Millisecond Pulsars:Decoding MagnetospheresbyShauna Michele SallmenB.Sc. (University of Toronto, Canada) 1990M.A. (University of California at Berkeley) 1992A dissertation submitted in partial satisfaction of therequirements for the degree ofDoctor of PhilosophyinAstronomyin theGRADUATE DIVISIONof theUNIVERSITY of CALIFORNIA at BERKELEYCommittee in charge:Professor Donald C. Backer, ChairProfessor Jonathan A. AronsProfessor Robert LinSpring 1998

Millisecond Pulsars:Decoding MagnetospheresCopyright c Spring 1998by Shauna Michele Sallmen

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AbstractMillisecond Pulsars:Decoding MagnetospheresbyShauna Michele SallmenDoctor of Philosophy in AstronomyUniversity of California at BerkeleyProfessor Donald C. Backer, ChairA hollow-cone model explains the pulse pro�le morphology and polarization prop-erties of long-period (1 second) pulsars. The radio emission originates in the open-�eldline region above the polar cap, which is larger in millisecond pulsars. The emission inthese rapidly rotating objects may occur at altitudes which rotate at a speed closer tothat of light. Relativistic e�ects and magnetic �eld distortions may therefore be moreimportant. Pulse pro�le studies of millisecond pulsars indicate that the long-periodpulsar classi�cation system fails to account for the properties of these objects.Multi-frequency polarization observations with high temporal resolution are pre-sented for several millisecond pulsars. Secure classi�cation of the pulse pro�le mor-phology remains elusive for many objects. Pulse components are narrower than ex-pected, and the spectral behaviour makes core and cone component identi�cationuncertain. The fractional polarization of these objects remains relatively constantwith frequency, in contrast to the behaviour of slow pulsars. The polarization posi-tion angle curves are similar at all frequencies, suggesting that they are geometric inorigin. Their small slopes can be reconciled with the results for long-period pulsarsby a simple period-scaling of the pulsar magnetosphere. Long-term variations in theintensity and polarization pro�les are observed; polarization variations are seen morefrequently in millisecond pulsars than in slow pulsars.Single pulses studies of normal pulsars revealed the phenomenon of microstructure- radio emission on very short time scales. This modulation may be due to either anangular or a temporal e�ect. In the former case, it would be expected to scale with

vi Abstractpulse period. Giant pulses in the Crab pulsar dominate the emission at some radiofrequencies. Simultaneous dual-frequency observations of these pulses reveal that theemission mechanism must be broadband. Both temporal and angular models canaccount for the modulation. Giant pulses are also seen in PSR B1937+21. Theseare unexpectedly delayed relative to the average pulse peaks, and are di�cult toexplain in an angular model. Single-pulse observations of PSR B1534+12 also revealno evidence for microstructure which scales with pulse period, although an angularbeaming origin for the intensity modulation cannot be ruled out.

vii

This dissertation is dedicated toJohn Sallmen Lawrence BostwickGertrude Sallmen Irene Bostwick

Acknowledgements 'Cause you know that -People like you help people like me go on, go onPeople like you help people like me go on, go onPeople like you help people like me go on, go on, go on\People Like You" by Bob BossinThere are many people to thank, and it is hard to know where to begin. Exceptthat this thesis could not have been completed without the cooperation, encourage-ment, and candy-making of my husband Steve, who takes me as I am.Who I am today results from my family and my past. So I would like to thankmy parents for encouraging me to always do my best, and Mrs. Buchwitz, for herpatience with capricious �ve-year-olds. My brother Mark showed me that a thesiscan take a long time, but still be done! All my aunts, uncles, and cousins bringwarm memories to mind, while the courage of my grandparents gives me strength.Meanwhile Sarah keeps me tied to my roots, and encourages freedom in life.There are many in my \other life", the one outside astronomy, that deserve men-tion. I would like to thank Cavan for being the best housemate imaginable, and forwillingly feeding Steve and I at a moment's notice. And my Trinity family, for beingthemselves: Odette, for her gracious calm whenever I needed it, despite her chaoticlife; Chuckie, for wonderful massages; Amelia, for entertaining my lonely husbandwhile I was away, and for being generous with her horse; Dolly, for being silly onthe trail; and Deborah, for losing her co�ee virginity with us. Betsy and Voices forChange kept me sane when I most needed it, and reminded me how to live a life.Thanks to Aimee, for dancing with my husband, but having lunch with me, and Em-ilie, for being an excellent observing partner in the cold dome in Toronto. Margaret'sjoy and silliness have been a source of great pleasure, and her advice and support havebeen greatly appreciated. The members of the Society of the Great Round One knowwhat they have done. Bonnie helped me get through this. And I cannot stop withoutthanking: Stinky, for being a staunch mascot of the GBPP; Woo�e, for his watchfuleye on my computer; Robin, for her company on many observing trips; Bruce Moose,for being so squishable; Roberta, for her comforting sounds, Tess, for keeping theothers under control, and all the rest of the menagerie, for their cheerful attitudes.

