly0[revind]) } #scale it by C to fill out parameter space totaly=totaly /( sqrt (10)) C ∗ if (verbose) print (newfirsthalf) return (totaly) } mrk421-real.R: Find the flares in Mrk 421 rm( list=l s ( ) ) 109 dothecut< function (grabby , baseline) − { #simple physics cut provided by this function. If the data point with the maximum absolute value has a negative sign, replace the whole denoised series by the baseline (one double variable) if (max( abs (grabby)) != 1 min(grabby)) return (grabby) − ∗ else return ( rep (baseline , length (grabby))) } #input directory for exterior functions and output directo r y sourcepath=”/ gpfs /home/smm470/fromwindows/” outputloc=”/home8/ icecube / steve /mrk421 real2006 2/” − − #load in the overlapping coeff. cut and the other external functions source ( paste (sourcepath ,”reversep useR nn.R” ,sep=””)) − − source ( paste (sourcepath ,”supportfuncs3.R”,sep=””)) icestart=53775 #MJD when the IceCube campaign you want to study began; set to zero to process all data iceend=55050 #initialize variables and prepare R for EPS output setEPS() filecounter=1 triporigx=c ( ) triporigy=c ( ) tripnewx=c ( ) tripnewy=c ( ) tripsigs=c ( )

#load R packages for plotting , histograms, wavelet utiliti es , sparse matrix multiplication , and miscellanious output functions library (”prettyR”) library ( ”MASS” ) library (”wavethresh”) library (”SparseM”) library (”R. utils”) #VERY IMPORTANT: This variable sets the length of the sample time windows. I would leave this at 1024, I never needed to change it. gridsize=1024 #filevectloc=”/home8/ icecube / steve / swiftblankpointings /” #filevect=rep(0,1000)#eir(filevectloc ,pattern=glob2 r x (”XXX ”) ) ∗ allthexs=c ( ) 110

alltheys=c ( )

overallcount=1 #choice is a string setting flat , gaussian, bumpy gaussian, or real data used in the past to send toy data to the − algorithm mychoice=”data”# signoise=F #Do I want randomized errors (by adding noise)? ynoise=F #do I want to add noise to the Y a x i s data NEVER USE − WITH REAL DATA numruns=1 #how many times to iterate set to 1 for real data − scaleruns=1 #how many different amplitudes to test set to 1 for real data − buildstats=1 #how many times to run each width and amplitude setting, again, keep it at 1 for real data normalizeit=F #should I normalize the flux measurements to a max of 1 , NEVER FOR REAL DATA

if ( ! normalizeit) scaleruns=1 { } #load in the library that allows for repeatable experiments through input seeds KEY − library (”setRNG”) setRNG( kind=”Wichmann Hill”, seed=c (12345,123456,12345) , normal − . kind=”Ahrens Dieter”) − library (”rootSolve”) #initialize matsaver=list ( ) cleansaver=list ( ) oldxsaver=list ( ) newxsaver=list ( ) oldysaver=list ( ) oldsigsaver=list ( ) newsigsaver=list ( ) #initialize the outermost while loop keeprunning=1 #read in the data; these can be either stored on disk or R will pull them straight from the web, handy ! datain=read . table (”http: // swift.gsfc.nasa.gov/docs / swift / results / transients /weak/Mrk421.orbit . lc .txt”) #convert from Swift Mission Time to JD and then to MJD JD=datain$V1/ 60.0 / 60.0 /24.0+2451910.5 111

MJD=JD 2400000.5 − lastval=1 #main while loop while (keeprunning==1) { #unload the data from the input matrix thesedata0=datain$V2 thesesigmas=datain$V3 thesequals=datain$V11 thesediffs=MJD[2: length (thesedata0)] MJD[ 1 : ( length (thesedata0) − 1) ] − rangestart=lastval+1 startpt2=rangestart deltats=c ( ) #find the difference between each sample and the next in terms of time for (qqqq in c (1:( length (MJD) 2))) − { deltats=c (deltats ,(MJD[qqqq+2] MJD[ qqqq+1])) − } # } #this is the mode of those values modedelta=as . double (Mode(deltats )) #this should set targetlength so that the interpolated data have a length in time equal to 1024 mode(deltat) ∗ targetlength=modedelta gridsize ∗ stopstop=0 #inner while loop while (stopstop !=1) { dayind=min ((1.0 gridsize) ,( length (MJD) startpt2)) ∗ − #loop to move to at least the start date of the IceCube set in question while (MJD[ startpt2 ] < icestart) { startpt2=startpt2+1 rangestart=rangestart+1 } daysaver=MJD[ dayind+startpt2] MJD[ startpt2 ] − #cut down the data set in question to the target length while (daysaver > targetlength) { daysaver=MJD[ dayind+startpt2] MJD[ startpt2 ] − if (daysaver< 1 ) print ( ”ABORT! ” ) dayind=dayind 1 − } datalen=dayind+1 112

