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Search for VHE Gamma-Ray Emission from the Globular Cluster M13 with VERITAS

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Search for VHE Gamma-Ray Emission from the Globular Cluster M13 with VERITAS Search for VHE gamma-ray emission from the globular cluster M13 with VERITAS Michael Warren McCutcheon∗ Department of Physics McGill University, Montreal April 11, 2012 A thesis submitted to McGill University in partial fulfilment of the requirements of the degree of Doctor of Philosophy. c Michael Warren McCutcheon, 2011 ∗[email protected] Abstract Globular clusters, such as M13, are very dense star clusters and are known to contain many more millisecond pulsars per unit mass than the galaxy as a whole. These pulsars are concentrated in the core regions of globulars and are expected to generate relativistic winds of electrons. Such energetic electrons may then interact with the intense field of optical photons, which is supported by the numerous normal stars of the cluster, to generate Very High-Energy (VHE) gamma rays. Herein, this emission model, as imple- mented by Bednarek & Sitarek [36], is described and justified in more detail and data from observations of M13, undertaken to confront this model, are analysed. No evidence for VHE gamma-ray emission from M13 is found. A decorrelated, integral upper limit of 0.306 × 10−12 cm−2 s−1 above 0.8 TeV , at a confidence level of 95%, is determined. Spectral upper limits are also determined and compared to emission curves presented in [36]. A detailed examination of the parameters of the model is performed and it is found that the predicted curves were based upon over-optimistic estimations of several of these. Nonetheless, the model can be related to existing theories of pulsar winds and, thereby, it is found that the acceleration of electrons in millisec- ond pulsar winds (outside pulsar light-cylinders) to TeV energies is excluded by these observations, under self-consistent assumptions of the properties of this population of millisecond pulsars. Resume´ Les amas globulaires, tels que M13, sont des amas d’´etoilestr`es denses et sont connus pour contenir beaucoup plus de pulsars milliseconde par unit´e de masse que la galaxie dans son ensemble. Ces pulsars sont concentr´es dans les r´egions centrales d’amas globulaires et sont suppos´esg´en´ererdes vents relativistes d’´electrons. Ces ´electrons ´energ´etiquespeuvent alors interagir avec le champ intense de photons optiques, qui est soutenu par les nombreuses ´etoilesnormales de l’amas, afin de g´en´ererdes rayons gamma de Tr`esHaute Energie´ (THE). Dans la pr´esente th`ese,ce mod`eled’´emission,mis en œuvre par Bednarek & Sitarek [36], est d´ecritet justifi´ede mani`ereplus d´etaill´ee et des donn´ees, recueillies `apartir d’observations de M13, ont ´et´eanalys´ees dans le but de confronter ce mod`ele. Aucune preuve d’´emissiondes rayons gamma THE de M13 n’a ´et´etrouv´ee. Une limite sup´erieure int´egrale et d´ecorr´el´eeest d´etermin´ee,soit 0.306 × 10−12 cm−2 s−1 en dessus de 0.8 TeV, `aun niveau de confiance de 95%. Des limites sup´erieures spectrales sont ´egalement d´etermin´eeset compar´eesaux courbes d’´emissionpr´esent´ees dans [36]. L’examen d´etaill´edes param`etres du mod`eler´ev`ele que les courbes attendues ´etaient fond´ees sur des estimations trop optimistes de plusieurs de ces param`etres. N´eanmoins,le mod`elepeut ˆetre li´eaux th´eories existantes des vents des pulsars et, ce faisant, `atravers ces observations, on trouve que l’acc´el´eration des ´electrons dans les vents des pulsars millisecondes (en dehors des cylindres lumi`eriques des pulsars) aux ´energiesTeV est `aexclure, selon des hypoth`eses auto-coh´erentes des propri´et´esde cette population des pulsars millisecondes. In memory of my mother, Carol. In honour of my father, Niall. With love, for Erica. With hope, for L´eahand Ad`ele. How must our wonder and admiration be increased when we consider the prodigious distance and multitude of the stars. — Christian Huygens The stars that we follow can lead us astray. — ‘The Plough’, Neil Hannon Contents Disclaimer xv Acknowledgements xvii Thesis Outline xix Statement of Original Contributions xxi I Introduction 1 1 Gamma-ray Astronomy & Globulars 3 1.1 Gamma-Ray Astronomy ..................... 4 1.1.1 HE Gamma-Ray Astronomy ............... 8 1.1.1.1 Fermi Catalogue ................ 11 SNRs and starburst galaxies ........... 11 Pulsars and PWNe ................ 12 AGN ........................ 13 HMXBs / Micro-quasars ............. 13 Globulars ..................... 13 1.1.2 VHE Gamma-Ray Astronomy .............. 14 1.1.2.1 TeV Catalogue ................. 16 Relation to HE-astronomy source classes .... 16 1.2 Globular Clusters ......................... 18 1.2.1 Globular Characteristics ................. 18 1.2.2 Binaries and Recycled Pulsars .............. 21 CVs may create young pulsars .......... 