x AcknowledgementsWithin the astronomy department, there are many people not directly involvedwith my research who should be thanked. Jay was a wonderful o�ce mate, andlunches with Charles were always interesting. I appreciated Eric's company duringthesis ups and downs, and am grateful to Rosa for proving a thesis *could* be �nishedwhen I needed to see that. Paquito's company in I-House was welcome.The sta� in the astronomy department here at UC Berkeley have been incrediblyhelpful, especially Joyce Wong & Robi Carmack for help with travel, Graduate Assis-tants Mary Brunn, Beverly Skinner, and Kim Patton (and recently Juliane Monroe)for always knowing who I needed to see, and Patrice for help with the ever-importantpayroll.My advisor Don Backer is responsible for getting me hooked on pulsars. The orig-inal motivation of studying a gravitational wave background via pulsar timing gaveway to an insatiable curiousity about the objects themselves, which he cheerfullyencouraged. His knowledge, guidance, and support have made this research inter-esting, challenging, and enjoyable. Berkeley pulsar post-docs Alex Zepka and AndyFruchter, and fellow pulsar students Tony and Andrea kept me in touch with aspectsof pulsar research other than those contained in this dissertation. Jon Arons clari�edcomplicated magnetospheric theories, allowing this observer to have a clue.Matt Dexter and his expertise with BPPs made the bulk of the observations inthis thesis possible. I especially appreciated his long hours of long-distance assistanceduring my observations at the E�elsberg 100-m telescope in Germany. The entirepulsar group at Bonn made me feel welcome, but without Axel Jessner the EBPPwould not have been usable. Michael Kramer was a wonderful host during thatobserving trip, and his enthusiasm for millisecond pulsars is infectious. Although Ihave not met her, e-mail discussions with Kiriaki Xilouris about millisecond pulsarpolarization were invaluable.Alex Wolszczan's technical assistance at Arecibo made the observations for Chap-ter 6 possible.The sta� at the Green Bank observatory have been very friendly and helpful.My many trips to Wild, Wonderful West Virginia were always enjoyable. BeckyWarner, in concert with the Charlottesville, VA NRAO sta�, made sure I alwaysgot there and had a place to stay. The cafeteria and housekeeping sta� saved mespinach salad on request, and let me back into my room after I locked myself out.My thanks to the drivers who occasionally transported me back to Charlottesvilleon the return journey, for diverting conversation. The 85-3 operators have alwaysbeen helpful and responsive, helping to track ethernet cables across the ceiling, aswell as monitoring the telescope and GBPP when we were absent. George Liptakmade sure the GBPP moved from the 85-3 and back again on cue, and the movers