#ensures that the data to be interpolated have at least a length of 50 if (datalen <50) { startpt2=startpt2+1 rangestart=rangestart+1 } #if so, quit the while loop else stopstop=1 } #if you’ve reached the end of the data set of interest, quit the while loop after this iteration if (MJD[ dayind]> iceend) keeprunning=0 #move the rangestop place holder to the end of the current data window rangestop=datalen+rangestart #safety check to make sure that rangestop doesn’t extend pas t the end of the data file if (rangestop >= length (MJD) ) { rangestop=length (MJD) keeprunning=0 } #initalize variables thesequalsbig=thesequals[ rangestart:rangestop] sigmasbig=thesesigmas [ rangestart:rangestop] thesedatabig=thesedata0 [ rangestart:rangestop]

origts=c ( ) MJDsmall=c ( ) thesedata=c ( ) sigmas=c ( ) qualind2=2 qualind=1 startpt=0 x=MJD origtsbig=x[rangestart:rangestop]

#check the data quality flags while (qualind2 <= length (sigmasbig)) { if (thesequalsbig [( startpt+qualind2 1)] == 0) − { sigmas=c (sigmas ,sigmasbig[( startpt+qualind2 1)]) − thesedata=c (thesedata , thesedatabig [( startpt+qualind2 1)]) − 113

origts=c (origts , origtsbig[( startpt+qualind2 1)]) − qualind=qualind+1 } #check for the endpoints else { if (qualind2==2 qualind==1) rangestart=rangestart+1 | | if (qualind2==length (sigmasbig)) rangestop=rangestop 1 − } qualind2=qualind2+1 } #uncomment the next line to baseline subtract picky=thesedata# mean(thesedata ) − #add noise to data , DONT USE WITH REAL DATA if ( y n ois e==T) picky=noisemaker(picky ,sigmas) { } #normalize the times between 0 and 1 for input into Kovac interpolation code normX=(origts min(origts)) − normX=normX/(max(normX) ) xold=origts x=normX

#kovac interpolation code gridthis=makegrid(x,picky , gridsize) #work with variances, not standard deviations sigmas=sigmas 2 ∗∗ #do the 2D wavelet transform by hand to allow for error bars to propagate to the wavelet domain THIS IS THE BIG CHANGE − rvector=rep (0,gridsize length (origts)) ∗ for (rindex in c (0:( gridsize 1))) − { if (gridthis $Gindex[ rindex+1] < (gridsize 1) ) − { rvector[rindex length (origts)+gridthis $Gindex[ rindex+1]+1]= ∗ gridthis $G[ rindex+1] rvector[rindex length (origts)+gridthis $Gindex[ rindex+1]+2]=1 ∗ − gridthis $G[ rindex+1] } rvector[ length (rvector)]=1 } #the interpolation matrix for the 2d tranform is found Rmatrix=matrix (rvector ,gridsize , length (origts) ,byrow=1) sigvect=rep (0 , length (origts) length (origts)) ∗ #put the errorbars into a diagonal matrix for (sigindex in c (0:(( length (origts) 1)))) − { sigvect [sigindex length (x)+sigindex+1]=sigmas [ sigindex+1] ∗ } sigmaMat=matrix (sigvect , length (origts), length (origts) ,byrow=1) 114