21 LMXBs and recycled pulsars ........... 22 ix x CONTENTS 1.2.3 MSP Population ..................... 23 1.2.4 VHE Predictions and Observations ........... 23 1.2.4.1 VHE Emission Models ............. 24 1.2.4.2 VHE Observations ............... 26 Terzan 5 ...................... 26 1.2.4.3 Target Selection ................ 27 2 Emission from Globulars 29 2.1 Particle Acceleration ....................... 30 2.1.1 Observational Evidence .................. 31 ‘Black-widow’ pulsars ............... 31 Fermi millisecond pulsars ............. 31 2.1.2 Goldreich & Julian Magnetosphere ........... 33 2.1.3 Vacuum Gap Acceleration ................ 36 2.1.3.1 Polar-Cap .................... 37 2.1.3.2 Slot-Gap .................... 39 2.1.3.3 Outer-Gap ................... 40 2.2 Gamma-Ray Production ..................... 41 2.2.1 Inverse Compton Scattering ............... 41 2.2.1.1 Scattering Rate and Particle Densities .... 44 2.2.1.2 Cross-Section and Scattered Spectrum .... 45 Klein-Nishina suppression ............ 46 Spectral saturation ................ 47 2.3 Model of VHE Emission ..................... 50 2.3.1 Photon Field and Luminosity Profile .......... 52 2.3.2 Electron Diffusion and Energy Losses .......... 55 2.3.3 Electron Spectrum and Model Parameters ....... 56 2.3.4 Flaws ........................... 59 Stellar photon spectrum ............. 59 Stellar density function .............. 60 Synchrotron emission ............... 60 2.3.5 Summary ......................... 61 II Technique 63 3 Detection Technique & Apparatus 65 3.1 Detecting Gamma Rays ..................... 70 CONTENTS xi 3.1.1 Design Considerations .................. 70 3.1.1.1 Optics ...................... 71 3.1.1.2 Camera ..................... 72 3.1.1.3 Trigger ..................... 73 3.2 VERITAS ............................. 74 3.2.1 Optics ........................... 75 3.2.1.1 PSF ....................... 76 3.2.1.2 Alignment .................... 79 3.2.1.3 Reflectivity ................... 82 3.2.2 Camera .......................... 83 3.2.3 Trigger & Readout .................... 85 3.2.3.1 Trigger ..................... 87 ZCFD (Level 1) .................. 88 Pattern trigger (Level 2) ............. 88 Array trigger (Level 3) .............. 89 3.2.3.2 Readout ..................... 91 3.2.4 Calibration and Auxiliary Data ............. 92 3.2.4.1 Calibration ................... 93 Pedestal ...................... 93 Relative gain .................... 93 3.2.4.2 Auxiliary .................... 94 4 Analysis & Statistics 95 Image processing ................. 96 Principle of gamma/hadron separation ..... 96 Statistical treatment of gamma-like events ... 98 4.1 Image Processing & Shower Reconstruction ........... 100 Image parametrisation .............. 103 Image and reconstruction quality ........ 107 4.1.1 Arrival Direction Reconstruction ............ 111 4.1.2 Core Location Reconstruction .............. 115 4.1.3 Energy Estimation with Lookup Tables ......... 115 4.2 Coping with Background ..................... 117 4.2.1 Source Region ....................... 118 4.2.2 Hadron Rejection ..................... 119 4.2.3 Background Estimation .................. 122 4.2.4 Statistical Treatment ................... 126 4.3 Event Sensitivity ......................... 128 xii CONTENTS III Results 131 5 Analysis Results 133 5.1 Data Selection ........................... 133 Array-trigger-rate stability ............ 134 Remedial action .................. 136 5.2 Analysis Software ......................... 138 5.2.1 eventdisplay ....................... 139 5.2.2 mscw energy ....................... 140 5.2.3 anasum ........................... 140 5.3 Results for M13 .......................... 142 5.3.1 Excess, Significance and Quality ............. 143 5.3.2 Flux Upper Limits .................... 151 5.3.2.1 Upper limit derivation ............. 151 Flux calculation .................. 153 5.3.2.2 Integral Flux Upper Limits .......... 156 5.3.2.3 Spectral Upper Limits ............. 159 5.4 Comparison to Modelled Emission ................ 165 6 Discussions & Conclusions 171 6.1 Feasible Ranges of the Model Parameters ............ 171 6.1.1 Pulsar Population ..................... 173 6.1.1.1 Radio Luminosity Distribution Function ... 174 6.1.1.2 X-Ray Source Counts ............. 177 6.1.1.3 Feasible Values ................. 179 6.1.2 Spin-Down Luminosity .................. 180 6.1.2.1 Globular-Cluster MSPs ............ 181 6.1.2.2 Pulsar Population Statistics .......... 181 6.1.2.3 Feasible Values ................. 183 6.1.3 Conversion Efficiency to Relativistic Electrons ..... 185 Energy budget ................... 186 Composition of the pulsar wind ......... 186 Acceleration and magnetic dissipation ...... 187 6.1.3.1 Energy Balance ................. 190 6.1.3.2 Radiation-Reaction Limited Luminosity ... 192 6.1.3.3 Feasible Values ................. 193 6.2 Limits
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