xiwere careful when driving over the potholes, so the system remained operational. BillShank responded to requests for �lters, feed changes, power meters, ampli�ers, andcorrelated calibration signals with good humour, and kept the radio signals coming.Ed Childers kept the GBPP PC connected to the ethernet, and Preston providedextra cables on request. The 140-foot operators kept an eye on it all, and let mecatch a little sleep on occasion. Jay Lockman snagged me for the weekly science talkmore than once, but always signed my travel forms and made sure I had all the helpI needed. Mark Clark and Rick Fisher kept the spectral processor going during thetiming runs, allowing me to concentrate on the GBPP. Pulsar discussions with MarkMcKinnon were always enlightening, and he also taught me the basics of polarizationcalibration. The Minters and Langstons welcomed me to their homes for dinner morethan once.My thanks go to Tim Hankins, Dave Mo�ett, and Scott Lundgren, for makingthe simultaneous giant pulse observations of Chapter 5 possible, and for stimulatingdiscussions on the outcome. I am also grateful to the observatory sta� at GreenBank and at the VLA for minimizing internet tra�c during the two hours of thatexperiment.Many members of the pulsar community, encountered at conferences large andsmall, have been welcoming and helpful. These are too numerous to mention, butGreen Bank encounters with David Nice, Scott Lundgren, and Zaven Arzoumaniantaught me a great deal about pulsars and observing. Dan Stinebring was especiallyhelpful in clarifying my understanding of polarization calibration using pulsars, duringone summer session there.Finally, I must again thank my beloved Moose, for his patience, support, and calmin my storms. It's teamworkI couldn't make it on my ownIt takes teamwork...\Teamwork" by Tamarack

ContentsAbstract vAcknowledgements ixTable of Contents xiiiList of Tables xviiList of Figures xix1 Introduction 11.1 Historical Background and Overview . . . . . . . . . . . . . . . . . . 11.2 Single Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Properties of Average Pro�les: Emission Region . . . . . . . . . . . . 61.4 Polarization Properties: Pulsar Geometry . . . . . . . . . . . . . . . . 131.5 Basic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.6 Pulsar Magnetospheres . . . . . . . . . . . . . . . . . . . . . . . . . . 211.7 Pulsar Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.8 Propagation E�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.8.1 Dispersion delay in cold plasma . . . . . . . . . . . . . . . . . 251.8.2 Faraday rotation . . . . . . . . . . . . . . . . . . . . . . . . . 261.8.3 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.9 Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

xiv ContentsI Polarimetry 332 Observing Particulars 352.1 Telescopes and Receivers . . . . . . . . . . . . . . . . . . . . . . . . . 352.1.1 Green Bank 1400 . . . . . . . . . . . . . . . . . . . . . . . . . 352.1.2 Green Bank 85-3 . . . . . . . . . . . . . . . . . . . . . . . . . 362.1.3 E�elsberg 100m . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2 Berkeley Pulsar Processors . . . . . . . . . . . . . . . . . . . . . . . . 372.2.1 GBPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.2 EBPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.3 Observing information . . . . . . . . . . . . . . . . . . . . . . . . . . 402.4 Gain Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.4.1 Practicalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.5 Polarization Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 452.5.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.5.1.1 Circular Basis . . . . . . . . . . . . . . . . . . . . . . 462.5.2 Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . 482.5.3 Application to Circular Polarization data . . . . . . . . . . . . 502.5.3.1 1410-MHz EBPP data . . . . . . . . . . . . . . . . . 512.5.3.2 575-MHz GBPP data . . . . . . . . . . . . . . . . . 542.5.3.3 820-MHz GBPP data . . . . . . . . . . . . . . . . . 552.5.4 The e�ects of � 6= 0 on PPA . . . . . . . . . . . . . . . . . . . 582.5.5 Application to Linear Polarization data . . . . . . . . . . . . . 592.5.5.1 Application to 1400 800-MHz Data . . . . . . . . . . 592.5.5.2 Application to 85-3 data . . . . . . . . . . . . . . . . 602.6 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Polarization Observations of Millisecond Pulsars 653.1 Data Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.2 PSR J0613�0200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3 PSR J1012+5307 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.4 PSR J1022+1001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.5 PSR B1620�26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.6 PSR J1713+0747 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.7 PSR J1730�2304 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.8 PSR B1821�24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.9 PSR B1937+21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.10 PSR J2145�0750 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Contents xv3.11 1410-MHz Polarization Pro�les . . . . . . . . . . . . . . . . . . . . . 1073.11.1 PSR J0751+1807 . . . . . . . . . . . . . . . . . . . . . . . . . 1073.11.2 PSR 1518+4904 . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.11.3 PSR 1640+2224 . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.11.4 PSR 1643�1224 . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.12 PSR B0531+21 at 610 MHz . . . . . . . . . . . . . . . . . . . . . . . 1104 Polarization Analysis of Millisecond Pulsars 1134.1 Pulsar Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.2 PPA Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.2.1 PSR J0613�0200 . . . . . . . . . . . . . . . . . . . . . . . . . 1174.2.2 PSR J1012+5309 . . . . . . . . . . . . . . . . . . . . . . . . . 1194.2.3 PSR J1022+1001 . . . . . . . . . . . . . . . . . . . . . . . . . 1234.2.4 PSR B1620�26 . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.2.5 PSR J1713+0747 . . . . . . . . . . . . . . . . . . . . . . . . . 1294.2.6 PSR J1730�2304 . . . . . . . . . . . . . . . . . . . . . . . . . 1324.2.7 PSR B1821�24 . . . . . . . . . . . . . . . . . . . . . . . . . . 1334.2.8 PSR B1937+21 . . . . . . . . . . . . . . . . . . . . . . . . . . 1364.2.9 PSR J2145�0750 . . . . . . . . . . . . . . . . . . . . . . . . . 1394.3 Shallow PPA Slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.4 Characteristics of Pulse Pro�les . . . . . . . . . . . . . . . . . . . . . 1444.5 Frequency Dependence of Polarization . . . . . . . . . . . . . . . . . 1454.6 Moding Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1474.7 Polarization Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 150