#put the R (interp matrix) and Sigma (covariance matrix) int o sparse data type for faster processing Rsmat=as . matrix . csr(Rmatrix) sigmaSmat=as (sigmas ,”matrix.diag. csr”) #interpolate the matrix and find the variances RRTsmat=Rsmat% %sigmaSmat% %t (Rsmat) ∗ ∗ RRTmatrix=as . matrix (RRTsmat) newsigmas=diag (RRTmatrix)

cursig=RRTmatrix csaver=rep (0,gridsize 1) − csaverind=1 for (sizeindex in c (1:( log (gridsize)/log (2)) 1) ) − { thisgridsize=gridsize /(2 (sizeindex)) ∗∗ Hformcurr=rep (0,thisgridsize thisgridsize /2) ∗ Gformcurr=Hformcurr #create the low pass and high pass filter matrices and store them as sparse matrices for faster processing for (hindex in c (1: thisgridsize)) { Hformcurr[ thisgridsize (hindex 1)+2 hindex 1]=1.0/( sqrt (2)) ∗ − ∗ − Hformcurr[ thisgridsize (hindex 1)+2 hindex]=1.0/( sqrt (2)) ∗ − ∗ Gformcurr[ thisgridsize (hindex 1)+2 hindex 1]=1.0/( sqrt (2)) ∗ − ∗ − ∗ ( 1) (2 hindex) − ∗∗ ∗ Gformcurr[ thisgridsize (hindex 1)+2 hindex]=1.0/( sqrt (2)) ( 1) ∗ − ∗ ∗ − (2 hindex+1) ∗∗ ∗ } Hmatcurr=matrix (Hformcurr , thisgridsize /2,thisgridsize ,byrow=1) Gmatcurr=matrix (Gformcurr, thisgridsize /2,thisgridsize ,byrow=1) Gsmat=as . matrix . csr(Gmatcurr) Hsmat=as . matrix . csr(Hmatcurr) cursigs=as . matrix .csr(cursig) #find the error bars for the next level of decomposition and the next level of decomposition’s RRt matrix cursigtwiddles=Gsmat% %cursigs% %t (Gsmat) ∗ ∗ cursigs=Hsmat% %cursigs% %t (Hsmat) ∗ ∗ cursigtwiddle=as . matrix (cursigtwiddles ) cursig=as . matrix (cursigs) thesecs=diag (cursigtwiddle)

#store the error bars in Kovac’s data structure so they can be used in thresholding for ( citer in c ( 1 : length (thesecs))) { csaver[csaverind]=thesecs[ citer ] csaverind=csaverind+1 }} 115

#do the wavelet transform of the time series data wdthis0=irregwd(gridthis , filter .number=1,family=”DaubExPhase”) wdthis=wdthis0 wdthis$c=csaver wdthis00=wdthis class (wdthis00)< ”wd” − #use the visushrink threshold #run my thresholding code which uses the error bar for each individual wavelet coefficient threshval=sqrt (2 log (gridsize)) ∗ maxlev=log (gridsize)/log (2) 1 − thresholdthis=dumbthresh(wdthis , gridsize) #return to the time domain after denoising cleanedit=wr(thresholdthis) #run the overlapping coefficient cut reversed=reverseuseRnn(thresholdthis ,300) reverseclean=wr(reversed)

overallcount=overallcount+1 #save the values from this iteration for output to text file interpedx=gridthis $ gridt (origts[ length (origts)] origts [1])+ ∗ − origts [1]#rangestop allthexs=c (allthexs ,interpedx) alltheys=c (alltheys ,reverseclean) lastval=rangestart+gridthis $Gindex[340]

tripsigs=c (tripsigs , sqrt (newsigmas)) triporigy=c (triporigy ,gridthis $ gridy) tripnewx=c (tripnewx ,interpedx) tripnewy=c (tripnewy, reverseclean)