xvi ContentsII Single Pulses 1515 Dual Frequency Crab Giant Pulses 1535.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1595.4.1 Wide Bandwidth Correlation . . . . . . . . . . . . . . . . . . 1595.4.2 Pro�le Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 1635.4.3 Energies and Spectral Indices . . . . . . . . . . . . . . . . . . 1665.4.4 Models of the Emission Beam . . . . . . . . . . . . . . . . . . 1685.4.5 The Emission Mechanism . . . . . . . . . . . . . . . . . . . . 1695.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1716 Individual Pulses in Millisecond Pulsars 1736.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1736.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1746.3 Observations & Data Reduction . . . . . . . . . . . . . . . . . . . . . 1756.4 Analysis of PSR B1534+12 . . . . . . . . . . . . . . . . . . . . . . . . 1766.5 Analysis of PSR B1937+21 . . . . . . . . . . . . . . . . . . . . . . . . 1786.5.1 Giant Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1826.5.2 Temporal variations . . . . . . . . . . . . . . . . . . . . . . . . 1856.6 Discussion of Giant Pulses . . . . . . . . . . . . . . . . . . . . . . . . 1886.6.1 Comparison to the Crab Giant Pulses . . . . . . . . . . . . . . 1886.6.2 Models of the Emission Beam . . . . . . . . . . . . . . . . . . 1886.6.3 Further Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1927 Conclusions 193References 197

List of Tables2.1 Observing Information for Millisecond Pulsars . . . . . . . . . . . . . 412.2 Gain Calibration Sources . . . . . . . . . . . . . . . . . . . . . . . . . 442.3 Polarization Calibration Summary . . . . . . . . . . . . . . . . . . . . 613.1 Gaussian Component Decomposition of Intensity Pro�les . . . . . . . 643.2 Polarization Pro�le Summary . . . . . . . . . . . . . . . . . . . . . . 663.3 Polarization of Millisecond Pulsars . . . . . . . . . . . . . . . . . . . 674.1 Pulsar Geometries and Moding Behaviour . . . . . . . . . . . . . . . 116

List of Figures1.1 P � _P diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Single pulses from PSR B1133+16 . . . . . . . . . . . . . . . . . . . . 41.3 Average pro�les of PSR B1133+16 . . . . . . . . . . . . . . . . . . . 61.4 Lighthouse model of Pulsar Emission. . . . . . . . . . . . . . . . . . . 81.5 Hollow Cone Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Polarization Pro�le of pulsar B0355+54 . . . . . . . . . . . . . . . . . 141.7 Geometry of the emission region . . . . . . . . . . . . . . . . . . . . . 151.8 Rotating Vector Model . . . . . . . . . . . . . . . . . . . . . . . . . . 161.9 E�ects of Dispersion on Pulse arrival . . . . . . . . . . . . . . . . . . 262.1 Block diagram of BPP . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2 Stokes vs. � for PSR B1929+10 at 1410 MHz . . . . . . . . . . . . . 522.3 Instrumental Polarization Parameters for E�elsberg . . . . . . . . . . 532.4 Corrected Stokes vs. � for PSR B1929+10 . . . . . . . . . . . . . . . 542.5 V=P vs. Feed Angle � for PSR B1929+10 at 575 MHz . . . . . . . . 552.6 V=P vs. � at 820 MHz for 1997 April . . . . . . . . . . . . . . . . . . 562.7 Stokes vs. � for PSR B1929+10 at 820 MHz for 1997 July . . . . . . 572.8 E�ect of � 6= 0 on PPA . . . . . . . . . . . . . . . . . . . . . . . . . . 582.9 The e�ects of �yy on PSR B1929+10 . . . . . . . . . . . . . . . . . . 603.1 Component Decomposition for PSR J0613�0200 . . . . . . . . . . . . 693.2 Polarization Pro�les of PSR J0613�0200 . . . . . . . . . . . . . . . . 703.3 Expanded 575-MHz Polarization Pro�le of PSR J0613�0200 . . . . . 713.4 Component Decomposition for PSR J1012+5307 . . . . . . . . . . . . 733.5 Polarization Pro�les of PSR J1012+5307 . . . . . . . . . . . . . . . . 743.6 Expanded 1410-MHz Polarization Pro�le of PSR J1012+5307 . . . . 753.7 Component Decomposition for PSR J1022+1001 . . . . . . . . . . . . 773.8 Polarization Pro�les of PSR J1022+1001 . . . . . . . . . . . . . . . . 783.9 Expanded 575-MHz Polarization Pro�le of PSR J1022+1001 . . . . . 793.10 Component Decomposition for PSR B1620�26 . . . . . . . . . . . . . 81

xx List of Figures3.11 Polarization Pro�les of PSR B1620�26 . . . . . . . . . . . . . . . . . 823.12 Expanded 1410-MHz Polarization Pro�le of PSR B1620�26 . . . . . 833.13 Component Decomposition for PSR J1713+0747 . . . . . . . . . . . . 853.14 Polarization Pro�les of PSR J1713+0747 . . . . . . . . . . . . . . . . 863.15 Expanded 1410-MHz Polarization Pro�le of PSR J1713+0747 . . . . 873.16 Polarization Pro�le of PSR J1713+0747 at 800 MHz . . . . . . . . . 883.17 Component Decomposition for PSR J1730�2304 . . . . . . . . . . . . 893.18 Polarization Pro�les of PSR J1730�2304 . . . . . . . . . . . . . . . . 903.19 Expanded 1410-MHz Polarization Pro�le of PSR J1730�2304 . . . . 913.20 Component Decomposition for PSR B1821�24 . . . . . . . . . . . . . 933.21 Polarization Pro�les of PSR B1821�24 . . . . . . . . . . . . . . . . . 943.22 Expanded 820-MHz Polarization Pro�le of PSR B1821�24 . . . . . . 953.23 Polarization Pro�les of PSR B1821�24 at 820 MHz . . . . . . . . . . 973.24 Component Decomposition for PSR B1937+21 . . . . . . . . . . . . . 993.25 Polarization Pro�les of PSR B1937+21 . . . . . . . . . . . . . . . . . 1003.26 Expanded 1410-MHz Polarization Pro�le of PSR B1937+21 . . . . . 1013.27 Component Decomposition for PSR J2145�0750 . . . . . . . . . . . . 1033.28 Polarization Pro�les of PSR J2145�0750 . . . . . . . . . . . . . . . . 1043.29 Expanded 820-MHz Polarization Pro�le of PSR J2145�0750. . . . . . 1053.30 Polarization Pro�le of PSR J2145�0750 at 800 MHz . . . . . . . . . 1063.31 1410-MHz Polarization Pro�les of PSRs J0751+1807, J1518+4904,J1640+2224, and J1643�1224 . . . . . . . . . . . . . . . . . . . . . . 1083.32 Expanded Polarization Pro�les of PSRs J0751+1807, J1518+4904,J1640+2224, and J1643�1224 . . . . . . . . . . . . . . . . . . . . . . 1093.33 610-MHz Polarization Pro�le of PSR B0531+21 . . . . . . . . . . . . 1103.34 Expanded Polarization Pro�le of PSR B0531+21 . . . . . . . . . . . . 1114.1 Log-Polar Diagram of Intensity for PSR J0613�0200 . . . . . . . . . 1174.2 PPA model for PSR J0613�0200 . . . . . . . . . . . . . . . . . . . . 1184.3 Log-Polar Diagram of Intensity for PSR J1012+5307 . . . . . . . . . 1204.4 PPA model for PSR J1012+5307 . . . . . . . . . . . . . . . . . . . . 1214.5 Log-Polar Diagram of Intensity for PSR J1022+1001 . . . . . . . . . 1234.6 PPA model for PSR J1022+1001 . . . . . . . . . . . . . . . . . . . . 1244.7 PPA model for PSR J1022+1001 . . . . . . . . . . . . . . . . . . . . 1254.8 Log-Polar Diagram of Intensity for PSR B1620�26 . . . . . . . . . . 1264.9 PPA model for PSR B1620�26 . . . . . . . . . . . . . . . . . . . . . 1274.10 Log-Polar Diagram of Intensity for PSR J1713+0747 . . . . . . . . . 1294.11 PPA model for PSR J1713+0747 . . . . . . . . . . . . . . . . . . . . 130