if (overallcount > 3) { #after every three iterations , plot the overlapping tiles collist=c ( rep (”black”,1024) , rep (”red”,1024) , rep (”green”,1024)) png2( paste (outputloc , filevect [filecounter],overallcount ,”tria d . png” ,sep=””)) plot (tripnewx , triporigy ,type=”p”,pch=” ” , col=”light grey”, main ∗ =paste (”Final cleaned sample after a l l cuts , tile #” , overallcount) ,xlab=”MJD” ,ylab=”Cleaned time series flux ( counts/cm/ s ec / sec)”) arrows (tripnewx , triporigy tripsigs ,tripnewx, triporigy+tripsigs , − length =.05,angle=90,code=3, col=”light grey”) 116 matplot (tripnewx [1:1024] ,tripnewy [1:1024] ,type=”p”,pch=”x” , col= ”red”,add=T) matplot (tripnewx[1025:2048] ,tripnewy[1025:2048] ,type=”p”,pch=”x ” , col=”blue” ,add=T) matplot (tripnewx[2049:3072] ,tripnewy[2049:3072] ,type=”p”,pch=”x ” , col=”green” ,add=T) dev . off ( ) xx=tripnewy divcount=1 #calculate the baseline while ( i s . na( as . double (Mode(tripnewy [1: floor ( length (xx)/ divcount)])))) divcount=divcount+1 { } themode=as . double (Mode(xx [1: floor ( length (xx)/ divcount)])) tripnewy2=tripnewy #run the physivs cut on each time window tripnewy2[1:1024]=dothecut(tripnewy2 [1:1024] ,themode ) tripnewy2[1025:2048]= dothecut(tripnewy2[1025:2048] , themode) tripnewy2[2049:3072]= dothecut(tripnewy2[2049:3072] , themode) abs1=abs (tripnewy [1:1024]) abs2=abs (tripnewy [1025:2048]) abs3=abs (tripnewy [2049:3072]) abs12=abs (tripnewy2 [1:1024]) abs22=abs (tripnewy2[1025:2048]) abs32=abs (tripnewy2[2049:3072]) addstring=”” #check if the all other cuts except the physics cut are passed if ( (max(abs1) > mean(abs1))+(max(abs2) > mean(abs2))+(max(abs3 ) > mean(abs3)) > 1) addstring=”signalgood” #check if the physics cut is passed, this modifies the output text file name for easy identification of flares if ( (max(abs12) > mean(abs12))+(max(abs22) > mean(abs22))+(max( abs32) > mean(abs32)) > 1) addstring=paste (addstring ,” passcuts”) #write out the text files write . table ( t (tripnewx) , col . names=F, row . names=F, append=T, sep=” , ” , file=paste (outputloc ,”tripnewx”,overallcount ,addstring , filevect [filecounter ],sep=””)) write . table ( t (tripnewy) , col . names=F, row . names=F, append=T, sep=” , ” , file=paste (outputloc ,”tripnewy”,overallcount ,addstring , filevect [filecounter ],sep=””)) write . table ( t (tripnewx) , col . names=F, row . names=F, append=T, sep=” , ” , file=paste (outputloc ,”tripoldx”,overallcount ,addstring , filevect [filecounter ],sep=””)) 117 write . table ( t (triporigy), col . names=F, row . names=F, append=T, sep=” , ” , file=paste (outputloc ,”tripoldy”,overallcount ,addstring , filevect [filecounter ],sep=””)) write . table ( t (tripsigs), col . names=F, row . names=F, append=T, sep=” , ” , file=paste (outputloc ,”tripsigs”,overallcount ,addstring , filevect [filecounter ],sep=””))

#drop the earliest window and move on triporigy=triporigy [1025: length (triporigy)] tripnewx=tripnewx [1025: length (tripnewx)] tripnewy=tripnewy [1025: length (tripnewy)] tripsigs=tripsigs [1025: length (tripsigs)]

}

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Rice University Houston, TX 1999-2003 B.S. in Astrophysics , B.A. in Statistics Awards and Honors Downsborough Graduate Fellowship 2009 Sigma Xi Grant-in-Aid Recepient 2004 Nellie H. and Oscar L. Roberts Fellowship 2003

Research Experience Doctoral Research The Pennsylvania State University 2004-Present Thesis Advisor: Prof. Douglas F. Cowen I modified and implemented a wavelet algorithm for denoising unevenly sampled, het- eroscedastic time series for use in cleaning Swift BAT orbit-by-orbit data, to be used to build a catalog of potential flares from AGN in energetic X-rays. These flare times were correlated with neutrino candidates from IceCube to search for coincidences. In addition, I worked on calibration and software development for integration of AMANDA and IceCube, along with a filter for selecting low energy cascade candi- dates from South Pole data. Undergraduate Research Rice University 2002-2003 Research Advisor: Prof. Uwe Oberlack I developed new event reconstruction code for liquid Xe gamma-ray telescopes based on look up tables and scattering distributions. Teaching Experience Teaching Assistant The Pennsylvania State University 2003 I taught two sections of a laboratory course for non-majors and developed one lab from scratch and prepared my own lectures.