List of Figures xxi4.12 Log-Polar Diagram of Intensity for PSR J1730�2304 . . . . . . . . . 1324.13 PPA model for PSR J1730�2304 . . . . . . . . . . . . . . . . . . . . 1334.14 Log-Polar Diagram of Intensity for PSR B1821�24 . . . . . . . . . . 1344.15 PPA model for PSR B1821�24 . . . . . . . . . . . . . . . . . . . . . 1354.16 Log-Polar Diagram of Intensity for PSR B1937+21 . . . . . . . . . . 1374.17 PPA data for PSR B1937+21 . . . . . . . . . . . . . . . . . . . . . . 1384.18 Log-Polar Diagram of Intensity for PSR J2145�0747 . . . . . . . . . 1394.19 PPA model for PSR J2145�0750 . . . . . . . . . . . . . . . . . . . . 1404.20 Distribution of PPA slopes . . . . . . . . . . . . . . . . . . . . . . . . 1424.21 Linear Polarization vs. Frequency . . . . . . . . . . . . . . . . . . . . 1465.1 Single Crab Giant Pulse at 1.4 GHz . . . . . . . . . . . . . . . . . . . 1605.2 Single Crab Giant Pulse at 0.61 GHz . . . . . . . . . . . . . . . . . . 1615.3 Correlation in Arrival Times of 1.4-GHz and 0.61-GHz Giant Pulses . 1625.4 Component Fitting to a 1.4-GHz Giant Pulse . . . . . . . . . . . . . 1645.5 Component Fitting to a 1.4-GHz Giant Pulse . . . . . . . . . . . . . 1655.6 Energy Correlation of Dual Frequency Giant Pulses . . . . . . . . . . 1676.1 Pulse energy distribution for PSR B1534+12 . . . . . . . . . . . . . . 1776.2 ACF of individual pulses from PSR B1534+12 . . . . . . . . . . . . . 1776.3 Probability density distribution of pulse energies . . . . . . . . . . . . 1796.4 Very strong main pulse and interpulse from PSR B1937+21 . . . . . 1816.5 Integrated probability distribution for Very strong pulses . . . . . . . 1826.6 Shape of very strong pulses in PSR B1937+21 . . . . . . . . . . . . . 1856.7 �2 of PDF for a very strong pulse . . . . . . . . . . . . . . . . . . . . 187